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RF signal waveform after going through (a) sigma-delta modulation, reconstruction, sample repetition, and envelope detection in sequence and (b) sigma-delta modulation, sample repetition, reconstruction, and envelope detection in sequence.
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A pre-delay reconstruction sigma-delta beamformer (SDBF) was recently proposed to achieve a higher level of integration in ultrasound imaging systems. Nevertheless, the high-order reconstruction filter used in each channel of SDBF makes the beamformer highly complex. The beamformer can be simplified by reconstructing the signal after the delay-and-...
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Context 1
... to the high sampling frequency of SDBF, suffi- cient delay resolution can be achieved directly with the delay-and-sum approach. The delay-and-sum beamform- ing method selects a sample in each channel according to the quantized delay profile. A dynamic delay is realized by repeating a sample. However, in SDBF, when sigma-delta modulator output samples are repeated, the signal cannot be reconstructed properly and artifacts will be introduced in the final image. This effect is shown in Fig. 1 where Fig. 1(a) and 1(b) show point phantom images (in 60 dB dynamic range when a dynamic aperture is applied at f- number ≥ 2) with and without dynamic focusing artifacts, respectively. As indicated in Fig. 1(b), dynamic focusing artifacts cause background noise in the image, resulting in severe reduction of the image contrast resolution. The sample repetition inserts extra noise that is not properly shaped by the noise-shaping function. A set of simulations was carried out to study the effect of quantization noise on dynamic focusing artifacts, and the re- sults are shown in Fig. 2. In these simulations, a radio frequency (RF) signal consisting of a 0.6 fractional band- width and a 3.5 MHz Gaussian pulse with −50 dB white noise was used. The RF signal was digitized at 111 MHz using a single-bit 2nd-order low-pass sigma-delta modula- tor, and reconstruction was done using a 160-tap low-pass FIR filter to achieve a 2 MHz transition band (4 MHz to 6 MHz), 0.01 dB peak passband ripple, and 50 dB minimum stopband attenuation. A higher order sigma-delta modulator provides better bit resolution, but a 2nd-order sigma-delta modulator was used because any single bit sigma-delta modulator higher than 2nd order is not inher- ently stable [13]. Fig. 2(a) shows the normalized waveform of the RF signal after it goes through sigma-delta modulation, re- construction, single sample repetition (every 50 sample interval), and then envelope detection in sequence. On the other hand, Fig. 2(b) shows the normalized waveform of the RF signal after it goes through the sequence of sigma- delta modulation, single sample repetition (at 50-sample intervals), reconstruction, and envelope detection. The peak signal-to-noise ratio (PSNR) of the 2 cases can be obtained from the results in Fig. 2 as the ratio of the peak signal power to the average noise floor level [14]. The ratio is calculated based on the assumption that the signal distortion (noise floor) is low compared with the signal power. The PSNR of the 2 cases are, respectively, 45 dB and 28 dB for an average of 5 runs. It demon- strates that sample repetition before signal reconstruction increases the noise floor of the final output. An additional 160-tap low pass FIR filter was inserted into the simulation setup as the adjustable 1st filter shown in Fig. 3 to vary the quantization noise level before sample repetition and to study the effect of sample repetition at different pre-delay quantization noise levels. The signal now goes through sigma-delta modulation, adjustable 1st filter, sample repetition, 2nd reconstruc- tion filter, and then envelope detection. By adjusting the out-of-band attenuation of the 1st filter, a pre-delay signal with different quantization noise levels can be obtained. The PSNR value of the envelope-detected signal after 2nd reconstruction filter was plotted against the pre-delay sig- nal-to-quantization noise ratio (SQNR) of the signal after 1st filter, as shown in Fig. 4. Because, in practice, the sample repetition rate is dynamically changing along the imaging depth, the simulation was repeated for different sample repetition rates. As shown in Fig. 4, when the sample repetition is less frequent, PSNR is higher. In addition, as the pre-delay SQNR increases, the PSNR achieved at that channel af- ter sample repetition increases as well. It shows that the pre-delay quantization noise level affects the degree of dy- namic focusing artifacts. The lower the quantization noise level, the lower the dynamic artifacts caused by sample repetition. Fig. 4 also shows that when the pre-delay SQNR is high, the increment of PSNR with respect to pre- delay SQNR will become gradual, and testing additional increments of the pre-delay SQNR will not make much improvement on the PSNR. It is therefore not necessary to reconstruct the signal fully before the delay-and-sum process; a partial reconstruction is sufficient. Another frequency domain simulation was carried out to study the effect of dynamic focusing on the spectrum of sigma-delta modulated signals. A similar simulation setup as shown in Fig. 3 was used. The only difference is that the samples were repeated dynamically to model the delay profile at the outermost channel of a 64-channel beamformer. The input signal is a pre-compressed waveform, which when properly delayed according to the dynamic delay profile will be a single tone sinusoidal wave at 3.5 MHz. The input signal was digitized using a 2nd-order low-pass sigma-delta modulator at 160 MHz. The frequency spec- tra of the sigma-delta modulated signal before and after the dynamic delay without applying any pre-delay filter- ing are shown in Fig. 5(a). When an 8-tap boxcar filter is used as the pre-delay filter, the frequency spectra of the signal before and after the dynamic delay are as shown in Fig. 5(b). As depicted in Fig. 5(a), besides the compression and shifting of the signal frequency, the noise power at low fre- quency increases significantly, and no noise shaping func- tion is observed after dynamic delay is applied. The low frequency noise causes image artifacts because it cannot be removed by the low-pass reconstruction filter. On the other hand, when an 8-tap boxcar filter is used before de- lay, the noise level caused by dynamic delay is 20 dB lower compared with the previous case without any pre-delay filtering. The frequency domain analysis again justifies the hypothesis that reducing pre-delay quantization noise can alleviate the dynamic focusing artifacts. Based on the findings, we proposed and developed a SDBF based on cascaded reconstruction, which reduces the pre-delay quantization noise to suppress the dynamic focusing ...
Context 2
... to the high sampling frequency of SDBF, suffi- cient delay resolution can be achieved directly with the delay-and-sum approach. The delay-and-sum beamform- ing method selects a sample in each channel according to the quantized delay profile. A dynamic delay is realized by repeating a sample. However, in SDBF, when sigma-delta modulator output samples are repeated, the signal cannot be reconstructed properly and artifacts will be introduced in the final image. This effect is shown in Fig. 1 where Fig. 1(a) and 1(b) show point phantom images (in 60 dB dynamic range when a dynamic aperture is applied at f- number ≥ 2) with and without dynamic focusing artifacts, respectively. As indicated in Fig. 1(b), dynamic focusing artifacts cause background noise in the image, resulting in severe reduction of the image contrast resolution. The sample repetition inserts extra noise that is not properly shaped by the noise-shaping function. A set of simulations was carried out to study the effect of quantization noise on dynamic focusing artifacts, and the re- sults are shown in Fig. 2. In these simulations, a radio frequency (RF) signal consisting of a 0.6 fractional band- width and a 3.5 MHz Gaussian pulse with −50 dB white noise was used. The RF signal was digitized at 111 MHz using a single-bit 2nd-order low-pass sigma-delta modula- tor, and reconstruction was done using a 160-tap low-pass FIR filter to achieve a 2 MHz transition band (4 MHz to 6 MHz), 0.01 dB peak passband ripple, and 50 dB minimum stopband attenuation. A higher order sigma-delta modulator provides better bit resolution, but a 2nd-order sigma-delta modulator was used because any single bit sigma-delta modulator higher than 2nd order is not inher- ently stable [13]. Fig. 2(a) shows the normalized waveform of the RF signal after it goes through sigma-delta modulation, re- construction, single sample repetition (every 50 sample interval), and then envelope detection in sequence. On the other hand, Fig. 2(b) shows the normalized waveform of the RF signal after it goes through the sequence of sigma- delta modulation, single sample repetition (at 50-sample intervals), reconstruction, and envelope detection. The peak signal-to-noise ratio (PSNR) of the 2 cases can be obtained from the results in Fig. 2 as the ratio of the peak signal power to the average noise floor level [14]. The ratio is calculated based on the assumption that the signal distortion (noise floor) is low compared with the signal power. The PSNR of the 2 cases are, respectively, 45 dB and 28 dB for an average of 5 runs. It demon- strates that sample repetition before signal reconstruction increases the noise floor of the final output. An additional 160-tap low pass FIR filter was inserted into the simulation setup as the adjustable 1st filter shown in Fig. 3 to vary the quantization noise level before sample repetition and to study the effect of sample repetition at different pre-delay quantization noise levels. The signal now goes through sigma-delta modulation, adjustable 1st filter, sample repetition, 2nd reconstruc- tion filter, and then envelope detection. By adjusting the out-of-band attenuation of the 1st filter, a pre-delay signal with different quantization noise levels can be obtained. The PSNR value of the envelope-detected signal after 2nd reconstruction filter was plotted against the pre-delay sig- nal-to-quantization noise ratio (SQNR) of the signal after 1st filter, as shown in Fig. 4. Because, in practice, the sample repetition rate is dynamically changing along the imaging depth, the simulation was repeated for different sample repetition rates. As shown in Fig. 4, when the sample repetition is less frequent, PSNR is higher. In addition, as the pre-delay SQNR increases, the PSNR achieved at that channel af- ter sample repetition increases as well. It shows that the pre-delay quantization noise level affects the degree of dy- namic focusing artifacts. The lower the quantization noise level, the lower the dynamic artifacts caused by sample repetition. Fig. 4 also shows that when the pre-delay SQNR is high, the increment of PSNR with respect to pre- delay SQNR will become gradual, and testing additional increments of the pre-delay SQNR will not make much improvement on the PSNR. It is therefore not necessary to reconstruct the signal fully before the delay-and-sum process; a partial reconstruction is sufficient. Another frequency domain simulation was carried out to study the effect of dynamic focusing on the spectrum of sigma-delta modulated signals. A similar simulation setup as shown in Fig. 3 was used. The only difference is that the samples were repeated dynamically to model the delay profile at the outermost channel of a 64-channel beamformer. The input signal is a pre-compressed waveform, which when properly delayed according to the dynamic delay profile will be a single tone sinusoidal wave at 3.5 MHz. The input signal was digitized using a 2nd-order low-pass sigma-delta modulator at 160 MHz. The frequency spec- tra of the sigma-delta modulated signal before and after the dynamic delay without applying any pre-delay filter- ing are shown in Fig. 5(a). When an 8-tap boxcar filter is used as the pre-delay filter, the frequency spectra of the signal before and after the dynamic delay are as shown in Fig. 5(b). As depicted in Fig. 5(a), besides the compression and shifting of the signal frequency, the noise power at low fre- quency increases significantly, and no noise shaping func- tion is observed after dynamic delay is applied. The low frequency noise causes image artifacts because it cannot be removed by the low-pass reconstruction filter. On the other hand, when an 8-tap boxcar filter is used before de- lay, the noise level caused by dynamic delay is 20 dB lower compared with the previous case without any pre-delay filtering. The frequency domain analysis again justifies the hypothesis that reducing pre-delay quantization noise can alleviate the dynamic focusing artifacts. Based on the findings, we proposed and developed a SDBF based on cascaded reconstruction, which reduces the pre-delay quantization noise to suppress the dynamic focusing ...
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Citations
... Besides the baseband content, ΣΔ modulated signals also preserve the short sampling interval which may be useful to improve accuracy in applications based on time delay estimations, such as speech enhancement, sonar, seismology, ultrasonics, camera steering and so forth. With this purpose, recent works have implemented beamforming [4,11,13,17,32], cross correlation [15,18,31] and other methods to ΣΔ sequences, aiming to reduce the bit-width of operations with multiple signals. ...
Among other uses, oversampling can be useful for systems that aim to accurately estimate the time delay between two signals. Due to the simplicity of its implementation, \(\varSigma \varDelta \) analog-to-digital converters have been largely used when oversampled signals are required. In this work, two methods for parallel evaluation of the discrete Fourier transform (DFT) of \(\varSigma \varDelta \) signals are presented, targeting frequency domain analysis of oversampled signals. The basic proposed method relies on the partial storage of DFT outputs in memories, considering binary inputs and using a technique named bitstream decomposition to reduce the dimensionality. Additionally, the basic method has been combined to the Cooley–Tukey algorithm to derive a more efficient method. When compared to conventional strategies to compute partial DFTs sequentially, the proposed methods had shown similar results, using feasible memory resources. However, the method allows highly parallel implementations with linear increase in performance as new processing units are added. It has been shown that its implementation on FPGA not only may improve performance but may also reduce memory utilization in more than 80%, enabling low resource FPGAs to compute the FFT of oversampled \(\varSigma \varDelta \) sequences.
... Although the hardware is reduced, undesirable artifact problem is introduced when dynamic focusing is applied to the post-delay reconstruction beamforming process. This artifact problem would reduce the contrast resolution in the final image [5]. Since then, different artifact correction techniques have been proposed to resolve the problem for example the insert zero and divide-by-two methods[2], [6], insert +1, -1 [4], symmetrical hold methods [7] , and multiplierless pre-delay reconstruction beamformer [8], [9]. ...
... Since then, different artifact correction techniques have been proposed to resolve the problem for example the insert zero and divide-by-two methods[2], [6], insert +1, -1 [4], symmetrical hold methods [7] , and multiplierless pre-delay reconstruction beamformer [8], [9]. In addition, Cheong et al. developed a cascaded reconstruction SDBF, which performs closely to the pre-delay reconstruction beamformer and is more hardware efficient than the multiplier-less structure [5]. The cascaded reconstruction SDBF effectively suppresses the dynamic focusing artifacts by reducing the pre-delay quantization noise. ...
... For a SDBF, the sigma-delta modulator in each channel oversamples the input signal to achieve the required ADC resolution. In order to achieve 60dB dynamic range for a 128 channel, rectangular apodization windowed array, the oversampling ratio (OSR, defined as the ratio of the sampling frequency to twice of the signal bandwidth) of the single bit sigma-delta modulator in each channel has to be at least 10.1 [5]. On the other hand, for the same array to achieve sufficient delay resolution, OSR of 5.5 is needed [5]. ...
Sigma-delta beamformer (SDBF) was proposed in recent year to increase the integration level of an ultrasound imaging system. However, the hardware efficient post-delay reconstruction structure suffers from artifact problem when dynamic focusing is applied. A sigma-delta beamformer based on cascaded reconstruction has successfully corrected the artifact problem by reducing the pre-delay quantization noise level. Based on the same principle, we developed a multi-bit SDBF. The multi-bit SDBF provides comparable image quality as the pre-delay reconstruction SDBF without any extra artifact correction processing. It also reduces the operation frequency as well as the power compared to the single-bit SDBF. Real point and cyst phantom images are presented to compare the performance of the proposed beamformer with other existing techniques. Synthesis results shows that the proposed beamformer can save up to 78% of the power consumed by pre-delay reconstruction SDBF.
... The details are discussed in this chapter. The relevant work is also reported in [46], [47]. ...
Pre-delay reconstruction sigma-delta beamformer (SDBF) was proposed in recent years to achieve a higher level of integration in ultrasound imaging systems. The high-order reconstruction filter used in each channel of SDBF makes the beamformer highly complex. The beamformer can be simplified by reconstructing the signal only after the delay-and-sum process. It requires only one reconstruction filter for the entire beamformer. However, this post-delay reconstruction-based beamformer degrades the image quality when dynamic focusing is performed. This thesis studied the cause of the dynamic focusing artifact problem suffered by the sigma-delta beamformer. It was found that the degree of the problem is related to the pre-delay quantization noise that is present in the signal. Hence, similar performance to the conventional pre-delay reconstruction SDBF can be achieved by simply employing a simple pre-delay filter, as long as the pre-delay filter provides the required pre-delay signal-to-quantization noise ratio (SQNR). Based on this finding, a cascaded reconstruction beamformer was developed that utilizes a boxcar filter as the pre-delay filter in each channel to achieve the required pre-delay SQNR value. Simulations using real phantom data demonstrated that the proposed cascaded reconstruction beamforming method can achieve a contrast resolution comparable to that of the pre-delay reconstruction beamforming method. In addition, the savings on hardware and power can be as much as 85% and 68% respectively, as compared to the pre-delay reconstruction SDBF. DOCTOR OF PHILOSOPHY (EEE)
... The phased array and synthetic aperture beamforming set the top and bottom boundaries in array beamforming; the former produces the best beam quality but with the highest cost, whereas the latter offers the simplest beamformer but with poor beam quality. To simplify the array front-end and beamforming, researchers have investigated numerous approaches, such as multi-element synthetic aperture [18][19][20][21], sparse array [22][23], subarray [4,[24][25][26], and ΔΣ beamforming [27][28][29][30][31][32][33][34][35][36][37][38]. ...
... This is a major flaw for the beamformer that significantly reduces the image quality. Different approaches have been proposed to handle this problem, such as multi-bit recoding and modified modulation [29][30], non-uniform oversampling [31], sparse sample processing [36], subfiltering [37], and cascaded filtering [38] based reconstruction. Thorough this study, non-uniform oversampling is applied to overcome that problem. ...
In this study, an ultrasonic digital beamformer based on subarray processing of 1-bit delta-sigma (ΔΣ) oversampled echo signals is presented. The single-bit oversampling ΔΣ conversion simplifies the coherent processing in beamforming with improved timing accuracy. Subarray processing also aims to simplify the beamforming complexity, where the partial-beam sums (low-resolution beams) are acquired from small sub-arrays, and then these partial beams are coherently processed for producing high-resolution beams. In the ΔΣ subarray beamforming, the ΔΣ coded echo signals are summed over the subarray channels, and then these partial beam-sums are first ΔΣ demodulated, then processed for beam-interpolation, followed by coher-ent summation. This method requires decimation filtering of partial-beam sums from each subarray. The hardware complexity of the ΔΣ subarray beamformer is compared with other beamformers and significant front-end savings are explained. The system is tested experimentally and the results are compared with oth-ers using B-scan images reconstructed from archival experimental raw RF data. Both wire targets and cyst phantom are used to show the differences in Signal to Noise Ratio (SNR) and Contrast to Noise Ratio (CNR) measurements.
This paper presents a pixel pitch-matched readout chip for 3-D photoacoustic (PA) imaging, featuring a dedicated signal conditioning and delta-sigma modulation integrated within a pixel area of 250 $\mu \text{m}$ by 250 $\mu \text{m}$ . The proof-of-concept receiver was implemented in an STMicroelectronics’s 28-nm Fully Depleted Silicon On Insulator technology, and interfaces to a $4 \times 4$ subarray of capacitive micromachined ultrasound transducers (CMUTs). The front-end signal conditioning in each pixel employs a coarse/fine gain tuning architecture to fulfill the 90-dB dynamic range requirement of the application. The employed delta-sigma beamforming architecture obviates the need for area-consuming Nyquist ADCs and thereby enables an efficient in-pixel A/D conversion. The per-pixel switched-capacitor $\Delta \Sigma $ modulator leverages slewing-dominated and area-optimized inverter-based amplifiers. It occupies only 1/4th of the pixel, and its area compares favorably with state-of-the-art designs that offer the same SNR and bandwidth. The modulator’s measured peak signal-to-noise-and-distortion ratio is 59.9 dB for a 10-MHz input bandwidth, and it consumes 6.65 mW from a 1-V supply. The overall subarray beamforming approach improves the area per channel by 7.4 times and the single-channel SNR by 8 dB compared to prior art with similar delay resolution and power dissipation. The functionality of the designed chip was evaluated within a PA imaging experiment, employing a flip-chip bonded 2-D CMUT array.
Fully digitized 2D ultrasound transducer arrays require one ADC per channel with a beamforming architecture consuming low power. We give design considerations for per-channel digitization and beamforming, and present the design and measurements of a continuous time delta-sigma modulator (CTDSM) for cardiac ultrasound applications. By integrating a mixer into the modulator frontend, the phase and frequency of the input signal can be shifted, thereby enabling both improved conversion efficiency and narrowband beamforming. To minimize the power consumption, we propose an optimization methodology using a simulated annealing framework combined with a C++ simulator solving linear electrical networks. The 3rd order single-bit feedback type modulator, implemented in a 65 nm CMOS process, achieves an SNR/SNDR of 67.8/67.4 dB across 1 MHz bandwidth consuming 131 [Formula: see text] of power. The achieved figure of merit of 34.2 fJ/step is comparable with state-of-the-art feedforward type multi-bit designs. We further demonstrate the influence to the dynamic range when performing dynamic receive beamforming on recorded delta-sigma modulated bit-stream sequences.
Dynamic receive beamforming on a delta-sigma modulator's low-resolution output bit-stream suffers from a severely increased noise floor, rendering the promising method infeasible. This work addresses the mechanism behind the increased noise floor. By using multirate theory and bifrequency analysis, we show that the increased noise floor is caused by aliasing/imaging of the powerful quantization noise from specific frequency regions according to the focus depth. We analyze both the conventional delay-and-sum method and the previously proposed insert zero compensation method. For the latter technique, we show that the alias/image bands have first order suppression because of a zero at the origin. This finding leads to the proposal of an architecture combining a CIC filter with the insert zero compensation method. Backed by simulations of beamformed delta-sigma modulated sequences and point spread functions, we compare this architecture to different compensation methods and the ideal delta sigma beamformer. The proposed technique is shown to have low implementation cost and achieve levels of dynamic range comparable to those of the ideal delta-sigma beamformer.
In this study, an ultrasonic digital beamformer based on subarray processing of 1-bit delta-sigma (ΔΣ) oversampled echo signals is presented. The single-bit oversampling ΔΣ conversion simplifies the coherent processing in beamforming with improved timing accuracy. Subarray processing also aims to simplify the beamforming complexity, where the partial-beam sums (low-resolution beams) are acquired from small subarrays, and then these partial beams are coherently processed for producing high-resolution beams. In the ΔΣ subarray beamforming, the ΔΣ coded echo signals are summed over the subarray channels, and then these partial beam-sums are first ΔΣ demodulated, then processed for beam-interpolation, followed by coherent summation. This method requires decimation filtering of partial-beam sums from each subarray. The hardware complexity of the ΔΣ subarray beamformer is compared with other beamformers and significant front-end savings are explained. The system is tested experimentally and the results are compared with others using B-scan images reconstructed from archival experimental raw RF data. Both wire targets and cyst phantom are used to show the differences in Signal to Noise Ratio (SNR) and Contrast to Noise Ratio (CNR) measurements.
Sigma-Delta (Σ−Δ) beamformers have been proposed to reduce hardware complexity of the phased array front-end circuitry in digital ultrasound imaging systems. However, the sample repetitions involved in dynamic focusing degrades the image quality due to the elevated noise level. Thus, conventional low-pass decimators are deemed to be insufficient to suppress the elevated in-band noise floor. This paper shows that, adaptive rank-order filters in combination with the low-pass decimators following the beam summation are adequate to suppress the in- band noise components. As a result, we propose a novel hardware efficient digital beamformer employing single-bit Σ−Δ modulators incorporated with adaptive reconstruction filters. Simulations using experimental phantom data sets have shown that the proposed structure ensures high quality B-scan images comparable to the ones obtained by multi-bit A/D beamformers by preserving the hardware simplicity of the conventional single-bit Σ−Δ beamformers.
ΣΔ beamforming is a promising technique for small analog front-end (AFE) of the medical ultrasound imaging system. Nonetheless, the high data rate from the ΣΔ modulator in the AFE and the high-Q reconstruction filter put harsh requirements on the digital beamforming circuits. Although the BScan-sample-based ΣΔ beamformer structure with FIR reconstruction filter reduces the speed requirement on multipliers so as to make the ΣΔ beamformer implementable in conventional digital platforms, it still requires large area for high-speed adders. In this work, a new BScan-sample-based ΣΔ beamformer structure with IIR reconstruction filter is developed. The new structure greatly reduces the hardware cost. Both ΣΔ beamformers are implemented in FPGAs and digital ICs. The new beamformer is 8 times smaller than the FIR beamformer. For a 128-element, 5MHz ultrasound medical imaging system with 256 beamformers, the new ΣΔ beamformer can be implemented with 2 FPGA chips or a 5.2mmÃ5.2mm digital IC in 0.18μm CMOS logic process.
