# Compressed Sensing Approach for Reducing the Number of Receive Elements in Synthetic Transmit Aperture Imaging

18 May 2020-IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 67, Iss: 10, pp 2012-2021

TL;DR: This work adopts a CS framework to MSTA, with a motivation to reduce the number of receive elements and data and finds that the images recovered using CS were comparable to those of reference full-aperture case in terms of estimated lateral resolution, contrast-to-noise ratio, and structural similarity indices.

Abstract: Recently, researchers have shown an increased interest in ultrasound imaging methods alternate to conventional focused beamforming (CFB). One such approach is based on the synthetic aperture (SA) scheme; more popular are the ones based on synthetic transmit aperture (STA) schemes with a single-element transmit or multielement STA (MSTA). However, one of the main challenges in translating such methods to low-cost ultrasound systems is the tradeoffs among image quality, frame rate, and complexity of the system. These schemes use all the transducer elements during receive, which dictates a corresponding number of parallel receive channels, thus increasing the complexity of the system. A considerable amount of literature has been published on compressed sensing (CS) for SA imaging. Such studies are aimed at reducing the number of transmissions in SA but still recover images of acceptable quality at high frame rate and fail to address the complexity due to full-aperture receive. In this work, we adopt a CS framework to MSTA, with a motivation to reduce the number of receive elements and data. The CS recovery performance was assessed for the simulation data, tissue-mimicking phantom data, and an example in vivo biceps data. It was found that in spite of using 50% receive elements and overall using only 12.5% of the data, the images recovered using CS were comparable to those of reference full-aperture case in terms of estimated lateral resolution, contrast-to-noise ratio, and structural similarity indices. Thus, the proposed CS framework provides some fresh insights into translating the MSTA imaging method to affordable ultrasound scanners.

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TL;DR: In this paper, the authors extended the compressed sensing-based synthetic transmit aperture (CS-STA) to the in-phase/quadrature (IQ) domain for the recovery of baseband STA IQ dataset.

Abstract: Compressed sensing-based synthetic transmit aperture (CS-STA) was previously proposed to recover the full radio-frequency (RF) channel dataset of synthetic transmit aperture (STA) from that of a smaller number of randomly apodized plane wave (PW) transmissions. In this way, the imaging frame rate (FR) and contrast are improved with maintained spatial resolution, compared with those of STA. Because CS-STA reconstruction is repeated for all receive elements and RF samples (with a high sampling frequency), the recovery of STA dataset in RF domain is time-consuming. In the meantime, a large amount of RF data needs to be transferred and stored, resulting in an increase of system complexity and required memory space. In this study, CS-STA is extended to in-phase/quadrature (IQ) domain (with lower sampling frequency) for the recovery of baseband STA IQ dataset to accelerate the CS-STA reconstruction by reducing the amount of data to be processed. More importantly, CS-STA reconstruction using IQ data is of practical importance, as clinical ultrasound systems typically record baseband IQ signal instead of RF signal. Simulations, phantom and in vivo experiments verify the feasibility of CS-STA in IQ domain for the recovery of STA dataset. More specifically, CS-STA using IQ data achieves similar image quality and appreciably improves reconstruction speed (by ∼3 times) compared with that using RF data. These findings demonstrate that IQ-domain CS-STA is capable of relieving the computational and storage burdens, which may facilitate the implementation of CS-STA in practical ultrasound systems.

6 citations

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TL;DR: In this paper , the authors extended the compressed sensing-based synthetic transmit aperture (CS-STA) to the in-phase/quadrature (IQ) domain for the recovery of baseband STA IQ dataset.

Abstract: Compressed sensing-based synthetic transmit aperture (CS-STA) was previously proposed to recover the full radio-frequency (RF) channel dataset of synthetic transmit aperture (STA) from that of a smaller number of randomly apodized plane wave (PW) transmissions. In this way, the imaging frame rate (FR) and contrast are improved with maintained spatial resolution, compared with those of STA. Because CS-STA reconstruction is repeated for all receive elements and RF samples (with a high sampling frequency), the recovery of STA dataset in RF domain is time-consuming. In the meantime, a large amount of RF data needs to be transferred and stored, resulting in an increase of system complexity and required memory space. In this study, CS-STA is extended to in-phase/quadrature (IQ) domain (with lower sampling frequency) for the recovery of baseband STA IQ dataset to accelerate the CS-STA reconstruction by reducing the amount of data to be processed. More importantly, CS-STA reconstruction using IQ data is of practical importance, as clinical ultrasound systems typically record baseband IQ signal instead of RF signal. Simulations, phantom and in vivo experiments verify the feasibility of CS-STA in IQ domain for the recovery of STA dataset. More specifically, CS-STA using IQ data achieves similar image quality and appreciably improves reconstruction speed (by ∼3 times) compared with that using RF data. These findings demonstrate that IQ-domain CS-STA is capable of relieving the computational and storage burdens, which may facilitate the implementation of CS-STA in practical ultrasound systems.

4 citations

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TL;DR: In this article , a compressive sensing (CS) approach was applied to experimental data measured from samples containing artificial flaws and the results demonstrated that the proposed CS method allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery.

Abstract: Phased array ultrasonic testing (PAUT) based on full matrix capture (FMC) has recently been gaining popularity in the scientific and nondestructive testing communities. FMC is a versatile acquisition method that collects all the transmitter–receiver combinations from a given array. Furthermore, when postprocessing FMC data using the total focusing method (TFM), high-resolution images are achieved for defect characterization. Today, the combination of FMC and TFM is becoming more widely available in commercial ultrasonic phased array controllers. However, executing the FMC-TFM method is data-intensive, as the amount of data collected and processed is proportional to the square of the number of elements of the probe. This shortcoming may be overcome using a sparsely populated array in transmission followed by an efficient compression using compressive sensing (CS) approaches. The method can therefore lead to a massive reduction of data and hardware requirements and ultimately accelerate TFM imaging. In the present work, a CS methodology was applied to experimental data measured from samples containing artificial flaws. The results demonstrated that the proposed CS method allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery. Such results indicate the possibility of recovering experimental FMC signals using sampling rates under the Nyquist theorem limit. The TFM images obtained from the FMC, CS-FMC, and sparse CS approaches were compared in terms of contrast-to-noise ratio (CNR). It was seen that the CS-FMC combination produced images comparable to those acquitted using the FMC. Implementation of sparse arrays improved CS reconstruction times by up to 11 folds and reduced the firing events by approximately 90%. Moreover, image formation was accelerated by 6.6 times at the cost of only minor image quality degradation relative to the FMC.

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TL;DR: In this article , a self-supervised network is proposed to adaptively select a group of optimized receive elements from a limited number of channels in each STA transmit-receive event.

Abstract: Ultrasound beamforming with reduced receive channel count is necessary when the system contains fewer channels than the elements in the probe to be controlled. While synthetic transmit aperture (STA) imaging with two-way dynamic focusing can improve image quality, it requires sequential full-aperture receives. This paper proposes a self-supervised network to adaptively select a group of optimized receive elements from a limited number of channels in each STA transmit-receive event. The selection procedure is achieved by modifying a fully-connected encoder to characterize the relationship between the full-aperture channel data and their sub-sampled components. The decoder of this network can also recover the full-aperture channel data from the subsamples. The network trained by phantom data can be utilized to evaluate the data from computer simulations and in-vivo experiments. Compared with a compressed-sensing based method, the proposed method achieves more accurate image reconstruction and better image contrast performance.

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TL;DR: In this article , a CS methodology was applied to experimental data measured from samples containing artificial flaws, which allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery.

Abstract: Phased array ultrasonic testing (PAUT) based on full matrix capture (FMC) has recently been gaining in popularity in the scientific and nondestructive testing communities. FMC is a versatile acquisition method that collects all the transmitter-receiver combinations from a given array. Furthermore, when post-processing FMC data using the total focusing method (TFM), high-resolution images are achieved for defect characterization. Today, the combination of FMC and TFM are becoming more widely available in commercial ultrasonic phased array controllers. However, executing the FMC-TFM method is data-intensive, as the amount of data collected and processed is proportional to the square of the number of elements of the probe. This shortcoming may be overcome using a sparsely populated array in transmission followed by an efficient compression using compressive sensing (CS) approaches. The method can therefore lead to a massive reduction of data and hardware requirements and ultimately accelerate TFM imaging. In the present work, a CS methodology was applied to experimental data measured from samples containing artificial flaws. The results demonstrated that the proposed CS method allowed a reduction of up to 80% in the volume of data while achieving adequate FMC data recovery. Such results indicate the possibility of recovering experimental FMC signals using sampling rates under the Nyquist theorem limit. The TFM images obtained from the FMC, CS-FMC, and sparse CS approaches were compared in terms of contrast-to-noise ratio (CNR). It was seen that the CS-FMC combination produced images comparable to those acquitted using the FMC. Implementation of sparse arrays improved CS reconstruction times by up to 11 folds and reduced the firing events by approximately 90%. Moreover, image formation was accelerated by 6.6 times at the cost of only a minor image quality degradation relative to the FMC.

##### References

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TL;DR: In this article, a structural similarity index is proposed for image quality assessment based on the degradation of structural information, which can be applied to both subjective ratings and objective methods on a database of images compressed with JPEG and JPEG2000.

Abstract: Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a structural similarity index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MATLAB implementation of the proposed algorithm is available online at http://www.cns.nyu.edu//spl sim/lcv/ssim/.

40,609 citations

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TL;DR: It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients, and a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing.

Abstract: Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0

18,609 citations

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TL;DR: A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested, which relies on the Tupholme-Stepanishen method for calculating pulsing pressure fields and can also handle the continuous wave and pulse-echo case.

Abstract: A method for simulation of pulsed pressure fields from arbitrarily shaped, apodized and excited ultrasound transducers is suggested. It relies on the Tupholme-Stepanishen method for calculating pulsed pressure fields, and can also handle the continuous wave and pulse-echo case. The field is calculated by dividing the surface into small rectangles and then Summing their response. A fast calculation is obtained by using the far-field approximation. Examples of the accuracy of the approach and actual calculation times are given. >

2,340 citations

### "Compressed Sensing Approach for Red..." refers methods in this paper

...For this analysis, a cyst phantom was simulated with Field II [40], [41]....

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TL;DR: It is shown that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the numberof nonzero components in x 0, and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|.

Abstract: We consider the problem of reconstructing a sparse signal x 0 2 R n from a limited number of linear measurements. Given m randomly selected samples of Ux 0 , where U is an orthonormal matrix, we show that ‘1 minimization recovers x 0 exactly when the number of measurements exceeds m Const ·µ 2 (U) ·S · logn, where S is the number of nonzero components in x 0 , and µ is the largest entry in U properly normalized: µ(U) = p n · maxk,j |Uk,j|. The smaller µ, the fewer samples needed. The result holds for “most” sparse signals x 0 supported on a fixed (but arbitrary) set T. Given T, if the sign of x 0 for each nonzero entry on T and the observed values of Ux 0 are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples.

2,187 citations

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TL;DR: A root-finding algorithm for finding arbitrary points on a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution is described, and it is proved that this curve is convex and continuously differentiable over all points of interest.

Abstract: The basis pursuit problem seeks a minimum one-norm solution of an underdetermined least-squares problem. Basis pursuit denoise (BPDN) fits the least-squares problem only approximately, and a single parameter determines a curve that traces the optimal trade-off between the least-squares fit and the one-norm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a root-finding algorithm for finding arbitrary points on this curve; the algorithm is suitable for problems that are large scale and for those that are in the complex domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem with an explicit one-norm constraint. Only matrix-vector operations are required. The primal-dual solution of this problem gives function and derivative information needed for the root-finding method. Numerical experiments on a comprehensive set of test problems demonstrate that the method scales well to large problems.

2,033 citations

### "Compressed Sensing Approach for Red..." refers background in this paper

...Equation (3) can be solved using basis pursuit with inequality constraints (BPICs), which can be solved using basis pursuit denoising (BPDN) solvers [39] as follows:...

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