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![The Grangeat equation and the parameters used in it, reproduced, with permission from [51].](publication/278963383/figure/fig31/AS:1086775221067800@1636118812655/The-Grangeat-equation-and-the-parameters-used-in-it-reproduced-with-permission-from.jpg)
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In X-ray computed tomography (CT) an important objective is to reduce the radiation dose without significantly degrading the image quality. Compressed sensing (CS) enables the radiation dose to be reduced by producing diagnostic images from a limited number of projections. However, conventional CS-based algorithms are computationally intensive and...
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Citations
... Les techniques de reconstruction itérative ont permis de répondre partiellement à ce problème grâce à des termes de régularisation avancées et l'injection de connaissances a priori [1]. Ces dernières années, ces techniques itératives ont été améliorées par la théorie et le développement de l'acquisition comprimé, dit compressed sensing (CS), qui permet la reconstruction d'images de haute qualité malgré un nombre de vues inférieur à celui requis pour les algorithmes analytiques de rétroprojection filtrée [2]. Cependant, les reconstructions CT conventionnelles basées sur le CS sont coûteuses en termes de calcul car les méthodes de reconstruction associées résolvent un système à haute dimension avec la norme 1. Pour surmonter ce problème, le sparse coding, un développement particulier du CS, utilise une stratégie patch-based. ...
Cet article évalue le potentiel du convolutional sparse coding (CSC) pour réduire les artefacts dans les images 3D par tomographie rayons X dans le cas où peu de projections sont disponibles. La méthode CSC proposée est testée sur des échantillons métalliques fabriqués par fabrication additive, qui présentent des défis uniques pour les applications de débruitage en raison de la structure fine du matériau. Les résultats indiquent que le CSC surpasse les dictionnaires traditionnels en termes de performance de débruitage et de vitesse de calcul, ce qui en fait une méthode prometteuse pour les applications d'imagerie tomographique à grande échelle.
... As this test reveals, there are a significant number of practical applications where uniform recovery is not the correct model for compressed sensing. This list of applications includes magnetic resonance imaging (MRI) [37,52], other areas of medical imaging such as computerized tomography (CT) [23,39], nuclear magnetic resonance (NMR) [43], electron tomography [36,49], as well as other fields such as fluorescence microscopy [59,61], surface scattering such as helium atom scattering [44], and radio interferometry [53]. ...
... The notation DFT, HAD, and DWT N is used throughout this article to represent the discrete Fourier transform, the Hadamard transform, and the discrete wavelet transform (with Daubechies wavelets with N vanishing moments), respectively. These different types of matrices are represented in a variety of applications including (but not limited to) MRI [37,52], radio interferometry [53], helium atom scattering [44], electron tomography [36,49], CT [23,39], fluorescence microscopy [59,61], and NMR [43]. ...
The purpose of this paper is twofold. The first is to point out that the property of uniform recovery, meaning that all sparse vectors are recovered, does not hold in many applications where compressed sensing is successfully used. This includes fields like magnetic resonance imaging (MRI), nuclear magnetic resonance computerized tomography, electron tomography, radio interferometry, helium atom scattering, and fluorescence microscopy. We demonstrate that for natural compressed sensing matrices involving a level based reconstruction basis (e.g., wavelets), the number of measurements required to recover all $s$-sparse signals for reasonable $s$ is excessive. In particular, uniform recovery of all $s$-sparse signals is quite unrealistic. This realization explains why the restricted isometry property (RIP) is insufficient for explaining the success of compressed sensing in various practical applications. The second purpose of the paper is to introduce a new framework based on a generalized RIP and a generalized nullspace property that fit the applications where compressed sensing is used. We demonstrate that the shortcomings previously used to prove that uniform recovery is unreasonable no longer apply if we instead ask for structured recovery that is uniform only within each of the levels. To examine this phenomenon, a new tool, termed the “restricted isometry property in levels” (RIP$_L$) is described and analyzed. Furthermore, we show that with certain conditions on the RIP$_L$, a form of uniform recovery within each level is possible. Fortunately, recent theoretical advances made by Li and Adcock demonstrate the existence of large classes of matrices that satisfy the RIP$_L$. Moreover, such matrices are used extensively in applications such as MRI. Finally, we conclude the paper by providing examples that demonstrate the optimality of the results obtained.
Computed tomography (CT) imaging is a non-invasive diagnostic technique and is widely used for severe diseases in the field of medical imaging. X-ray beam, γ-ray, ultrasonic and other signals, are employed to detect the cross-sectional scanning of a certain part of the human body with high sensitivity. CT has the characteristics of fast scanning time and clear image, and can be applied for the examination of many diseases. In industrial inspection, CT plays an a vital role in nondestructive testing and reverse engineering. This technology is related to integrated instruments and computational imaging methods. In this chapter, we will systematically introduce this imaging method from the origin of X-rays, including the principles, classification, development and application of CT imaging equipment. Algorithms are categorized and typical reconstruction algorithms are given in detail. Finally, the new technologies and future development directions for CT are envisioned.
In 1970, the use of a linear system of equations in the form of algebraic reconstruction technique (ART) was an initial step to be used as an iterative reconstruction technique in the domain of computer tomography (CT). The method used by Gordon and Herman was popularly known as the Kaczmarz method in numerical linear algebra. There are many advantages of such an iterative reconstruction technique, however ART never took off for clinical trials due to a lack of computational power. Hence, the filtered back projection (FBP) method enjoyed as THE most popular and commercially used CT image reconstruction algorithm for decades. In 2009, the first iterative algorithm popularly known as the iterative algorithm in image space (IRIS) got FDA approval for commercial use as a CT image reconstruction algorithm. Such an advancement truly boosted researchers and commercial vendors to look for advanced iterative algorithms. As a result, the number of publications in the domain of iterative CT image reconstruction techniques is countless. Recent advancements in artificial intelligence have attracted researchers to explore the possibilities for the development of CT image reconstruction algorithms using the techniques of neural networks or deep learning. In this work, we intend our discussion to understand and explore the developments of major iterative reconstruction algorithms, especially as inverse problems, and optimization-based approaches for CT image reconstruction. We aim to understand what these algorithms have achieved in terms of radiation dose reduction while maintaining the image quality.KeywordsAlgebraic reconstruction technique (ART)Computer tomography (CT)Filtered back projection (FBP)Compressive sensingOrthogonal matching pursuit (OMP)Restricted isometry property (RIP)Deep learningMathematics Subject Classification (2010)68T0168T07
Purpose
The long acquisition time of CBCT discourages repeat verification imaging, therefore increasing treatment uncertainty. In this study, we present a fast volumetric imaging method for lung cancer radiation therapy using an orthogonal 2D kV/MV image pair.
Methods
The proposed model is a combination of 2D and 3D networks. The proposed model consists of five major parts: (1) kV and MV feature extractors are used to extract deep features from the perpendicular kV and MV projections. (2) The feature‐matching step is used to re‐align the feature maps to their projection angle in a Cartesian coordinate system. By using a residual module, the feature map can focus more on the difference between the estimated and ground truth images. (3) In addition, the feature map is downsized to include more global semantic information for the 3D estimation, which is useful to reduce inhomogeneity. By using convolution‐based reweighting, the model is able to further increase the uniformity of image. (4) To reduce the blurry noise of generated 3D volume, the Laplacian latent space loss calculated via the feature map that is extracted via specifically‐learned Gaussian kernel is used to supervise the network. (5) Finally, the 3D volume is derived from the trained model. We conducted a proof‐of‐concept study using 50 patients with lung cancer. An orthogonal kV/MV pair was generated by ray tracing through CT of each phase in a 4D CT scan. Orthogonal kV/MV pairs from nine respiratory phases were used to train this patient‐specific model while the kV/MV pair of the remaining phase was held for model testing.
Results
The results are based on simulation data and phantom results from a real Linac system. The mean absolute error (MAE) values achieved by our method were 57.5 HU and 77.4 HU within body and tumor region‐of‐interest (ROI), respectively. The mean achieved peak‐signal‐to‐noise ratios (PSNR) were 27.6 dB and 19.2 dB within the body and tumor ROI, respectively. The achieved mean normalized cross correlation (NCC) values were 0.97 and 0.94 within the body and tumor ROI, respectively. A phantom study demonstrated that the proposed method can accurately re‐position the phantom after shift. It is also shown that the proposed method using both kV and MV is superior to current method using kV or MV only in image quality.
Conclusion
These results demonstrate the feasibility and accuracy of our proposed fast volumetric imaging method from an orthogonal kV/MV pair, which provides a potential solution for daily treatment setup and verification of patients receiving radiation therapy for lung cancer.
Compressive sensing (CS) plays a critical role in sampling, transmitting, and storing the color medical image, i.e., magnetic resonance imaging, colonoscopy, wireless capsule endoscopy, and eye images. Although CS for medical images has been extensively investigated, a challenge remains in the reconstruction time of the CS. This paper considers a reconstruction of CS using sparsity averaging (SA)-based basis pursuit (BP) for RGB color space of eye image, referred to as RGB-BPSA. Next, an enhanced RGB-BPSA (E-RGB-BPSA) is proposed to reduce the reconstruction time of RGB-BPSA using a simple SA generated by the combination of Daubechies-1 and Daubechies-8 wavelet filters. In addition, variable density sampling is proposed for the measurement of E-RGB-BPSA. The performance metrics are investigated in terms of structural similarity (SSIM) index, signal-to-noise ratio (SNR), and CPU time. The simulation results show the superior E-RGB-BPSA over the existing RGB-BPSA at a CRI with a resolution 512×512 pixels into a measurement rate 10% with SSIM of 0.9, SNR of 20 dB, and CPU time of 20 seconds. The E-RGB-BPSA can be a solution to massive data transmissions and storage for the future of medical imaging.
Background:
Reconstruction of high quality two dimensional images from fan beam computed tomography (CT) with a limited number of projections is already feasible through Fourier based iterative reconstruction method. However, this article is focused on a more complicated reconstruction of three dimensional (3D) images in a sparse view cone beam computed tomography (CBCT) by utilizing Compressive Sensing (CS) based on 3D pseudo polar Fourier transform (PPFT).
Method:
In comparison with the prevalent Cartesian grid, PPFT re gridding is potent to remove rebinning and interpolation errors. Furthermore, using PPFT based radon transform as the measurement matrix, reduced the computational complexity.
Results:
In order to show the computational efficiency of the proposed method, we compare it with an algebraic reconstruction technique and a CS type algorithm. We observed convergence in <20 iterations in our algorithm while others would need at least 50 iterations for reconstructing a qualified phantom image. Furthermore, using a fast composite splitting algorithm solver in each iteration makes it a fast CBCT reconstruction algorithm. The algorithm will minimize a linear combination of three terms corresponding to a least square data fitting, Hessian (HS) Penalty and l1 norm wavelet regularization. We named it PP-based compressed sensing-HS-W. In the reconstruction range of 120 projections around the 360° rotation, the image quality is visually similar to reconstructed images by Feldkamp-Davis-Kress algorithm using 720 projections. This represents a high dose reduction.
Conclusion:
The main achievements of this work are to reduce the radiation dose without degrading the image quality. Its ability in removing the staircase effect, preserving edges and regions with smooth intensity transition, and producing high-resolution, low-noise reconstruction results in low-dose level are also shown.
This paper proposes novel compressed sensing (CS) of colored iris images using three RGB iterations of basis pursuit (BP) with sparsity averaging (SA), called RGB-BPSA. In RGB-BPSA, a sparsity basis is performed using the average of multiple coherent dictionaries to improve the BP reconstruction. In the experiment, first, the decomposition level of wavelet is studied to analyze the best reconstruction result. Second, the effect of compression rate (CR) is considered. Third, the effect of resolution is investigated. Last, the sparse basis of SA is compared to existing basis, i.e., curvelet, Daubechies-1 or haar, and Daubechies-8. The superior RGB-BPSA over existing CS is shown by better visual quality with higher signal to noise ratio (SNR) and structural similarity (SSIM) index in the same CR. In addition, reconstruction time also investigated where RGB-BPSA outperforms curvelet and two times longer than haar and Daubechies-8.
Computed tomography (CT) in medical is an imaging procedure employed to generate detailed images of bones, soft tissue, internal organs, and blood vessels. However, prolonged acquisition time is yet a bottleneck that can lead to patient discomfort in addition to the cost constrain and exposure to X-rays used by CT. In medical imaging technologies and implementations, effective sampling and transmission techniques are some of the main areas of study to overcome such problems. To fulfill this requirement, the compressive sensing (CS) technique was introduced demonstrating that such compression is possible and can be accomplished throughout the process of data restoration; and that the uncompressed frames can be recovered employing a scalable approach of computational optimization. Sparsity averaging reweighted analysis (SARA) was proposed in compressed imaging, exploiting multi-basis sparsity with averaging approach and basis pursuit denoise (BPDN) with high signal to noise (SNR) results. In SARA, the processing time is not considered due to the high processing time because of iteration in the reweighted process and it is not feasible for the medical image that needs fast processing with high SNR result. To fulfill this gap, this paper proposes total variation based average sparsity model with reweighted analysis for CT imaging. The SNR, structural similarity index (SSIM), and processing time are used as performance metrics for the comparison of the proposed and existing techniques. From detailed experimental results, the proposed technique outperforms the existing CS techniques and is considered as a feasible solution for compressed sensing (CS) based CT images compression with faster delay process and better visual quality for medical images.
