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Spike sorting based on discrete wavelet transform coefficients
Abstract
Using the novel mathematical technique known as wavelet analysis, a new method (WSC) is presented to sort spikes according to a decomposition of neural signals in the time-frequency space. The WSC method is implemented by a pyramidal algorithm that acts upon neural signals as a bank of quadrature mirror filters. This algorithm is clearly explained and an overview of the mathematical background of wavelet analysis is given. An artificial spike train, especially designed to test the specificity and sensibility of sorting procedures, was used to assess the performance of the WSC method as well as of methods based on principal component analysis (PCA) and reduced feature set (RFS). The WSC method outperformed the other two methods. Its superior performance was largely due to the fact that spike profiles that could not be separated by previous methods (because of the similarity of their temporal profile and the masking action of noise) were separable by the WSC method. The WSC method is particularly noise resistant, as it implicitly eliminates the irrelevant information contained in the noise frequency range. But the main advantage of the WSC method is its use of parameters that describe the joint time-frequency localization of spike features to build a fast and unspecialized pattern recognition procedure.
... In recent years, the good performance in the spike sorting algorithms that used wavelet coefficients as features has encouraged research groups to use this transform. In the study (Letelier and Weber, 2000) discrete wavelet coefficients were extracted by selecting Daubechies-8 as the mother wavelet and implementing a five-level multiresolution decomposition. To select the coefficients with maximum impact on clustering, the standard deviation criterion was used.. ...
... Most wavelet-based spike sorting algorithms in previous studies have used DWT (as a few examples (Letelier and Weber, 2000;Hulata et al., 2002;Shalchyan et al., 2012;Yang and Mason, 2016)) in which the scale parameters are limited to a finite amount by dyadic sampling. However, to find the best wavelet features capable of separating spikes well, one may need to project spikes on basis functions that are scaled to some scales other than dyadic 2 j scales. ...
... In evaluating neural spike sorting methods, the use of signal simulation using true spike waveforms is a conventional and efficient way to evaluate methods based on predetermined labels. Given the spatial geometry of neurons, what has been studied in most previous studies in spike sorting has been the evaluation of the problem on three different spike waveforms in terms of complexity (Letelier and Weber, 2000;Quiroga et al., 2004;Wang et al., 2006), which we also examined in this study. Therefore, two simulated signals are made, each with three different spike waveforms. ...
Spike sorting is an essential step in extracting neuronal discharge patterns which help to decode different activities in the neural system. Therefore, improving the spike sorting accuracy can improve neural decoding performance subsequently. Although many methods are suggested for spike sorting, few studies have evaluated the effect of them on neural decoding performance. In this paper, a method of spike sorting based on an optimized selection of the parameters in the continuous wavelet transform is proposed. The proposed algorithm was tested on a simulated dataset and two publicly available benchmark datasets to evaluate its performance in spike sorting; To evaluate the effect of utilizing different spike sorting algorithms on neural decoding performance, real data was used in which the aim was to decode the force applied by the rat's hand to a pedal continuously from the intra-cortical data of the primary motor area of the cortex. The extracted neuronal firing rates by the spike sorting algorithms were applied to a partial least squares regression to decode the force signal. In the simulation study, the proposed spike sorting algorithm based on optimized wavelet parameter selection outperformed both the WaveClus spike sorting and traditional PCA-based spike sorting algorithms. The results showed the superiority of the spike sorting algorithm based on optimal wavelet parameters compared to classical discrete wavelet transform or PCA-based spike sorting methods in decoding real intracortical data. Overall, the results indicate that it is possible to improve neural decoding performance by improving the spike sorting accuracy.
... Изучение процессов кодирования информации нейронными сетями в качестве процедуры предварительной обработки экспериментальных данных приводит к необходимости решения проблемы идентификации сигнала отдельной клетки в коллективной динамике ансамбля нейронов (или задачи сортировки спайков) [2][3][4]. Чтобы зарегистрировать электрическую активность нескольких нейронов и при этом не повредить их, традиционно проводятся эксперименты по внеклеточной записи электрического потенциала. Этот подход позволяет изучать динамику клеток, которые находятся в малой окрестности микроэлектрода, причем чем дальше будет находиться нейрон, тем меньше амплитуда сигнала, который принимается в точке регистрации. ...
... На рис. 1 изображена довольно простая ситуация -наблюдаются хорошо отличающиеся сигналы двух типов, отмеченные стрелками (и их легко различить по амплитудам). В общем случае рассмотрение амплитуды как основной характеристики для идентификации сигналов разных нейронов оказывается неэффективным подходом [3]. Это связано с тем, что амплитуда зависит от расстояния между нейроном и микроэлектродом: если микроэлектрод располагается вблизи клетки, то сигнал, полученный от данного нейрона, будет превосходить сигналы отдаленных клеток и фоновый шум. ...
... Проблема автоматической идентификации нейронных спайков неоднократно обсуждалась в научной печати [2][3][4]. Можно от-метить несколько распространённых подходов, которые наряду с вышеупомянутым амплитудным детектированием включают анализ главных компонент (АГК) и вейвлетанализ. ...
... The CE-index quantifies the similitude between the observed classification matrix and the expected classification matrix. This index is an adaptation of the error index proposed by Letelier and Weber (2000) 8 . In the present work, the observed classification matrix, based on the mean correlation coefficients (template vs. spikes), was defined as: ...
... The CE-index quantifies the similitude between the observed classification matrix and the expected classification matrix. This index is an adaptation of the error index proposed by Letelier and Weber (2000) 8 . In the present work, the observed classification matrix, based on the mean correlation coefficients (template vs. spikes), was defined as: ...
... A perfect performance of the sorting procedure, at Δ 1 (i.e., the strongest mutualcorrelations possible) with 1, … , , should produce the following expected classification matrix: In order to compare our approach with other methods 8,9 of spike sorting, we also estimated the observed and expected classification matrices, as well as, the CE-index and the customized ...
... Overview of other spike-sorting methods/algorithms based on feature extraction. Note that in general, the authors cited here have used only three (F 14 , F 18 and F 19 common features) of the 24 features (F 1 -F 24 ) proposed in this work (see Table 3). ...
... and validate the proposed spike-sorting method/algorithm, simulated data (see Methods), without noise and with added noise [40][41][42] , were analyzed. Simulated data (sampling frequency of 44 kHz and duration of 180 s) were very similar to those reported by other authors 24 [with three spike templates (T1, T2 and T3) and an important noise component] but in their study only 100 spikes from each neuron at an average rate of 30 spikes/s were analyzed, containing 19 superpositions. In this study, we added 2700 instances of each template randomly to the background noise, avoiding template overlapping. ...
... The results obtained after performing the two validation tests on simulated data (with and without noise) were similar -i.e., three clusters of activity patterns. The three identified clusters allowed to determine the three templates of spike events (color traces in Fig. 4b and white traces in Fig. 4e), which were in perfect correspondence to those three default templates (T1, T2 and T3) of the simulated data with embedded simulated spikes obtained by Scientific other authors 24,40,41 . In summary, Table 4 shows the observed classification matrices resulting from our SS-SPDF method/algorithm [comprising K-TOPS clustering, -that is, applying the sequence of first, K-means (for sorting the single-unit spikes), and then, template optimization in the phase space (for sorting the overlapping waveforms)]. ...
Spike sorting is one of the most important data analysis problems in neurophysiology. The precision in all steps of the spike-sorting procedure critically affects the accuracy of all subsequent analyses. After data preprocessing and spike detection have been carried out properly, both feature extraction and spike clustering are the most critical subsequent steps of the spike-sorting procedure. The proposed spike sorting approach comprised a new feature extraction method based on shape, phase, and distribution features of each spike (hereinafter SS-SPDF method), which reveal significant information of the neural events under study. In addition, we applied an efficient clustering algorithm based on K-means and template optimization in phase space (hereinafter K-TOPS) that included two integrative clustering measures (validity and error indices) to verify the cohesion-dispersion among spike events during classification and the misclassification of clustering, respectively. The proposed method/algorithm was tested on both simulated data and real neural recordings. The results obtained for these datasets suggest that our spike sorting approach provides an efficient way for sorting both single-unit spikes and overlapping waveforms. By analyzing raw extracellular recordings collected from the rostral-medial prefrontal cortex (rmPFC) of behaving rabbits during classical eyeblink conditioning, we have demonstrated that the present method/algorithm performs better at classifying spikes and neurons and at assessing their modulating properties than other methods currently used in neurophysiology.
... Since each neuron fires EAPs of a particular shape, features from EAPs are extracted to emphasize this point. Examples of these features include EAP shape-related features [10,15] such as height, width, peak-to-peak amplitude, principal components (PCs) [10], and wavelet coefficients [16,17]. With the help of an appropriate basis, the latter two feature categories can be extracted by directly projecting the EAPs onto the basis. ...
... Depending on the position relative to the neurons, this resulted in a signal-to-noise ratio (SNR) ranging from 0.349 to 8.723 with a mean and median of 1.576 and 1.043, respectively, when σ w = 0.01 mV. The SNR was calculated using SNR = RMS(s k i ) σ w (16) with RMS(s k i ) representing the root-mean-square value of the recorded EAP signal of the i-th neuron from the k-th electrode. ...
... This was done by removing the portions of the recordings corresponding to the identified EAPs, and then calculating the standard deviation of the remaining data. Once σ w was obtained, the SNR was calculated using Equation (16). These 250 EAP bundles were then used for performance evaluation. ...
Information from extracellular action potentials (EAPs) of individual neurons is of particular interest in experimental neuroscience. It advances the understanding of brain functions and is essential in the emerging field of brain-machine interfaces. As EAPs from distinct neurons are generally not recorded individually, a process to separate them from the multi-unit recordings, referred to as spike sorting, is required. For spike sorting, the feature extraction step is crucial. Starting from acquired data, the task of feature extraction is to find a set of derived values or “features” that are informative and non-redundant to facilitate efficient and accurate sorting, compared with using the raw data directly. It not only reduces the dimensionality of the data but also the impact of noise. In this paper, two novel feature extraction algorithms for sorting multi-electrode EAPs are proposed. These algorithms can be seen as generalizations of principal component analysis and linear discriminant analysis, but the features that match the dominant subspaces observed in the multi-electrode data are obtained without the need for vectorizing a multi-electrode EAP or breaking it into separate EAP channels. These algorithms require no construction of EAP templates and are applicable to multi-electrode recordings regardless of the number of electrodes. Clustering using both simulated data and real EAP recordings taken from area CA1 of the dorsal hippocampus of rats demonstrates that the proposed approaches yield features that are discriminatory and lead to promising results.
... This algorithm is named the multiresolution decomposition [54]. Various mother wavelets can be used, amongst which the Haar wavelet and the Daubechies wavelets are the most popular for analyzing neurophysiological recordings due to their compact support and orthogonality, which allows for discriminative features of the spikes to be identified by a few wavelet coefficients without a priori assumptions on the spike shapes [40,47,55]. Common wavelet families are shown in Fig. 4 ...
... One of the challenges that arise is the massive increase in data rate generated from these high density probes. Neuropixel probes can generate 1GB/min for 382 channels at 30kHz [55], which requires algorithms that are resource efficient and able to process input from all channels simultaneously. As seen in the previous sections, some spike sorting pipelines are designed from the ground up to maximize the use of parallel computing, such as in [22,89,135,136]. ...
Objective: Spike sorting is a set of techniques used to analyze extracellular neural recordings, attributing individual spikes to individual neurons. This field has gained significant interest in neuroscience due to advances in implantable microelectrode arrays, capable of recording thousands of neurons simultaneously. High-density electrodes, combined with efficient and accurate spike sorting systems, are essential for various
applications, including Brain Machine Interfaces (BMI), experimental neural prosthetics, real-time neurological disorder monitoring, and neuroscience research. However, given the resource constraints of modern applications, relying solely on algorithmic innovation is not enough. Instead, a co-optimization approach that combines hardware and spike sorting algorithms must be taken to develop neural recording systems suitable for resource-constrained environments, such as wearable devices and BMIs. This co-design requires careful consideration when selecting appropriate spike-sorting algorithms that match specific hardware and use cases.
Approach: We investigated the recent literature on spike sorting, both in terms of hardware advancements and algorithms innovations. Moreover, we dedicated special attention to identifying suitable algorithm-hardware combinations, and their respective real-world applicabilities.
Main Results: In this review, we first examined the current progress in algorithms, and described the recent departure from the conventional ”3-
step” algorithms in favor of more advanced template matching or machine-learning-based techniques. Next, we explored innovative hardware options, including Application-Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), and In-Memory Computing Devices (IMCs). Additionally, the challenges and future opportunities for spike sorting are discussed.
Significance: This comprehensive review systematically summarizes the latest spike sorting techniques and demonstrates how they enable researchers to overcome traditional obstacles and unlock novel applications. Our goal is for this work to serve as a roadmap for future researchers seeking to identify the most appropriate spike sorting implementations for various experimental settings. By doing so, we aim to facilitate the advancement of this exciting field and promote the development of innovative solutions that drive progress in neural engineering
research.
... The proper choice of the wavelet function is sometimes made according to what we expect from the transform. Fig. 6 presents some of the wavelet functions that have been previously used for the processing of neuronal spikes [24], [71]- [82]. ...
... Due to their computational simplicity, single-level and multi-level digital Haar wavelet transform (DHWT) has been previously suggested for this purpose [76], [89]. To improve signal-noise discrimination, the Coiflet [72], [73], [90], biorthogonal [91], Mexican-hat [74], Daubechies4 [92], and Daubechies8 [71] wavelet families have been proposed as other alternatives. Moreover, symmlet-based stationary wavelet transform (SWT), which is equivalent to the symmlet wavelet transform without sub-sampling, has been employed to extract more precise timing of spike events [84]. ...
Neuroscientists seek efficient solutions for deciphering the sophisticated unknowns of the brain. Effective development of complicated brain-related tools is the focal point of research in neuroscience and neurotechnology. Thanks to today's technological advancements, the physical development of high-density and high-resolution neural interfaces has been made possible. This is where the critical bottleneck in receiving the expected functionality from such devices shifts to transferring, processing, and subsequently analyzing the massive neurophysiological extra-cellular data recorded. To respond to this inevitable concern, a spectrum of neuronal signal processing techniques have been proposed to extract task-related informative content of the signals conveying neuronal activities, and eliminate the irrelevant contents. Such techniques provide powerful tools for a wide range of neuroscience research, from low-level perception to high-level cognition. Data transformations are among the most efficient processing techniques that serve this purpose by properly changing the data representation. Mapping the data from its original domain (i.e., the time-space domain) to a new representational domain, data transformations change the viewing angle of observing the informative content of the data. This paper reviews the employment of data transformations in order to process neuronal signals and their three key applications, including spike detection, spike sorting, and data compression.
... So far, several spike sorting algorithms have been proposed. A wavelet-based spike classifier was introduced in [3] according to the time-frequency wavelet spectrum analysis. The main idea of that method was based on the selection of the limited numbers of wavelet coefficients that distinguish waveforms. ...
... The main idea of that method was based on the selection of the limited numbers of wavelet coefficients that distinguish waveforms. For such purpose, the wavelet coefficients with bimodal or multimodal distribution among all action potentials were selected manually [3]. Although the wavelet-based methods are potent in spike sorting procedures, such methods are susceptible to the selection of basis function. ...
Analysis of neuronal activities is essential in studying nervous system mechanisms. True interpretation of such mechanisms relies on detecting and sorting neuronal activities, which appear as action potentials or spikes in the recorded neural data. So far, several algorithms have been developed for spike sorting. In this paper, spike sorting was addressed using entropy measures. A method based on a modified version of approximate entropy was proposed for feature extraction, which captured the local variations in spike waveforms as well as global variation to create the feature space. Results showed that the entropy-based feature extraction method created more distinguishing features, which reduces spike sorting errors. The proposed method was capable of separate different spikes in small-scale structures, where the technique such as principal component analysis fails.
... We also perform joint feature learning and clustering, using a mixture of factor analyzers construction as in [6], but we do so in a fully Bayesian, multi-channel setting (additionally, [6] did not account for time-varying statistics). The learned factor loadings are found to be similar to wavelets, but they are matched to the properties of neuron spikes; this is in contrast to previous feature extraction on spikes [11] based on orthogonal wavelets, that are not necessarily matched to neuron properties. ...
... The dictionary elements show shapes similar to both neuron spikes in Figure 3(d) and wavelets. The spiky nature of the learned dictionary can give factors similar to those use in the discrete wavelet transform cluster in [11], which choose to use the Daubechies wavelet for its spiky nature (but here, rather than a priori selecting an orthogonal wavelet basis, we learn a dictionary that is typically not orthogonal, but is wavelet-like). ...
Nonparametric Bayesian methods are developed for analysis of multi-channel spike-train data, with the feature learning and spike sorting performed jointly. The feature learning and sorting are performed simultaneously across all channels. Dictionary learning is implemented via the beta-Bernoulli process, with spike sorting performed via the dynamic hierarchical Dirichlet process (dHDP), with these two models coupled. The dHDP is augmented to eliminate refractory-period violations, it allows the "appearance" and "disappearance" of neurons over time, and it models smooth variation in the spike statistics.
... Якщо розглядати тільки сигнал , то моделі (3) та (7) дають можливість частотно-часового розділення функції автокогерентності на дві ортогональні складові: за частотою та за часом. Таке розділення можливо, якщо застосувати двомірне представлення сигналу на локальному інтервалі спостереження тривалістю за допомогою вейвлет-перетворення [11]. Практичне використання таких перетворень [12] засвідчує, що вони також дозволяють подавляти шуми, підвищуючи інформативність двовимірних (за частотою і за часом) спектральних зображень. ...
... У рамках термінології й умовних позначень вейвлет-аналізу [11] коефіцієнти , як спектральні складові, за прямого неперервного вейвлетперетворення розраховуються за допомогою виразу: ...
In the article investigations of probabilistic models of parametrization of local changes of non-stationary random metering signals are carried out. The formalization of the probabilistic properties of non-stationary random signals was carried out, the choice of research models was carried out, the influence of the effects of spectral non-stationary on the correlation of the harmonic components of the measurement signals was analyzed, the time-frequency auto-coherence models were obtained and investigated; discrete continuous wavelet transforms were used to increase the efficiency of the control (diagnosis) of spectral changes measuring signal in mathematical expectations of mutual spectral correlation. The research is carried out to solve the scientific and practical problem of imperfection and limitations of theoretical substantiation in the creation of computerized information measuring devices for monitoring and diagnosing dynamic objects locally and globally unsteady in their spectral properties.
... The spike-sorting approaches are mainly focused on extracting various features of the spike waveform (waveform-based features) to be able to interpret physiologically the obtained results. Most of the features used by different authors have been separated as (1) shape-based features (directly extracted from the detected action potential; see [1]), (2) phase-based features (extracted from the trajectory of the action potential in the phase space; see [2]), (3) geometric-based features (extracted as the area under the spike waveform; see [3]), and (4) transformation-based features (coefficients, factors, or components extracted from different mathematical transformations; see [4]). ...
... An efficient index of cohesion-dispersion among and within clusters (CD index) during the neural events classification was also applied. Furthermore, a modified index of clustering error (CE index) taken from [4] upon completion of the classification process was included. ...
Pattern recognition of neuronal discharges is the electrophysiological basis of the functional characterization of brain processes, so the implementation of a spike-sorting algorithm is an essential step for the analysis of neural codes and neural interactions in a network or brain circuit. We developed an unsupervised automatic computational algorithm for the detection, identification, and classification of the neural action potentials distributed across electrophysiological recordings and for the clustering of these potentials based on the shape, phase, and distribution features, which are extracted from the first-order derivative of the potentials under study. This algorithm was implemented in a customized spike-sorting software called VISSOR (Viability of Integrated Spike Sorting of Real Recordings). The validity and effectiveness of this software were tested by the classification of the action potentials detected in extracellular recordings of the rostro-medial prefrontal cortex (rmPFC) of rabbits during the classical eyelid conditioning.
... No reuse allowed without permission. sorted into clusters using the discrete wavelet transform for feature extraction, and 208 coefficients were selected to maximize the clusters' distance (Letelier and Weber 2000). ...
Lab rodent species used to study the visual system and its development (hamsters, rats, and mice) are nocturnal, altricial, and possess simpler visual systems than carnivores and primates. To widen the spectra of studied species, here we introduce an alternative model, the Chilean degu (Octodon degus), a diurnal, precocial Caviomorph rodent with a cone enriched, well-structured retina, and well-developed central visual projections. To assess degu visual physiological properties, we characterized the visual responses and receptive field (RF) properties of isolated neurons in the superficial layers of the superior colliculus (sSC). To facilitate comparison with studies in other rodent species, we used four types of stimuli: (1) a moving white square, (2) sinusoidal gratings, (3) an expanding black circle (looming), and (4) a stationary black circle. We found that as in other mammalian species, RF size increases from superficial to deeper SC layers. Interestingly, compared to other lab rodents, degus have smaller RF sizes, likely indicating higher acuity. sSC neurons displayed spatial frequency tuning to grating stimuli from 0.08 to 0.24 cycles/degree. Additionally, neurons from sSC showed transient ON, OFF, or ON-OFF responses to stationary stimuli but increased their firing rates as a looming object increased in size. Our results suggests that degus have higher visual acuity, higher frequency tuning, and lower contrast sensitivity than commonly used nocturnal lab rodents, positioning degus as a well-suited model for studies of diurnal vision that are more relevant to humans.
... In a nutshell, it captures covariance between features of a dataset. Discrete wavelet transform [22], which applies a temporal frequency decomposition to the signal, provides another common way for feature extraction. Here, each waveform is represented by a variety of wavelet coefficients that capture the characteristics of the spike-waveforms. ...
Objective. Spike sorting, i.e. the detection and separation of measured action potentials from different extracellularly recorded neurons, remains one of the bottlenecks in deciphering the brain. In recent years, the application of neural networks (NNs) for spike sorting has garnered significant attention. Most methods focus on specific sub-problems within the conventional spike sorting pipeline, such as spike detection or feature extraction, and attempt to solve them with complex network architectures. This paper presents DualSort, a simple NN that gets combined with downstream post-processing for real-time spike sorting. It shows high efficiency, low complexity, and requires a comparatively small amount of human interaction. Approach. Synthetic and experimentally obtained extracellular single-channel recordings were utilized to train and evaluate the proposed NN. For training, spike waveforms were labeled with respect to their associated neuron and position in the signal, allowing the detection and categorization of spikes in unison. DualSort classifies a single spike multiple times in succession, as it runs over the signal in a step-by-step manner and uses a post-processing algorithm that transmits the network output into spike trains. Main results. With the used datasets, DualSort was able to detect and distinguish different spike waveforms and separate them from background activity. The post-processing algorithm significantly strengthened the overall performance of the model, making the system more robust as a whole. Although DualSort is an end-to-end solution that efficiently transforms filtered signals into spike trains, it competes with contemporary state-of-the-art technologies that exclusively target single sub-problems in the conventional spike sorting pipeline. Significance. This work demonstrates that even under high noise levels, complex NNs are not necessary by any means to achieve high performance in spike detection and sorting. The utilization of data augmentation on a limited quantity of spikes could substantially decrease hand-labeling compared to other studies. Furthermore, the proposed framework can be utilized without human interaction when combined with an unsupervised technique that provides pseudo labels for DualSort. Due to the low complexity of our network, it works efficiently and enables real-time processing on basic hardware. The proposed approach is not limited to spike sorting, as it may also be used to process different signals, such as electroencephalogram (EEG), which needs to be investigated in future research.
... [18][19][20][21][22][23] It is based on the Fourier Analysis method which states that any periodic function can be represented as an infinite enumerable sum of trigonometric functions. 24 FFT is a method for efficiently computing the Discrete Fourier Transform (DFT) of time 5 series and facilitates power spectrum analysis and filter simulation of signals. All these measures are time-variant. ...
Amperometry is a commonly used electrochemical method for studying the process of exocytosis in real-time. Given the high precision of recording that amperometry procedures offer, the volume of data generated can span over several hundreds of megabytes to a few gigabytes and therefore necessitates systematic and reproducible methods for analysis. Though the spike characteristics of amperometry traces in the time domain hold information about the dynamics of exocytosis, these biochemical signals are, more often than not, characterized by time-varying signal properties. Such signals with time-variant properties may occur at different frequencies and therefore analyzing them in the frequency domain may provide statistical validation for observations already established in the time domain. This necessitates the use of time-variant, frequency-selective signal processing methods as well, which can adeptly quantify the dominant or mean frequencies in the signal. The Fast Fourier Transform (FFT) is a well-established computational tool that is commonly used to find the frequency components of a signal buried in noise. In this work, we outline a method for spike-based frequency analysis of amperometry traces using FFT that also provides statistical validation of observations on spike characteristics in the time domain. We demonstrate the method by utilizing simulated signals and by subsequently testing it on diverse amperometry datasets generated from different experiments with various chemical stimulations. To our knowledge, this is the first fully automated open-source tool available dedicated to the analysis of spikes extracted from amperometry signals in the frequency domain.
... In the last degrees of flexion, the electrical activity suddenly disappears, resulting in a myoelectrical silence [11,16,17]. As the sEMG silence is related to randomness data, a non-stationary analysis on muscles bursts, which are the result of the sum of motor units action potential trains during a contraction, can capture the spiky biological nature of sEMG signal more efficiently whether adjusted resolution (tilling) for different band frequencies is used i.e., using wavelet decomposition (coefficients) [18,19]. As there is inhibitory action on ECC contractions, differences between frequency bands (spectral characteristics) could be found for CON and ECC contractions as well as in muscles with different movement proposes, i.e., stabilizer versus more mobilizer muscles actions could elicit different activation patterns. ...
Purpose
Muscle activation can reflect the stability of the lumbar spine based on the electrical features and kinematics during a dynamic test. However, there is a lack of knowledge of the activation of paravertebral muscles i.e., during the flexion–relaxation test. Hence, we determine the band frequency differences between eccentric (ECC) and concentric (CON) contraction during the flexion–relaxation test in healthy untrained participants without lumbar pain, both multifidus lumborum and longissimus muscles.
Methods
40 healthy participants (aged 30.6 ± 6.9 years) were recruited. Kinematic and surface electromyography were collected to compare the ECC and CON spectral characteristics of both multifidus lumborum and longissimus. The bursts were transformed using a discrete wavelet transform (Daubechies). The band frequencies were compared through mean comparison test with alpha set to 5%.
Results
Both multifidus lumborum and longissimus muscles had higher intensity in ECC contraction than CON for frequency bands lower than 32 Hz (P < 0.05); meanwhile, there was a higher intensity in CON contraction than ECC for frequency bands higher than 32 or 64 Hz until 256 Hz (P < 0.05).
Conclusion
For both paravertebral muscles analyzed, discrete wavelet decomposition suggests that during the flexion–relaxation test there is an ECC contraction characterized by low-frequency bands compared with the CON phase characterized by medium- and higher-frequency bands both paravertebral muscles analyzed. The spectral characteristics might be a useful physiological neuromuscular reference to the pathophysiology adaptations of the paravertebral muscle contraction.
... Transform-based picture compression is one of the most effective wavelet applications [1] . Wavelets are mathematical functions that divide data into distinct frequency components and then examine each component with a resolution that corresponds to its scale [1,12] . They outperform classic Fourier methods in evaluating physical signals with discontinuities and strong spikes [11] . ...
The aim of this research is to develop an image compression system as part of a new satellite imaging photography transmission system. The wavelet transform has been used to build the picture compression technique in this research. The design presented and explained a thorough schematic model of the forward wavelet transform applied to images with only one decomposition level using only the operator symbols for filtering and downsampling. A thorough schematic diagram of the inverse wavelet transform utilised for reconstruction of pictures with only one synthesis level was also shown and explained using only the operator symbols for filtering and upsampling. The number of operations required for approximation of an image of size 512 x 512 pixels was calculated, as well as the schematic diagram for deploying the wavelet transform with three iterations (decomposition levels) to images shown. Every step of the computations is given on how the downsampling operator can reduce the number of operations, assuming that the wavelet filters employed in the process have four coefficients. The mean squared error of 378.6702 was obtained using MATLAB source code for image approximation.
... More recently, some methods use the full waveform directly when the number of electrodes remains small (Pouzat et al., 2002). Another standard technique is to project each waveform on a set of basis functions (Litke et al., 2004;Quiroga, Nadasdy, et al., 2004), that are either found by performing a principal component analysis (PCA) on the entire set of waveforms (Egert et al., 2002;Pouzat et al., 2002;Einevoll et al., 2012;Swindale and Spacek, 2015), or by choosing a wavelet basis (Letelier and Weber, 2000;Hulata et al., 2002;Quiroga, Nadasdy, et al., 2004). For a comparison between PCA and wavelet based analysis, see (Pavlov et al., 2007). ...
Neurons are the fundamental computing units of the central nervous system. Recent technological advances have made it possible to simultaneously record the activity of thousands of cells. A typical example is the development of microelectrode arrays with thousands of electrodes packed with a high density. A renewed challenge is to spike sort their recorded signals, by extracting the spiking activity of each neuron. I first review the issues associated with spike sorting methods, and compare the algorithms that have been proposed. I then present a new algorithm to sort spikes online from large-scale recordings. Online density-based clustering and template matching are key to reach good performances. The software has been validated on both synthetic and real ground-truth recordings. Finally, I present a specific application on the retina where online spike sorting might be useful. Classically, ganglion cells, the retinal output, are supposed to extract specific features from the visual scene such as increases or decreases of luminance (ON vs OFF cells). However, retinal processing depends on the visual context. Using a novel perturbative approach, I show that the same cell can turn ON or OFF depending on the natural context. I found that a convolutional neural network model fitted to the data can recapitulate context-dependence. Online perturbations are thus a promising tool to probe computations in sensory systems.
... Brain Sci. 2020, 10, 835 2 of 16 high-frequency noise and low-frequency field potential; (2) detecting the spikes by determining an amplitude threshold [14] or utilizing other improved methods [15], such as wavelet transforms [16] and fuzzy decision [2]; (3) extracting discriminative features from the detected spikes, frequently using approaches such as principal component analysis (PCA) [17][18][19] and wavelet transform coefficients [14,20,21]; (4) grouping the points in feature space to obtain clusters associated with individual neurons. Many classical and advanced methods have been adopted for this purpose, such as superparamagnetic clustering (SPC) [14], k-means clustering [22], and a mixture of Gaussians [23,24]. ...
In the fields of neuroscience and biomedical signal processing, spike sorting is a crucial step to extract the information of single neurons from extracellular recordings. In this paper, we propose a novel deep learning approach based on one-dimensional convolutional neural networks (1D-CNNs) to implement accurate and robust spike sorting. The results of the simulated data demonstrated that the clustering accuracy in most datasets was greater than 99%, despite the multiple levels of noise and various degrees of overlapped spikes. Moreover, the proposed method performed significantly better than the state-of-the-art method named “WMsorting” and a deep-learning-based multilayer perceptron (MLP) model. In addition, the experimental data recorded from the primary visual cortex of a macaque monkey were used to evaluate the proposed method in a practical application. It was shown that the method could successfully isolate most spikes of different neurons (ranging from two to five) by training the 1D-CNN model with a small number of manually labeled spikes. Considering the above, the deep learning method proposed in this paper is of great advantage for spike sorting with high accuracy and strong robustness. It lays the foundation for application in more challenging works, such as distinguishing overlapped spikes and the simultaneous sorting of multichannel recordings.
... For more details on spike sorting and statistical methods involved in the analysis of characteristic data, one has Pouzat et al. (2002), Lewicki (1998), Shoham et al. (2003, Einevoll et al. (2012) among others. Applications of wavelets in spike sorting occur in the works of Letelier and Weber (2000), Quiroga et al. (2004) and Shalchyan et al. (2012). The purpose here use the beta and triangular shrinkage rules in the wavelet domain for noise reduction. ...
In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this, we present a Bayesian approach for shrinkage of bounded wavelet coefficients in the context of non-parametric regression. We propose the use of a zero-contaminated beta distribution with a support symmetric around zero as the prior distribution for the location parameter in the wavelet domain in models with additive gaussian errors. The hyperparameters of the proposed model are closely related to the shrinkage level, which facilitates their elicitation and interpretation. For signals with a low signal-to-noise ratio, the associated Bayesian shrinkage rules provide significant improvement in performance in simulation studies when compared with standard techniques. Statistical properties such as bias, variance, classical and Bayesian risks of the associated shrinkage rules are presented and their performance is assessed in simulations studies involving standard test functions. Application to real neurological data set on spike sorting is also presented.
... Neuronal spike sorting is used for distinguishing different signals from numerous neurons in neural system [1]. Different signal handling procedures have been utilized to distinguish and sort. ...
Wavelet investigation is the novel scientific procedure utilizing for spike sorting, another technique wavelet based spike classifier (WSC) is introduced to sort spikes as indicated by a decay of neural signals in the time-recurrence space. The WSC technique is invoke by pyramidal calculation that followed upon neuronal signals as bank of quadrature reflect channels. Calculation and outline of the numerical foundation of wavelet examination is obviously clarified. A counterfeit spike train, particularly intended to test the explicitness and reasonableness of arranging strategies, was utilized to evaluate the presentation of the WSC technique as strategies dependent on head segment investigation principal component analysis (PCA) and decreased list of capabilities reduced feature set (RFS). Because of higher efficiency, WSC strategy beat the other two strategies. It prevalent the presentation was to a great extent since spike profiles that couldn't be isolated by past techniques (as a result of the similitude of their fleeting profile and the veiling activity of commotion) were distinct by the WSC strategy. The WSC strategy is especially clamor safe, as it certainly wipes out the unimportant data in the commotion recurrence extend. In this paper we clustered different spikes using different standard deviation by varying the temperature values.
... Each neuron produces a stereotypical voltage waveform at the electrode based on physical factors including cell geometry, neuron-electrode distance and tissue impedance (Camuñas-Mesa & Quiroga, 2013;Gold, 2006;Hild & Tasaki, 1962). Determining which waveforms are associated with the same source neuron is a process known as spike sorting (Chen, Carlson, & Carin, 2011;Gerstein & Clark, 1964;Hill, Mehta, & Kleinfeld, 2011;Keehn, 1966;Letelier & Weber, 2000;Lewicki, 1999;Prochazka, Conrad, & Sindermann, 1972;Quiroga, Nadasdy, & Ben-Shaul, 2004;Shoham, Fellows, & Normann, 2003;Yuan, Yang, & Si, 2012). Only after the waveforms are sorted can hypotheses be tested that depend on the temporal behavior of those neurons (Hubel & Wiesel, 1959). ...
Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing.
... Each neuron produces a stereotypical voltage waveform at the electrode based on physical factors including cell geometry, neuron-electrode distance and tissue impedance (Camuñas-Mesa & Quiroga, 2013;Gold, 2006;Hild & Tasaki, 1962). Determining which waveforms are associated with the same source neuron is a process known as spike sorting (Chen, Carlson, & Carin, 2011;Gerstein & Clark, 1964;Hill, Mehta, & Kleinfeld, 2011;Keehn, 1966;Letelier & Weber, 2000;Lewicki, 1999;Prochazka, Conrad, & Sindermann, 1972;Quiroga, Nadasdy, & Ben-Shaul, 2004;Shoham, Fellows, & Normann, 2003;Yuan, Yang, & Si, 2012). Only after the waveforms are sorted can hypotheses be tested that depend on the temporal behavior of those neurons (Hubel & Wiesel, 1959). ...
Bjånes DA, Fisher LE, Gaunt RA, Weber DJ
Heuristic Spike Sorting Tuner (HSST), a framework to determine optimal parameter selection for a generic spike sorting algorithm. bioRxiv First published May 21, 2020. Extracellular microelectrodes frequently record neural activity from more than one neuron in the vicinity of the electrode. The process of labeling each recorded spike waveform with the identity of its source neuron is called spike sorting and is often approached from an abstracted statistical perspective. However, these approaches do not consider neurophysiological realities and may ignore important features that could improve the accuracy of these methods. Further, standard algorithms typically require selection of at least one free parameter, which can have significant effects on the quality of the output. We describe a Heuristic Spike Sorting Tuner (HSST) that determines the optimal choice of the free parameters for a given spike sorting algorithm based on the neurophysiological qualification of unit isolation and signal discrimination. A set of heuristic metrics are used to score the output of a spike sorting algorithm over a range of free parameters resulting in optimal sorting quality. We demonstrate that these metrics can be used to tune parameters in several spike sorting algorithms. The HSST algorithm shows robustness to variations in signal to noise ratio, number and relative size of units per channel. Moreover, the HSST algorithm is computationally efficient, operates unsupervised, and is parallelizable for batch processing.
NEW & NOTEWORTHY
HSST incorporates known neurophysiological priors of extracellular neural recordings while simultaneously taking advantage of powerful abstract mathematical tools. Rather than simply selecting free parameters prior to running a sorting algorithm, HSST executes a sorting algorithm across a range of input parameters, using heuristic metrics to detect which spike-sorting output is most physiologically plausible. This novel approach enables unsupervised spike-sorting exceeding the performance of previous methods, thereby enabling the processing of large data sets with confidence.
... The result produces output data which is scanned vertically; the filters are repeated to generate characteristic frequency subbands [4]. After the subsampling stage, the transformation generates four LL, LH, HL and HH subbands, where each image represents 25% of the original image size [5][6][7][8]. ...
... This approach gives a detailed representation of the signal in the time-frequency domain. The DWT function (f) represents the linear combination of convolutions between the spike waveform and wavelet basis function, and is given by [95]: ...
Recent advances in the field of neuroscience have suggested that new generation brain computer interfaces demand a critical step in biomedical signal processing requiring online/on-chip spike sorting. Spike sorting is the process of grouping signals from an individual neuron by grouping action potentials (spikes) into a specific cluster based on the similarity of their shapes. The extraction of single-unit activity by sensors at a distance from specific neurons is necessary for a wide range of clinical applications such as disorder treatments, muscular stimulation (e.g., epidural spinal cord stimulation for treatment acceleration), cochlear implant and neural prostheses. A brain machine interface, for example, can potentially substitute the missing motor pathway/sensory information between the motor cortex and an artificial limb. With the aim of developing an energy-efficient spike sorting chip for hardware implantable systems, this thesis introduces a new feature extraction method based on extrema analysis (positive and negative peaks) of spike shapes and their discrete derivatives. The proposed method runs in real-time and does not require any offline training. Compared to other methods it offers a better tradeoff between accuracy and computational complexity using online sorting. It additionally eliminates multiplications which are computationally expensive, power hungry and require appreciable silicon area. A minimum power limit for implantable neural front-end interfaces is also derived. It involved: 1) system level optimization - the front-end specifications including the bandwidth, data converter resolution and sampling rate were defined by exploring the effect of the parameters on spike sorting via a standard spike bank; 2) block level optimization - The front-end power was minimized by using an opamp-less cyclic converter; and 3) estimating the power limit equation of the frontend. The new optimization methodology addresses the future demands of neural recording interfaces. Finally the thesis presents the design, implementation and testing of the first generation of an adaptive spike sorting processor. It enhances the accuracy-power characteristics by employing self-calibration of processing features. The chip prototype was fabricated in a 180-nm CMOS technology. It achieves an overall clustering accuracy of 84.5% using a standard spike data bank and has a power consumption of 148-μW from 1.8-V supply voltage. The fabricated spike processor has almost 10%higher clustering accuracy than the state-of-the-art.Measurements show good power-performance characteristics compared to the state-of-the-art online and offline clustering methods.
... In addition, softwares only provide the outcomes, they don't present the specific processing theory. Actually, many statistical and signal processing knowledge involved in the kernel code of these softwares [8,9], for example, spike-sorting algorithms and methods including threshold detection, principle component analysis and cluster analysis, etc [10]. Without these knowledges, clients are hard to understand the outcomes and perform further analysis. ...
... The latter stage is called peak alignment. Fourier transform cannot discriminate (Letelier and Weber 2000). The advantage of using wavelets for feature extraction is that much localized shape differences can be discerned because wavelet coefficients are localized in time. ...
Chronic pain (CP) is a complex sensory disorder characterized by structural changes, i.e. severe anatomical rearrangements of somatosensory cortex, and functional changes, i.e. anomalies in network functional connectivity and in information transmission at the level of thalamo-cortical circuit. From the structural point of view, within each cortical module, a morpho-functional unit can be recognized, also called neuro-glial-vascular unit, where the glial cells represent the bridging structures allowing for the transfer of metabolites and oxygen to neurons. Namely, the functional dependency between neuronal and vascular elements, largely explored by 3D confocal microscopy and two photon microscopy, has expanded the concept of synaptic space to a more complex form, indicated as “tripartite synapse”, where besides the presence of the pre- and post- synaptic neurons, a glial component is added facing on the microvascular context. Due to this dependency it appears, thus, correct to analyse the cortical microscopical effects of the macroscopical picture. Novel studies by our group have recently investigated CP origin and evolution in experimental CP rat models (Seltzer) through microstructural and functional analyses focused both on the cortical neuronal substrate and the blood micromorphological and vasculodynamic properties. The 3D microarchitecture of cortical vascular network has been revealed by means of synchrotron X-ray micro Computed Tomography (CT) at the ID17 and ID16A beamlines (ESRF, Grenoble) and the TOMCAT beamline (SLS, Villigen). A subsequent morphometric analysis of the 3D vascular network has been implemented by means of skeletonization and spatial graph transformation. Then, a comparative study “Neuropathic vs Control”, based on the estimated vascular network properties (number of vessels, branch points, skeleton segments and vessel diameter), showed evident changes in cortical microvascular compartments: a widespread increase of blood microvessels and capillaries in the investigated regions (the somatosensory [SSI] cortical area) has been found in all CP rats. In parallel, a reduced mean value of vessel diameter in all CP rats prove that capillaries and small microvessels are predominantly interested by these angiogenetic events. By investigating the time evolution of the neogenesis, it appears strongly present since the first stage of the neuropathy (2 weeks), fading away, but still present, during the last time stage considered (6 months). In addition, an increased maximum blood flow, sustained by the vascular network, has been found in CP condition, indicating that CP vascular networks are compatible with an enriched blood flow sustained by the promoted novel angiogenesis. These results from micro- and nano-tomography have been further confirmed also by immunofluorescence microscopy analysis: CP samples have shown the positivity to three markers of vascular neo-genesis (VEGFR1, VEGFR2 and VWF). In parallel, to functionally analyse the genesis and the evolution of the thalamo-cortical circuits in CP conditions, the neural activity has been recorded by means of 32-microelectrode matrices implanted in the brain, simultaneously receiving signals from the VPL thalamic nucleus and the SS1 cortex. All the CP groups show connectivity disorders exhibited also by the evolution of the network topology from “Modules and Hubs” to a “random” network organisation where the intra-community and inter-community functional connections decrease. These results clearly confirm how the neuronal dynamics is strictly linked to the vascular activity: the cortical microvessel neo-genetic events in CP are strongly correlated to the functional anomalies in neuronal network dynamic. The microvascular involvement in CP opens a new way of interpretation of CP disease, not only recognized as sensory pathology, but also as a neurological disease where neuronal and vascular connectivity networks are extensively involved in the whole system.
При використанні сучасних систем автоматизації та управління мікрокліматом приміщень з динамічною зміною надходження шкідливостей необхідно враховувати час реакції системи на зміни та передбачити зміни цих параметрів. Зміна забрудненості вуглекислим газом та вологості повітря спортивних споруд – таких, як фітнес-зали та плавальні басейни, є нестаціонарними випадковим процесом зі складним видом не стаціонарності й може бути описана статистичними характеристиками, отримання котрих ускладнюється імовірнісною природою усього процесу та наявністю випадкових й систематичних похибок вимірювання забрудненості та вологості повітря конкретної спортивної споруди, специфіка функціонування процесів тепломасообміну, вологообміну у приміщеннях спортивних споруд (плавальні басейни, зали для занять фітнесом, тренажерні зали і т. п.) у сучасній науковій літературі практично не вивчена. Тому дане дослідження проведене саме для того, щоб покращити ситуацію і вивести її з глухого кута (невизначеності) щодо спортивних споруд та їх приміщень для занять масовою фізичною культурою, відпочинку, дозвілля. В роботі запропонований комплексний метод дослідження динаміки зміни забрудненості та вологості повітря приміщення спортивної споруди (фітнес-зали, плавальні басейни, та ін.) дозволяє визначити статистичні характеристики процесу та ідентифікувати його за із задовільною для практичних цілей точністю (похибка складає не більше 10%).
Over the years, wavelet-based analyses have been responsible for remarkable achievements in physics and related sciences. Nevertheless, a deep inspection on wavelet-based strategies described in recent scientific papers, dissertations, and theses reveals that a significant number of authors, i.e., students and even researchers with a modest background on signal analysis, still misunderstand the fundamentals of wavelets. One classical source of confusion, for instance, involves two different but related approaches used to perform discrete-time wavelet transformations and their inverses: algebra- and filter-based. Although the latter is usually adopted in practice, the former reveals the beauty of multiresolution analysis over Heisenberg’s uncertainty principle, showing what really happens behind the scenes. Thus, based on the solid and easy-to-follow explanations provided in this smoothly written tutorial-review article, interested readers will definitively comprehend the different types of wavelet transforms and their specific applications, getting hands-on experience and insights on how to extract the most of their research by using that powerful tool. Because its mission is clarification, example wavelet-related applications are provided in this document to stimulate state-of-the-art research in a diversity of branches in physics.
Spike sorting—the process of separating spikes from different neurons—is often the first and most critical step in the neural data analysis pipeline. Spike-sorting techniques isolate a single neuron’s activity from background electrical noise based on the shapes of the waveforms obtained from extracellular recordings. Despite several advancements in this area, an important remaining challenge in neuroscience is online spike sorting, which has the potential to significantly advance basic neuroscience research and the clinical setting by providing the means to produce real-time perturbations of neurons via closed-loop control. Current approaches to online spike sorting are not fully automated, are computationally expensive and are often outperformed by offline approaches. In this paper, we present a novel algorithm for fast and robust online classification of single neuron activity. This algorithm is based on a deep contractive autoencoder (CAE) architecture. CAEs are neural networks that can learn a latent state representation of their inputs. The main advantage of CAE-based approaches is that they are less sensitive to noise (i.e., small perturbations in their inputs). We therefore reasoned that they can form the basis for robust online spike sorting algorithms. Overall, our deep CAE-based online spike sorting algorithm achieves over 90% accuracy in sorting unseen spike waveforms, outperforming existing models and maintaining a performance close to the offline case. In the offline scenario, our method substantially outperforms the existing models, providing an average improvement of 40% in accuracy over different datasets.
Spike sorting is one of the key techniques to understand brain activity. In this paper, we propose a novel deep learning approach based on convolutional neural networks (CNN) and long short term memory (LSTM) to implement overlapping spike sorting. The results of the simulated data demonstrated that the clustering accuracy was greater than 99.9% and 99.0% for non-overlapping spikes and overlapping spikes, respectively. Moreover, the proposed method performed better than our previous deep learning approach named “1D-CNN”. In addition, the experimental data recorded from the primary visual cortex of a macaque monkey were used to evaluate the proposed method in a practical application. It was shown that the method could successfully isolate most overlapping spikes of different neurons (ranging from two to five). In summary, the CNN + LSTM method proposed in this paper is of great advantage for overlapping spike sorting with high accuracy. It lays the foundation for application in more challenging works, such as distinguishing the simultaneous recordings of multichannel neuronal activities.
Предложен вычислительный метод обнаружения помех в геомагнитных данных, основанный на вейвлет-преобразовании и пороговых функциях. Эффективность метода показана на примере обработки результатов измерений с помощью вариационного феррозондового магнитометра FGE-DTU (обсерватория Паратунка , Камчатский край, ИКИР ДВО РАН). Рассмотрены некоторые виды помех от естественных источников (при землетрясениях на Камчатке) и техногенных помех, связанных с работой ионозонда. Детально изучена частотно-временная структура помех в вариациях Z- и D-составляющих геомагнитного поля (частота измерений 2 Гц). Для рассмотренного вида помех определены информативные масштабные уровни вейвлет-преобразования и оценены параметры алгоритма реализации метода.
The method of detection of noise in magnetic data based on wavelet transformation and threshold functions is considered. Efficiency is shown by the results of analysis of fluxgate magnetometer FGE-DTU measurements at Observatory Paratunka, Kamchatka, IKIR FEB RAS. The noise from natural sources such as earthquakes in Kamchatka region and from artificial sources such as the vertical sounding of ionosphere by the ionosonde near Observatory is considered. Detailed time-frequency structure of noise in 2 Hz records of Z and D components is investigated. To automation the method for considered examples of noise the informative scale levels of wavelet-transformation are determined and parameters of threshold functions appreciated.
http://deepblue.lib.umich.edu/bitstream/2027.42/63897/1/wiltschko_alex_2009.pdf
This chapter offers a brief introduction to the novel advanced mathematical methods of analysis and processing of neurophysiological data. First, we give the rationale for the development of specific mathematical approaches for decoding information from non-stationary neurophysiological processes with time-varying features. Second, we focus on the development of mathematical methods for automatic processing and analysis of neurophysiological signals, more specifically, in the development of brain-computer interfaces (BCIs). Finally, we give an overview of the main applications of wavelet analysis in neuroscience, from the microlevel (the dynamics of individual cells or intracellular processes) to the macrolevel (dynamics of large-scale neuronal networks in the brain as a whole, ascertained by analyzing electro- and magnetoencephalograms).
In this chapter, we consider the problem of spike separation from extracellularly recorded action potentials, which is important when studying the dynamics of small groups of neurons. We discuss general principles of spike sorting and propose several wavelet-based techniques to improve the quality of spike separation, including an approach for optimal sorting with wavelets and filtering techniques. Finally, we consider the application of artificial neural networks to solve this problem.
The main objective of the present study is to introduce new empirical equations for the determination of breach geometrical dimensions and peak outflow discharge (Qp). Therefore, a historic failure database of 109 embankments was collected and examined. The most important factors that affect the breach evolution, including grading size, hydraulic, and outflow characteristics are also studied. Some of the parameters used for the determination of Qp and average breach width (Bave) have a significant effect on the erosion process, but they are less reflected in the technical literature. To study the behavior of non-cohesive soils during overtopping, 15 physical tests were performed at the laboratory, and the effects of interfering parameters were investigated. The experimental output hydrograph was used to simulate the hydrographs resulting from the failure of real dams, and recent artificial intelligence techniques along with linear and nonlinear regression models were employed. The area-time analysis of the laboratory hydrographs shows that the soil particle size and the characteristics of reservoir-basin significantly affect the rate of breach formation and outflow discharge. New relationships are introduced, based on the breach characteristics, by a combination of historical and experimental data, as well as case studies conducted on the hypothetical failure of 10 operational dams. The mathematical model is also used to simulate the process of breach evaluation. Based on statistical indices, comparison of the results, and sensitivity analysis, the developed equations can better express the susceptibility of materials to erosion and their application can minimize downstream vulnerabilities.
The analysis of action potentials is an important task in neuroscience research, which aims to characterise neural activity under different subject conditions. The classification of action potentials, or “spike sorting”, can be formulated as an unsupervised clustering problem, and latent variable models such as mixture models are often used. In this chapter, we compare the performance of two mixture-based approaches when applied to spike sorting: the Overfitted Finite Mixture model (OFM) and the Dirichlet Process Mixture model (DPM). Both of these models can be used to cluster multivariate data when the number of clusters is unknown, however differences in model specification and assumptions may affect resulting statistical inference. Using real datasets obtained from extracellular recordings of the brain, model outputs are compared with respect to the number of identified clusters and classification uncertainty, with the intent of providing guidance on their application in practice.
We present a Bayesian approach for wavelet shrinkage in the context of non-parametric curve estimation with the use of the beta distribution with symmetric support around zero as the prior distribution for the location parameter in the wavelet domain in models with additive Gaussian errors. Explicit formulas of shrinkage rules for particular cases are obtained, statistical properties such as bias, classical and Bayesian risk of the rules are analyzed and performance of the proposed rules is assessed in simulations studies involving standard test functions. Application to Spike Sorting real data set is provided.
While in Chaps. 4 and 5 two-class discrimination applications are demonstrated that the proposed feature engineering play an important part in improving the accuracy performance results, this chapter illustrates the contribution of the feature learning scheme in a classification problem where some class information (e.g., number of classes) is not predefined. For example, in application of motor unit action potential (MUAP) sorting for intramuscular electromyography (nEMG) data, called nEMG spike sorting.
Deep brain stimulation (DBS) of the anterior nucleus of the thalamus (ANT) is a promising treatment for patients with refractory epilepsy. However, therapy response varies and precise positioning of the DBS lead is potentially essential for maximizing therapeutic efficacy. We investigate if single-cell recordings acquired by microelectrode recordings can aid targeting of the ANT during surgery and hypothesize that the neuronal firing properties of the target region relate to clinical outcome. We prospectively included 10 refractory epilepsy patients and performed microelectrode recordings under general anesthesia to identify the change in neuronal signals when approaching and transecting the ANT. The neuronal firing properties of the target region, anatomical locations of microelectrode recordings and active contact positions of the DBS lead along the recorded trajectory were compared between responders and nonresponders to DBS. We obtained 19 sets of recordings from 10 patients (five responders and five nonresponders). Amongst the 403 neurons detected, 365 (90.6%) were classified as bursty. Entry into the ANT was characterized by an increase in firing rate while exit of the ANT was characterized by a decrease in firing rate. Comparing the trajectories of responders to nonresponders, we found differences neither in the neuronal firing properties themselves nor in their locations relative to the position of the active contact. Single-cell firing rate acquired by microelectrode recordings under general anesthesia can thus aid targeting of the ANT during surgery, but is not related to clinical outcome in DBS for patients with refractory epilepsy.
This paper presents three lifting structures of Daubechies-8 (also known as D8) wavelet transform using efficient factorization of the polyphase matrix. All new filter coefficients are optimally mapped with integers resulting in low cost hardware implementation. We first derive the polyphase matrices using a factorization algorithm, which forms the basis of multiple lifting structures of D8. A theoretical framework is then derived and proven experimentally to eliminate the scaling stage of the algorithm that incurs computation error in conventional integer-based wavelets. This elimination of the scaling stage makes the proposed architecture lossless. Also due to the optimum integer mapping, the 8-bit implementation of our schemes produces very similar results than that of the classical double-precision D8 filter. Finally, we compare our results with other existing lifting wavelets to demonstrate the advantage in terms of lower cost, losslessness and improved performance.
Few-unit recordings were obtained using metal microelectrodes. Separation into single-unit spike trains was based on differences in spike amplitude and spike waveform. For that purpose a hardware microprocessor based spike waveform analyser was designed and built. Spikes are filtered by four matched filters and filter outputs at the moments of spike occurrence are read by a computer and used for off-line separation and spike waveform reconstruction. Thirty-one double unit recordings were obtained and correlation between the separated spike trains was determined. After stimulus correction correlation remained in only 8 of the double unit records. It appeared that in most cases this neural correlation was stimulus dependent. Continuous noise stimulation resulted in the strongest neural correlation remaining after correction for stimulus coupling, stimulation with 48 ms duration tonepips presented once per second generally did not result in a significant neural correlation after the correction procedure for stimulus lock. The usefulness of the additive model for neural correlation and the correction procedure based thereupon is discussed.
In this study, we introduce the wavelet transform (WT) as a method for characterizing the maturational changes in electrocortical activity in 24 fetal lambs ranging from 110–144 days gestation (term 145 days). The WT, based on multiresolution signal decomposition, is free of assumptions regarding the characteristics of the signal. The approximation of the electrocortical activity at resolutions varying from 2j+1 to 2j
can be extracted by decomposing the signal on a wavelet orthonormal basis of L
2(R). We performed multiresolution decomposition for four sets of parameters D
2j
, where -1 < j < -4. The four series WT represent the detail signal bandwidths: (1) 16–32 Hz, (2) 8–16 Hz, (3) 4–8 Hz, (4) 2–4 Hz. The data were divided into three groups according to gestational age: 110–122 days (early), 123–135 days (middle), and 136–144 days (late). In the early group, the power was highest in the fourth signal bandwidth, with relatively low power in the other bands. Increase in gestational age was characterized by increased power in all four bandwidths. Comparison of the cumulative distribution function of the power in the four wavelet bands confirmed the presence of two statistically different patterns in all three age groups. These two patterns correspond to the visually identified patterns of HVSA (high-voltage slow activity) and LVFA (low-voltage fast activity). The earliest development change occurred in HVSA, with progressive increase in power in the 2–8 Hz band. Later changes occurred in LVFA, with a significant increase in power in the 16–32 Hz band. The same database was also analyzed by the short-term Fourier transform (STFT) method, the most common time-frequency analysis method. Comparison of the results clearly show that the WT provided much better time-frequency resolution than the STFT method and was superior in demonstrating maturational changes in electrocortical activity.
A new spike discrimination procedure addressing the specific problem of spike superposition is described. The method, based on a shift-invariant wavelet transform and its amplitude-and-phase representation, has the advantage of both reducing the effect of noise present in the data and correcting the latency of specific components in a waveform. When spikes overlap and produce unknown patterns, the procedure extracts the constituent spikes and also estimates their exact time of occurrence. Fast implementation algorithms, having complexity of at most O (N log N), allow the use of the method in real-time applications.
This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.
This paper presents a nontechnical, conceptually oriented introduction to wavelet analysis and its application to neuroelectric waveforms such as the EEG and event related potentials (ERP). Wavelet analysis refers to a growing class of signal processing techniques and transforms that use wavelets and wavelet packets to decompose and manipulate time-varying, nonstationary signals. Neuroelectric waveforms fall into this category of signals because they typically have frequency content that varies as a function of time and recording site. Wavelet techniques can optimize the analysis of such signals by providing excellent joint time-frequency resolution. The ability of wavelet analysis to accurately resolve neuroelectric waveforms into specific time and frequency components leads to several analysis applications. Some of these applications are time-varying filtering for denoising single trial ERPs, EEG spike and spindle detection, ERP component separation and measurement, hearing-threshold estimation via auditory brainstem evoked response measurements, isolation of specific EEG and ERP rhythms, scale-specific topographic analysis, and dense-sensor array data compression. The present tutorial describes the basic concepts of wavelet analysis that underlie these and other applications. In addition, the application of a recently developed method of custom designing Meyer wavelets to match the waveshapes of particular neuroelectric waveforms is illustrated. Matched wavelets are physiologically sensible pattern analyzers for EEG and ERP waveforms and their superior performance is illustrated with real data examples.
A method for extracting single-unit spike trains from extracellular recordings containing the activity of several simultaneously active cells is presented. The technique is particularly effective when spikes overlap temporally. It is capable of identifying the exact number of neurons contributing to a recording and of creating reliable spike templates. The procedure is based on fuzzy clustering and its performance is controlled by minimizing a cluster-validity index which optimizes the compactness and separation of the identified clusters. Application examples with synthetic spike trains generated from real spikes and segments of background noise show the advantage of the fuzzy method over conventional template-creation approaches in a wide range of signal-to-noise ratios.
This writing is based on the lectures I gave at the SIAM one-day tutorial on “Wavelets and Applications” on July 11, the day before the 1993 SIAM Annual Meeting in Philadelphia. In preparation for these lectures, I focused on one theme among the multidisciplinary aspects of the fundamental concepts, theory, mathematical methods, and algorithms of the rapidly developing subject of wavelets. I chose signal processing as the main theme to help unify my presentation for this audience with a diverse background. The reasons for this choice were, first, I wanted to explore the notion of the (integral) wavelet transform, originally introduced by the geophysicist Jean Morlet for studying seismic waves, and, second, I had acquired a very strong interest in signal processing through research, guiding my electrical engineering and computer science students at Texas A&M University, and collaborating with several industrial companies.
To emphasize the importance of using wavelet analysis as a mathematical tool to understand and solve various problems in signal processing, I decided to sacrifice the mathematical generality, elegance, and abstraction. Instead, I outlined the wavelet analysis theory and its implications and included several illustrated examples. It was my goal that in so doing even an audience with undergraduate training in science or engineering could benefit from exposure to these lectures.
My goal agrees with the objectives of this new SIAM series edited by Joseph Flaherty. I would like to express my gratitude to Vickie Kearn and Susan Ciambrano of SIAM for bringing this series to my attention and for their encouragement and assistance in promptly publishing this volume. I would also like to thank Joe for his enthusiasm for this project as well as his cooperation throughout the reviewing process.
This is not a book on signal processing. Furthermore, it is not a comprehensive writing on the rapidly developing field of wavelet analysis.
The companion paper has described a new, fully automatic device for the sorting of action potential waveforms in real time. We present here a brief comparison of performance between this new device and several of the older, more traditional devices used for this purpose. We include in the comparison the performance of 3 human observers.
We describe a new, mostly software-based device for the sorting of waveforms in an extracellular multi-neuron recording situation. The sorting algorithm is largely unattended, and, after an initial 'learning' process, works in real time. Shape comparisons are based on up to 8 time points in the waveform; these points (the reduced feature set) are chosen automatically by analyzing the current incoming data stream. A feasibility version has been implemented on a LSI-11/2 system, using FORTRAN for set-up calculations and assembler for the real-time operations. Detailed comparisons with performance of other sorting devices are presented in the companion paper.
Frequency-specific, i.e., narrow-band brain, activity is traditionally analyzed on the basis of either a time- or frequency-domain representation of the signal. Here we demonstrate an alternative method based on Gabor functions which are well known for their optimal concentration in time and frequency. Using Gabor filtering, amplitude and frequency information can be separated clearly from one another and certain novel approaches to averaging become possible.
A software routine to reconstruct individual spike trains from multi-neuron, single-channel extracellular recordings was designed. Using a neural network algorithm that automatically clusters and sorts the spikes, the only user input needed is the threshold level for spike detection and the number of unit types present in the recording. Adaptive features are included in the algorithm to allow for tracking of spike trains during periods of amplitude variation and also to identify noise spikes. The routine will operate on-line during extracellular studies of the cochlear nucleus in cats.
This paper presents a method to analyze and filter digital signals of finite duration by means of a time-frequency representation. This is done by defining a purely invertible discrete transform, representing a signal either in the time or in the time-frequency domain, as simply as possible with the conventional discrete Fourier transform between the time and the frequency domains. The wavelet concept has been used to build this transform. To get a correct invertibility of this procedure, we have proposed orthogonal and periodic basic discrete wavelets. The properties of such a transform are described, and examples on brain-evoked potential signals are given to illustrate the time-frequency filtering possibilities.
The majority of techniques for separating multiple single-unit spike trains from a multi-unit recording rely on the assumption that different cells exhibit action potentials having unique amplitudes and waveforms. When this assumption fails, due to the similarity of spike shape among different cells or to the presence of complex spikes with declining intra-burst amplitude, these methods lead to errors in classification. In an effort to avoid these errors, the stereotrode (McNaughton et al., 1983) and later the tetrode (O'Keefe and Reece, 1993; Wilson and McNaughton, 1993) recording techniques were developed. Because the latter technique has been applied primarily to the hippocampus, we sought to evaluate its performance in the neocortex. Multi-unit recordings, using single tetrodes, were made at 28 sites in area 17 of 3 anesthetized cats. Neurons were activated with moving bars and square wave gratings. Single units were separated by identification of clusters in 2-D projections of either peak-to-peak amplitude, spike width, spike area, or the 1st versus 2nd principal components of the waveforms recorded on each channel. Using tetrodes, we recorded a total of 154 single cells (mean = 5.4, max = 9). By cross-checking the performance of the tetrode with the stereotrode and electrode, we found that the best of the 6 possible stereotrode pairs and the best of 4 possible electrodes from each tetrode yielded 102 (mean = 3.6, max = 7) and 95 (mean = 3.4, max = 6) cells, respectively. Moreover, we found that the number of cells isolated at each site by the tetrode was greater than the stereotrode or electrode in 16/28 and 28/28 cases, respectively. Thus, both stereotrodes, and particularly electrodes, often lumped 2 or more cells in a single cluster that could be easily separated by the tetrode. We conclude that tetrode recording currently provides the best and most reliable method for the isolation of multiple single units in the neocortex using a single probe.
The P300 response is conventionally obtained by averaging the responses to the task-relevant (target) stimuli of the oddball paradigm. However, it is well known that cognitive ERP components show a high variability due to changes of cognitive state during an experimental session. With simple tasks such changes may not be demonstrable by the conventional method of averaging the sweeps chosen according to task-relevance. Therefore, the present work employed a response-based classification procedure to choose the trials containing the P300 component from the whole set of sweeps of an auditory oddball paradigm. For this purpose, the most significant response property reflecting the P300 wave was identified by using the wavelet transform (WT). The application of a 5 octave quadratic B-spline-WT on single sweeps yielded discrete coefficients in each octave with an appropriate time resolution for each frequency range. The main feature indicating a P300 response was the positivity of the 4th delta (0.5-4 Hz) coefficient (310-430 ms) after stimulus onset. The average of selected single sweeps from the whole set of data according to this criterion yielded more enhanced P300 waves compared with the average of the target responses, and the average of the remaining sweeps showed a significantly smaller positivity in the P300 latency range compared with the average of the non-target responses. The combination of sweeps classified according to the task-based and response-based criteria differed significantly. This suggests an influence of changes in cognitive state on the presence of the P300 wave which cannot be assessed by task performance alone.
The standard methods for decomposition and analysis of evoked potentials are bandpass filtering, identification of peak amplitudes and latencies, and principal component analysis (PCA). We discuss the limitations of these and other approaches and introduce wavelet packet analysis. Then we propose the "single-channel wavelet packet model," a new approach in which a unique decomposition is achieved using prior time-frequency information and differences in the responses of the components to changes in experimental conditions. Orthogonal sets of wavelet packets allow a parsimonious time-frequency representation of the components. The method allows energy in some wavelet packets to be shared among two or more components, so the components are not necessarily orthogonal. The single-channel wavelet packet model and PCA both require constraints to achieve a unique decomposition. In PCA, however, the constraints are defined by mathematical convenience and may be unrealistic. In the single-channel wavelet packet model, the constraints are based on prior scientific knowledge. We give an application of the method to auditory evoked potentials recorded from cats. The good frequency resolution of wavelet packets allows us to separate superimposed components in these data. Our present approach yields estimates of component waveforms and the effects of experiment conditions on the amplitude of the components. We discuss future extensions that will provide confidence intervals and p values, allow for latency changes, and represent multichannel data.
In recent years, a particular challenge has arisen in noninvasive
medical diagnostic procedures. Because biosignals recorded on the body
surface reflect the internal behaviour and status of the organism or its
parts, they are ideally suited to provide essential information of these
organs to the clinician without any invasive measures. But how are the
recorded time courses of the signals to be interpreted with regard to a
diagnostic decision? What are the essential features and in what code is
the information hidden in the signals? These questions are typical of
so-called pattern-recognition tasks. This article reviews pattern
recognition as it applies to medical diagnostics and discusses the
concept of wavelet networks as a means of biosignal classification. An
example is presented in which this approach was used for classifying
preprocessed ECG signals to identify patients who were at high-risk of
developing ventricular tachycardia (VT)
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by piecewise constants is poor. To improve this first wavelet, we are led to dilation equations and their unusual solutions. Higher-order wavelets are constructed, and it is surprisingly quick to compute with them --- always indirectly and recursively. We comment informally on the contest between these transforms in signal processing, especially for video and image compression (including high-definition television). So far the Fourier Transform --- or its 8 by 8 windowed version, the Discrete Cosine Transform --- is often chosen. But wavelets are already competitive, and they are ahead for fingerprints. We present a sample of this developing theory.
Introduction to Wavelets and Wavelet Transforms: A Primer Chui CK. Wavelets: A Mathematical Tool for Signal Analysis Detection of P300 waves in single trials by the wavelet transform
- Burrus Cs Ra Gopinath
- Guo
- T Demiralp
- A Ademoglu
- M Schü
- C Basar-Eroglu
- Basar
Burrus CS, Gopinath RA, Guo H. Introduction to Wavelets and Wavelet Transforms: A Primer. Engelwood Cliffs, NJ: Prentice Hall, 1997. Chui CK. Wavelets: A Mathematical Tool for Signal Analysis. SIAM Monographs on Mathematical Modeling and Computation. Philadelphia, PA: SIAM, 1997. Demiralp T, Ademoglu A, Schü rmann M, Basar-Eroglu C, Basar E. Detection of P300 waves in single trials by the wavelet transform. Brain Language 1999;66:108 – 28.
The Fourier Integral and Its Applications Numerical Recipes in C: The Art of Scientific Computing A wavelet packet model of evoked potentials
- Papoulis A Press Wh
- Teukolsky
- Sa
- Wt Vetterling
- J Flannery Bp Raz
- L Dickerson
- Turetsky
Papoulis A. The Fourier Integral and Its Applications. New York: McGraw-Hill, 1962. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes in C: The Art of Scientific Computing. Cambridge: Cambridge University Press, 1993. Raz J, Dickerson L, Turetsky B. A wavelet packet model of evoked potentials. Brain Language 1999;66:61 – 88.
Wavelets: A Mathematical Tool for Signal Analysis. SIAM Monographs on Mathematical Modeling and Computation
- Ck Chui
Chui CK. Wavelets: A Mathematical Tool for Signal Analysis. SIAM
Monographs on Mathematical Modeling and Computation.
Philadelphia, PA: SIAM, 1997.
Wavelet analysis book report
- Meyer