Compressed Sensing Reconstruction of 3D Ultrasound Data Using Dictionary Learning and Line-Wise Subsampling

Spatial-frequency parallel subsampling for distributed compressive sensing in ultrasonic imaging inspection

To address the problem of the high hardware requirements and insufficient data storage capacity in current ultrasonic imaging testing, a novel approach is developed using a programmable device, which combines spatial-frequency parallel subsampling with the distributed compressive sensing simultaneous orthogonal matching pursuit (DCS-SOMP) algorithm to achieve fast and high-quality ultrasonic imaging inspection with a small amount of subsampled data. The spatial sparse measurement method was employed to achieve spatial subsampling and minimize the count of signals. Additionally, frequency subsampling was utilized to significantly reduce the data volume of time-domain signals while ensuring signal quality by truncating the primary testing frequency components. The subsampled data was then reconstructed using distributed compressive sensing (DCS) for multi-channel data reconstruction. The experiment of ultrasonic scanning imaging was conducted on a carbon steel specimen containing six transverse through-holes with a diameter of Ф1.5 mm at different depths. The ultrasonic signals were acquired using the spatial-frequency parallel subsampling method, and subsequently reconstructed using the DCS-SOMP algorithm. The results show that the proposed method achieves comparable image quality to that obtained with complete data, using only 1/8 of the complete data, while accurately locating and quantifying defects.

Adaptive machine learning method for photoacoustic computed tomography based on sparse array sensor data

BACKGROUND AND OBJECTIVE

Photoacoustic computed tomography (PACT) is a non-invasive biomedical imaging technology that has developed rapidly in recent decades, especially has shown potential for small animal studies and early diagnosis of human diseases. To obtain high-quality images, the photoacoustic imaging system needs a high-element-density detector array. However, in practical applications, due to the cost limitation, manufacturing technology, and the system requirement in miniaturization and robustness, it is challenging to achieve sufficient elements and high-quality reconstructed images, which may even suffer from artifacts. Different from the latest machine learning methods based on removing distortions and artifacts to recover high-quality images, this paper proposes an adaptive machine learning method to firstly predict and complement the photoacoustic sensor channel data from sparse array sampling and then reconstruct images through conventional reconstruction algorithms.

METHODS

We develop an adaptive machine learning method to predict and complement the photoacoustic sensor channel data. The model consists of XGBoost and a neural network named SS-net. To handle data sets of different sizes and improve the generalization, a tunable parameter is used to control the weights of XGBoost and SS-net outputs.

RESULTS

The proposed method achieved superior performance as demonstrated by simulation, phantom experiments, and in vivo experiment results. Compared with linear interpolation, XGBoost, CAE, and U-net, the simulation results show that the SSIM value is increased by 12.83%, 6.78%, 21.46%, and 12.33%. Moreover, the median R2 is increased by 34.4%, 8.1%, 28.6%, and 84.1% with the in vivo data.

CONCLUSIONS

This model provides a framework to predict the missed photoacoustic sensor data on a sparse ring-shaped array for PACT imaging and has achieved considerable improvements in reconstructing the objects. Compared with linear interpolation and other deep learning methods qualitatively and quantitatively, our proposed methods can effectively suppress artifacts and improve image quality. The advantage of our methods is that there is no need for preparing a large number of images as the training dataset, and the data for training is directly from the sensors. It has the potential to be applied to a wide range of photoacoustic imaging detector arrays for low-cost and user-friendly clinical applications.

Ultrafast Plane Wave Imaging Using Tensor Completion-Based Minimum Variance Algorithm

OBJECTIVE

Coherent plane wave compounding (CPWC) imaging is an efficient technique in high-frame-rate ultrasound imaging. To improve the image quality obtained from the CPWC, the adaptive minimum variance (MV) algorithm can be used. However, the high computational complexity of this algorithm negatively affects the frame rate. In other words, achieving a high frame rate and high-quality features simultaneously remains a challenge in medical ultrasound imaging. The aim of the work described here was to develop an algorithm to tackle this challenge and improve the frame rate while preserving the good quality of the resulting image.

METHODS

A tensor completion (TC)-based MV algorithm is proposed to simultaneously improve the frame rate and image quality in CPWC. In the proposed method, the MV algorithm is applied to a limited number of pixels in the beamforming grid. Then, the appropriate values are assigned to the remaining unprocessed pixels by using the TC algorithm. The proposed algorithm speeds up the beamforming process, and consequently, improves the frame rate.

RESULTS

The computational complexity of the proposed TC-based MV algorithm is reduced compared with that of the conventional MV algorithm while the good quality of this algorithm is preserved. The results indicate that, in particular, by processing 40% of the beamforming grid using the MV beamformer followed by the TC algorithm, a reconstructed image comparable to that in the case in which the MV algorithm is performed on the full beamforming grid is obtained; the difference between the contrast-to-noise ratio evaluation metric between these two cases is about 0.16 dB for the experimental-resolution phantom. Also, the resulting images obtained from the MV algorithm and the TC-based MV method have the same resolution, indicating that the TC-based MV algorithm can successfully achieve the quality of the MV algorithm with a lower computational complexity.

CONCLUSION

The TC-based MV algorithm is proposed in CPWC with the goal of improving frame rate and image quality. Qualitative and quantitative results reveal that by use of the proposed algorithm, the quality of the reconstructed image will be comparable to that of the conventional MV algorithm, and the frame rate will be improved.

Photoacoustic imaging with limited sampling: a review of machine learning approaches

Photoacoustic imaging combines high optical absorption contrast and deep acoustic penetration, and can reveal structural, molecular, and functional information about biological tissue non-invasively. Due to practical restrictions, photoacoustic imaging systems often face various challenges, such as complex system configuration, long imaging time, and/or less-than-ideal image quality, which collectively hinder their clinical application. Machine learning has been applied to improve photoacoustic imaging and mitigate the otherwise strict requirements in system setup and data acquisition. In contrast to the previous reviews of learned methods in photoacoustic computed tomography (PACT), this review focuses on the application of machine learning approaches to address the limited spatial sampling problems in photoacoustic imaging, specifically the limited view and undersampling issues. We summarize the relevant PACT works based on their training data, workflow, and model architecture. Notably, we also introduce the recent limited sampling works on the other major implementation of photoacoustic imaging, i.e., photoacoustic microscopy (PAM). With machine learning-based processing, photoacoustic imaging can achieve improved image quality with modest spatial sampling, presenting great potential for low-cost and user-friendly clinical applications.

High Frame Rate Ultrasound Imaging by Means of Tensor Completion: Application to Echocardiography

High frame rate ultrasound (US) imaging enables the monitoring of fast-moving organs. In echocardiography, this is especially needed due to the existence of rapidly moving structures, such as the heart valves. In the last two decades, various methods have been proposed to improve the frame rate. Here, we propose a novel method, based on binary coding patterns (BCPs) and tensor completion (TC), to increase the temporal resolution (i.e., frame rate) in the preprocessing stage of conventional focused ultrasound imaging (CFUI). The rationale behind our proposal is to perform, at first, the beamforming of a fraction of the scan lines, randomly selected in each frame based on BCP. Then, we reconstruct the missing scan lines through TC. The latter is an effective technique for recovering missing information from a low-rank tensor, based on a small number of observations using rank minimization. Following our approach, reducing the transmissions events needed to generate an image, the frame rate is increased by the same proportion. We have applied the proposed technique to a pre-beamformed radio frequency (RF) echocardiographic dataset. Our results show that we can improve the frame rate by a factor from 3 to 4, while keeping the structural similarity (SSIM) of the reconstructed tensor and the original one at values higher than 0.98.

Inverse Problem of Ultrasound Beamforming With Denoising-Based Regularized Solutions

During the past few years, inverse problem formulations of ultrasound beamforming have attracted growing interest. They usually pose beamforming as a minimization problem of a fidelity term resulting from the measurement model plus a regularization term that enforces a certain class on the resulting image. Here, we take advantage of alternating direction method of multipliers to propose a flexible framework in which each term is optimized separately. Furthermore, the proposed beamforming formulation is extended to replace the regularization term with a denoising algorithm, based on the recent approaches called plug-and-play (PnP) and regularization by denoising (RED). Such regularizations are shown in this work to better preserve speckle texture, an important feature in ultrasound imaging, than sparsity-based approaches previously proposed in the literature. The efficiency of the proposed methods is evaluated on simulations, real phantoms, and in vivo data available from a plane-wave imaging challenge in medical ultrasound. Furthermore, a comprehensive comparison with existing ultrasound beamforming methods is also provided. These results show that the RED algorithm gives the best image quality in terms of contrast index while preserving the speckle statistics.

Acceleration of reconstruction for compressed sensing based synthetic transmit aperture imaging by using in-phase/quadrature data

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.

Efficient synthetic transmit aperture ultrasound based on tensor completion

One of the most important methods in medical ultrasound imaging is the synthetic transmit aperture (STA). Despite the image quality improvement in the STA, this method suffers from several limitations, including a limited data acquisition rate and an increase in the overall time to form a single frame. Tensor completion (TC) is a powerful technique that uses rank minimization to recover missing information from a low-rank tensor. This paper provides a novel random synthetic transmit aperture (RSTA) method based on using only a randomly selected part (a fraction) of the linear array elements in the transmit mode to increase the data acquisition rate and then applying the tensor completion (TC) to improve the image quality. By the proposed method, as it is not necessary to transmit all elements sequentially, the data acquisition rate is improved and the overall time for creating an image is also significantly reduced. We investigated the proposed idea by using several simulated and experimental phantoms. Results showed that the proposed method could increase the data acquisition rate up to three times with the image quality difference of less than 6% compared to the original STA method.

Sparse channel sampling for ultrasound localization microscopy (SPARSE-ULM)

Ultrasound localization microscopy (ULM) has recently enabled the mapping of the cerebral vasculaturein vivowith a resolution ten times smaller than the wavelength used, down to ten microns. However, with frame rates up to 20000 frames per second, this method requires large amount of data to be acquired, transmitted, stored, and processed. The transfer rate is, as of today, one of the main limiting factors of this technology. Herein, we introduce a novel reconstruction framework to decrease this quantity of data to be acquired and the complexity of the required hardware by randomly subsampling the channels of a linear probe. Method performance evaluation as well as parameters optimization were conductedin silicousing the SIMUS simulation software in an anatomically realistic phantom and then compared toin vivoacquisitions in a rat brain after craniotomy. Results show that reducing the number of active elements deteriorates the signal-to-noise ratio and could lead to false microbubbles detections but has limited effect on localization accuracy. In simulation, the false positive rate on microbubble detection deteriorates from 3.7% for 128 channels in receive and 7 steered angles to 11% for 16 channels and 7 angles. The average localization accuracy ranges from 10.6μm and 9.93μm for 16 channels/3 angles and 128 channels/13 angles respectively. These results suggest that a compromise can be found between the number of channels and the quality of the reconstructed vascular network and demonstrate feasibility of performing ULM with a reduced number of channels in receive, paving the way for low-cost devices enabling high-resolution vascular mapping.

Towards practical implementation of the compressed sensing framework for multi-element synthetic transmit aperture imaging

Compressed sensing (CS) has been adapted to synthetic aperture (SA) ultrasound imaging to improve the frame-rate of the system. Recently, we proposed a novel CS framework using Gaussian under-sampling to reduce the number of receive elements in multi-element synthetic transmit aperture (MSTA) imaging. However, that framework requires different receive elements to be chosen randomly for each transmission, which may add to practical implementation challenges. Modifying the scheme to employ the same set of receive elements for all transmissions of MSTA leads to degradation of the recovered image quality. Therefore, this work proposes a novel sampling scheme based on a genetic algorithm (GA), which optimally chooses the receive element positions once and uses it for all the transmission of MSTA. The CS performance using GA sampling schemes is evaluated against the previously proposed CS framework on in-vitro and in-vivo datasets. The obtained results suggest that not only does the GA-based approach allows the use of the same set of sparse receive elements for each transmit, but also leads to the lowest CS recovery error (NRMSE) and 14% overall improvement in image contrast, in comparison to the previously-proposed Gaussian sampling scheme. Thus, using the CS framework along with GA, can potentially reduce the complexity in implementation of CS-framework to MSTA based systems.

Learning Sub-Sampling and Signal Recovery With Applications in Ultrasound Imaging

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that enables joint optimization of a task-adaptive sub-sampling pattern and a subsequent neural task model in an end-to-end fashion. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data.

Subsampling Approaches for Compressed Sensing with Ultrasound Arrays in Non-Destructive Testing

Full Matrix Capture is a multi-channel data acquisition method which enables flexible, high resolution imaging using ultrasound arrays. However, the measurement time and data volume are increased considerably. Both of these costs can be circumvented via compressed sensing, which exploits prior knowledge of the underlying model and its sparsity to reduce the amount of data needed to produce a high resolution image. In order to design compression matrices that are physically realizable without sophisticated hardware constraints, structured subsampling patterns are designed and evaluated in this work. The design is based on the analysis of the Cramér–Rao Bound of a single scatterer in a homogeneous, isotropic medium. A numerical comparison of the point spread functions obtained with different compression matrices and the Fast Iterative Shrinkage/Thresholding Algorithm shows that the best performance is achieved when each transmit event can use a different subset of receiving elements and each receiving element uses a different section of the echo signal spectrum. Such a design has the advantage of outperforming other structured patterns to the extent that suboptimal selection matrices provide a good performance and can be efficiently computed with greedy approaches.

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

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.

Temporal Super-resolution of Ultrasound Imaging Using Matrix Completion

The temporal super-resolution of the dynamic ultrasound imaging, a means to observe rapid heart movements, is considered an important subject in medical diagnosis of cardiac conditions. Here, a new technique based on the acquisition scheme using the matrix completion (MC) theory is offered for the temporal super-resolution of the two-dimensional (2D) and three-dimensional (3D) ultrasound imaging. MC mentions the problem of completing a low-rank matrix when only a subset of its elements can be observed. Here, the lower scan lines are acquired. Whereby, the proposed method uses temporal and spatial information of the radio frequency (RF) image sequences for the reconstruction of skipped RF lines. This is performed using the construction of the MC images and then reconstruction of them by the MC theory. The results of the proposed method are compared with the compressive sensing (CS) reconstruction methods. The qualitative and quantitative evaluations of 2D and 3D data demonstrate that in the proposed method, which uses the spatial and temporal relation of RF images and the MC theory, the reconstruction is more accurate, and the reconstruction error is lower. The computational complexity of this method is very low. It also does not require hardware adjustments. Therefore, it can be easily implemented in current ultrasound-imaging devices with the frame-rate enhancement. For instance, the frame rate up to two times the original sequence is feasible using the proposed methods, while root mean square error is decreased by about 35% and 30% for 2D and 3D data, respectively, compared with the CS reconstruction method.

Strategic Undersampling and Recovery Using Compressed Sensing for Enhancing Ultrasound Image Quality

In conventional focused beamforming (CFB), there is a known tradeoff between the active aperture size of the ultrasound transducer array and the resulting image quality. Increasing the size of the active aperture leads to an increase in the image quality of the ultrasound system at the expense of increased system cost. An alternate approach is to get rid of the requirement of having consecutive active receive elements and instead place them in a random order in a larger aperture. This, in turn, creates an undersampled situation where there are only M active elements placed in a larger aperture, which can accommodate N consecutive receive elements (with ). It is possible to formulate and solve the above-mentioned undersampling situation using a compressed sensing (CS) approach. In our previous work, we had proposed Gaussian undersampling strategy for reducing the number of active receive elements. In this work, we introduce a novel framework, namely Gaussian undersampling-based CS framework (GAUCS) with wave atoms as a sparsifying basis for CFB imaging method. The performance of the proposed method is validated using simulation and in vitro phantom data. Without an increase in the active elements, it is found that the proposed GAUCS framework improved the lateral resolution (LR) and image contrast by 27% and 1.5 times, respectively, while using 16 active elements and by 39% and 1.1 times, respectively, while using 32 active elements. Thus, the GAUCS framework can play a significant role in improving the performance, especially, of affordable point-of-care ultrasound systems.

Application of Compressive Sensing to Ultrasound Images: A Review

Compressive sensing (CS) offers compression of data below the Nyquist rate, making it an attractive solution in the field of medical imaging, and has been extensively used for ultrasound (US) compression and sparse recovery. In practice, CS offers a reduction in data sensing, transmission, and storage. Compressive sensing relies on the sparsity of data; i.e., data should be sparse in original or in some transformed domain. A look at the literature reveals that rich variety of algorithms have been suggested to recover data using compressive sensing from far fewer samples accurately, but with tradeoffs for efficiency. This paper reviews a number of significant CS algorithms used to recover US images from the undersampled data along with the discussion of CS in 3D US images. In this paper, sparse recovery algorithms applied to US are classified in five groups. Algorithms in each group are discussed and summarized based on their unique technique, compression ratio, sparsifying transform, 3D ultrasound, and deep learning. Research gaps and future directions are also discussed in the conclusion of this paper. This study is aimed to be beneficial for young researchers intending to work in the area of CS and its applications, specifically to US.

Compressed Sensing with Gaussian Sampling Kernel for Ultrasound Imaging

Recently, compressed sensing (CS) has been applied to ultrasound imaging for either data reduction or frame rate improvement. However, there are no detailed reports yet on strategies for lateral undersampling of channel data in conventional focused beamforming (CFB) and its recovery exploiting the CS approach. We propose a strategic lateral undersampling approach for channel data using the Gaussian sampling scheme and compare it with a direct extension of the often-used uniform undersampling reported for axial undersampling to the lateral direction and 2-D random sampling reported in the literature. As opposed to the reported 2-D random undersampling, we explore undersampling of channel data in the lateral direction by acquiring radiofrequency data from only a reduced number of chosen receive elements and subjecting these data to further undersampling in the axial direction. The effect of the sampling schemes on CS recovery was studied using data from simulations and experiments for various lateral and axial undersampling rates. The results suggest that CS-recovered data from the Gaussian distribution-based channel data subsampling yielded better recovery and contrast in comparison to those obtained from the often-used uniform distribution-based undersampling. Although 90% of the samples from the original data using the proposed sampling scheme were discarded, the contrast of the CS-recovered image was comparable to that of the reference image. Thus, CS with the proposed Gaussian sampling scheme for channel data subsampling not only reduces the data size significantly, but also strategically uses only a few active receive elements in the process; thus, it can provide an attractive option for the affordable point-of-care ultrasound system.

Compressed Ultrasound Signal Reconstruction Using a Low-Rank and Joint-Sparse Representation Model

With the introduction of very dense sensor arrays in ultrasound (US) imaging, data transfer rate and data storage can become a bottleneck in US system design. To reduce the amount of sampled channel data, we propose a new approach based on the low-rank and joint-sparse model that allows us to exploit the correlations between different US channels and transmissions. With this method, the minimum number of measurements at each channel can be lower than the sparsity in compressive sensing theory. The accuracy of the reconstruction is less dependent on the sparse basis. An optimization algorithm based on the simultaneous direction method of multipliers is proposed to efficiently solve the resulting optimization problem. Results on different data sets with different experimental settings show that the proposed method is better adapted to the US signals and can recover the image with fewer samples (e.g., 10% of the samples) than the existing compressive sensing-based methods, while maintaining reasonable image quality.

Compressed sensing reconstruction of synthetic transmit aperture dataset for volumetric diverging wave imaging

A high volume rate and high performance ultrasound imaging method based on a matrix array is proposed by using compressed sensing (CS) to reconstruct the complete dataset of synthetic transmit aperture (STA) from three-dimensional (3D) diverging wave transmissions (i.e. 3D CS-STA). Hereto, a series of apodized 3D diverging waves are transmitted from a fixed virtual source, with the ith row of a Hadamard matrix taken as the apodization coefficients in the ith transmit event. Then CS is used to reconstruct the complete dataset, based on the linear relationship between the backscattered echoes and the complete dataset of 3D STA. Finally, standard STA beamforming is applied on the reconstructed complete dataset to obtain the volumetric image. Four layouts of element numbering for apodizations and transmit numbers of 16, 32 and 64 are investigated through computer simulations and phantom experiments. Furthermore, the proposed 3D CS-STA setups are compared with 3D single-line-transmit (SLT) and 3D diverging wave compounding (DWC). The results show that, (i) 3D CS-STA has competitive lateral resolutions to 3D STA, and their contrast ratios (CRs) and contrast-to-noise ratios (CNRs) approach to those of 3D STA as the number of transmit events increases in noise-free condition. (ii) the tested 3D CS-STA setups show good robustness in complete dataset reconstruction in the presence of different levels of noise. (iii) 3D CS-STA outperforms 3D SLT and 3D DWC. More specifically, the 3D CS-STA setup with 64 transmit events and the Random layout achieves ~31% improvement in lateral resolution, ~14% improvement in ratio of the estimated-to-true cystic areas, a higher volume rate, and competitive CR/CNR when compared with 3D DWC. The results demonstrate that 3D CS-STA has great potential of providing high quality volumetric image with a higher volume rate.

Convergence Gain in Compressive Deconvolution: Application to Medical Ultrasound Imaging

The compressive deconvolution (CD) problem represents a class of efficient models that is appealing in high-resolution ultrasound image reconstruction. In this paper, we focus on designing an improved CD method based on the framework of a strictly contractive Peaceman–Rechford splitting method (sc-PRSM). By fully excavating the special structure of ultrasound image reconstruction, the improved CD method is easier to implement by partially linearizing the quadratic term of subproblems in the CD problem. The resulting subproblems can obtain closed-form solutions. The convergence of the improved CD method with partial linearization is guaranteed by employing a customized relaxation factor. We establish the global convergence for the new method. The performance of the method is verified via several experiments implemented in realistic synthetic data and in vivo ultrasound images.

Fourier-Domain Beamforming and Structure-Based Reconstruction for Plane-Wave Imaging

Ultrafast imaging based on coherent plane-wave compounding is one of the most important recent developments in medical ultrasound. It significantly improves the image quality and allows for much faster image acquisition. This technique, however, requires large computational load motivating methods for sampling and processing rate reduction. In this work, we extend the recently proposed frequency-domain beamforming (FDBF) framework to plane-wave imaging. Beamforming in frequency yields the same image quality while using fewer samples. It achieves at least fourfold sampling and processing rate reduction by avoiding oversampling required by standard processing. To further reduce the rate, we exploit the structure of the beamformed signal and use compressed sensing methods to recover the beamformed signal from its partial frequency data obtained at a sub-Nyquist rate. Our approach obtains tenfold rate reduction compared with standard time-domain processing. We verify performance in terms of spatial resolution and contrast based on the scans of a tissue mimicking the phantom obtained by a commercial Aixplorer system. In addition, in vivo carotid and thyroid scans processed using standard beamforming and FDBF are presented for qualitative evaluation and visual comparison. Finally, we demonstrate the use of FDBF for shear-wave elastography by generating velocity maps from the beamformed data processed at sub-Nyquist rates.

High-Volume-Rate 3-D Ultrasound Imaging Based on Synthetic Aperture Sequential Beamforming With Chirp-Coded Excitation

Three-dimensional (3-D) ultrasound imaging is a promising modality for many medical applications. Unfortunately, it generates voluminous data in the front end, making it unattractive for high-volume-rate portable medical applications. We apply synthetic aperture sequential beamforming (SASB) to greatly compress the front-end receive data. Baseline 3-D SASB has a low volume rate, because subapertures fire one by one. In this paper, we propose to increase the volume rate of 3-D SASB without degrading imaging quality through: 1) transmitting and receiving simultaneously with four subapertures and 2) using linear chirps as the excitation waveform to reduce interference. We design four linear chirps that operate on two overlapped frequency bands with chirp pairs in each band having opposite chirp rates. Direct implementation of this firing scheme results in grating lobes. Therefore, we design a sparse array that mitigates the grating lobe levels through optimizing the locations of transducer elements in the bin-based random array. Compared with the baseline 3-D SASB, the proposed method increases the volume rate from 8.56 to 34.2 volumes/s without increasing the front-end computation requirement. Field-II-based cyst simulations show that the proposed method achieves imaging quality comparable with baseline 3-D SASB in both shallow and deep regions.

Compressed Sensing Based Synthetic Transmit Aperture for Phased Array Using Hadamard Encoded Diverging Wave Transmissions

Previously, we proposed compressed sensing based synthetic transmit aperture (CS-STA) to improve the contrast and frame rate of STA while maintaining its spatial resolution in linear array by choosing uniform random matrix as the measurement matrix and transmitting the plane waves (PWs). In this paper, to extend CS-STA for phased array imaging and further improve its performance, we design four types of CS-STA implementations with different combinations of measurement matrices (i.e., uniform random and Hadamard matrices) and transmitted waves [i.e., PW and diverging wave (DW)]. Through simulations and phantom experiments with a 3 MHz, 64-element phased array, we find that type-IV CS-STA with the combination of a Hadamard matrix and DW outperforms the other three implementations including the previously proposed type-I CS-STA in terms of image quality and reconstruction time. Specifically, PW transmission produces visible discontinuity and the reconstruction time with uniform random matrix is about 100-fold longer than that with the Hadamard matrix. Compared with STA, with eightfold higher frame rate, type-IV CS-STA achieves 8.2 and 12.3 dB higher contrast-to-noise ratio and signal-to-noise ratio in the simulations, respectively. These improvements are slightly lower in the phantom experiments, which are 6.2 and 6.6 dB, respectively. In addition, CS-STA does not deteriorate the spatial resolution of STA, with the maximum deterioration being smaller than 1/8 wavelength. These results demonstrate that type-IV CS-STA can achieve phased array imaging with high image quality at high frame rate and may be beneficial to cardiac imaging.

Ultrasonic Phased Array Compressive Imaging in Time and Frequency Domain: Simulation, Experimental Verification and Real Application

Embracing the fact that one can recover certain signals and images from far fewer measurements than traditional methods use, compressive sensing (CS) provides solutions to huge amounts of data collection in phased array-based material characterization. This article describes how a CS framework can be utilized to effectively compress ultrasonic phased array images in time and frequency domains. By projecting the image onto its Discrete Cosine transform domain, a novel scheme was implemented to verify the potentiality of CS for data reduction, as well as to explore its reconstruction accuracy. The results from CIVA simulations indicate that both time and frequency domain CS can accurately reconstruct array images using samples less than the minimum requirements of the Nyquist theorem. For experimental verification of three types of artificial flaws, although a considerable data reduction can be achieved with defects clearly preserved, it is currently impossible to break Nyquist limitation in the time domain. Fortunately, qualified recovery in the frequency domain makes it happen, meaning a real breakthrough for phased array image reconstruction. As a case study, the proposed CS procedure is applied to the inspection of an engine cylinder cavity containing different pit defects and the results show that orthogonal matching pursuit (OMP)-based CS guarantees the performance for real application.

Ultrasound Imaging From Sparse RF Samples Using System Point Spread Functions

Upcoming phased-array 2-D sensors will soon enable fast high-definition 3-D ultrasound imaging. Currently, the communication of raw radio-frequency (RF) channel data from the probe to the computer for digital beamforming is a bottleneck. For reducing the amount of transferred data samples, this paper investigates the design of an adapted sparse sampling technique for image reconstruction inspired by the compressed sensing framework. Echo responses from isolated points are generated using a physically based simulation of ultrasound wave propagation through tissues. These point spread functions form a dictionary of shift-variant bent waves, which depend on the specific sound excitation and acquisition protocols. Speckled ultrasound images can be approximately decomposed in this dictionary where sparsity is enforced at the system matrix design. The Moore-Penrose pseudoinverse is precomputed and used at the reconstruction stage for fast minimum-norm recovery from nonuniform pseudorandom sampled raw RF data. Results on simulated and acquired phantoms demonstrate the benefits of an optimized basis function design for high-quality B-mode image recovery from few RF channel data samples.

Compressed Sensing Based Synthetic Transmit Aperture Imaging: Validation in a Convex Array Configuration

According to the linear acoustic theory, the channel data of a plane wave emitted by a linear array is a linear combination of the full data set of synthetic transmit aperture (STA). Combining this relationship with compressed sensing (CS), a novel CS based ultrasound beamforming strategy, named compressed sensing based synthetic transmit aperture (CS-STA), was previously proposed to increase the frame rate of ultrasound imaging without sacrificing the image quality for a linear array. In this paper, assuming linear transfer function of a pulse-echo ultrasound system, we derived and applied the theory of CS-STA for a slightly curved array and validated CS-STA in a convex array configuration. Computer simulations demonstrated that, in the convex array configuration, the normalized root-mean-square error between the beamformed radio-frequency data of CS-STA and STA was smaller than 1% while CS-STA achieved four-fold higher frame rate than STA. In addition, CS-STA was capable of achieving good image quality at depths over 100 mm. It was validated in phantom experiments by comparing CS-STA with STA, multielement synthetic transmit aperture (ME-STA), and the conventional focused method (focal depth = 110 mm). The experimental results showed that STA and CS-STA performed better than ME-STA and the focused method at small depths. At the depth of 110 mm, CS-STA, ME-STA, and the focused methods improved the contrast and contrast-to-noise ratio of STA. The improvements in CS-STA are higher than those in ME-STA but lower than those in the focused mode. These results can also be observed qualitatively in the in vivo experiments on the liver of a healthy male volunteer. The CS-STA method is thus proved to increase the frame rate and achieve high image quality at full depth in the convex array configuration.

Ultrafast Ultrasound Imaging as an Inverse Problem: Matrix-Free Sparse Image Reconstruction

Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution to the image reconstruction problem. An alternative to DAS consists in using iterative techniques, which require both an accurate measurement model and a strong prior on the image under scrutiny. Toward this goal, much effort has been deployed in formulating models for US imaging, which usually require a large amount of memory to store the matrix coefficients. We present two different techniques, which take advantage of fast and matrix-free formulations derived for the measurement model and its adjoint, and rely on sparsity of US images in well-chosen models. Sparse regularization is used for enhanced image reconstruction. Compressed beamforming exploits the compressed sensing framework to restore high-quality images from fewer raw data than state-of-the-art approaches. Using simulated data and in vivo experimental acquisitions, we show that the proposed approach is three orders of magnitude faster than non-DAS state-of-the-art methods, with comparable or better image quality.

Ultrafast Ultrasound Imaging Using Combined Transmissions With Cross-Coherence-Based Reconstruction

Plane-wave-based ultrafast imaging has become the prevalent technique for non-conventional ultrasound imaging. The image quality, especially in terms of the suppression of artifacts, is generally compromised by reducing the number of transmissions for a higher frame rate. We hereby propose a new ultrafast imaging framework that reduces not only the side lobe artifacts but also the axial lobe artifacts using combined transmissions with a new coherence-based factor. The results from simulations, in vitro wire phantoms, the ex vivo porcine artery, and the in vivo porcine heart show that our proposed methodology greatly reduced the axial lobe artifact by 25±5 dB compared with coherent plane-wave compounding (CPWC), which was considered as the ultrafast imaging standard, and suppressed side lobe artifacts by 15 ± 5 dB compared with CPWC and coherent spherical-wave compounding. The reduction of artifacts in our proposed ultrafast imaging framework led to a better boundary delineation of soft tissues than CPWC.

A Compressed Sensing Strategy for Synthetic Transmit Aperture Ultrasound Imaging

A novel beamforming technique, named compressed sensing based synthetic transmit aperture (CS-STA) is proposed to speed up the acquisition of ultrasound imaging. This technique consists of three steps. First, the ultrasound transducer transmits randomly apodized plane waves for a number of times and receives the backscattered echoes. Second, the recorded backscattered echoes are used to recover the full channel dataset of synthetic transmit aperture (STA) with a compressed sensing (CS) reconstruction algorithm. Finally, an STA image is beamformed from the recovered full STA dataset. As CS allows recovering a signal from its few linear measurements with high probability, CS-STA is capable of recovering the STA image with fewer firings (i.e., higher frame rate) and retaining the high resolution of STA. In addition, the contrast of the STA image can be improved at the same time owing to the higher energy of plane wave firing in CS-STA. Simulations demonstrate that CS-STA is capable of recovering the STA channel dataset with a smaller number of firings. The performance of CS-STA is evaluated in phantom experiments through comparisons with STA, multi-element STA, conventional focused mode and coherent plane wave imaging. The results demonstrate that, implemented with the same frame rate, CS-STA achieves higher or comparable resolution and contrast. Moreover, comparisons are conducted on the biceps brachii muscle and thyroid of a human subject, and the results demonstrate the feasibility and competitiveness of CS-STA in the in vivo conditions.

Compressed Sensing Techniques Applied to Ultrasonic Imaging of Cargo Containers

One of the key issues in the fight against the smuggling of goods has been the development of scanners for cargo inspection. X-ray-based radiographic system scanners are the most developed sensing modality. However, they are costly and use bulky sources that emit hazardous, ionizing radiation. Aiming to improve the probability of threat detection, an ultrasonic-based technique, capable of detecting the footprint of metallic containers or compartments concealed within the metallic structure of the inspected cargo, has been proposed. The system consists of an array of acoustic transceivers that is attached to the metallic structure-under-inspection, creating a guided acoustic Lamb wave. Reflections due to discontinuities are detected in the images, provided by an imaging algorithm. Taking into consideration that the majority of those images are sparse, this contribution analyzes the application of Compressed Sensing (CS) techniques in order to reduce the amount of measurements needed, thus achieving faster scanning, without compromising the detection capabilities of the system. A parametric study of the image quality, as a function of the samples needed in spatial and frequency domains, is presented, as well as the dependence on the sampling pattern. For this purpose, realistic cargo inspection scenarios have been simulated.

A Sparse Reconstruction Framework for Fourier-Based Plane-Wave Imaging

Ultrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared with traditional delay and sum methods. Motivated by the success of compressed sensing techniques in other Fourier imaging modalities, like magnetic resonance imaging, we propose a new sparse regularization framework to reconstruct highquality ultrasound (US) images. The framework takes advantage of both the ability to formulate the imaging inverse problem in the Fourier domain and the sparsity of US images in a sparsifying domain. We show, by means of simulations, in vitro and in vivo data, that the proposed framework significantly reduces image artifacts, i.e., measurement noise and sidelobes, compared with classical methods, leading to an increase of the image quality.

Reconstruction of Enhanced Ultrasound Images From Compressed Measurements Using Simultaneous Direction Method of Multipliers

High-resolution ultrasound (US) image reconstruction from a reduced number of measurements is of great interest in US imaging, since it could enhance both frame rate and image resolution. Compressive deconvolution (CD), combining compressed sensing and image deconvolution, represents an interesting possibility to consider this challenging task. The model of CD includes, in addition to the compressive sampling matrix, a 2-D convolution operator carrying the information on the system point spread function. Through this model, the resolution of reconstructed US images from compressed measurements mainly depends on three aspects: the acquisition setup, i.e., the incoherence of the sampling matrix, the image regularization, i.e., the sparsity prior, and the optimization technique. In this paper, we mainly focused on the last two aspects. We proposed a novel simultaneous direction method of multipliers based optimization scheme to invert the linear model, including two regularization terms expressing the sparsity of the RF images in a given basis and the generalized Gaussian statistical assumption on tissue reflectivity functions. The performance of the method is evaluated on both simulated and in vivo data.

Sub-Nyquist Sampling and Fourier Domain Beamforming in Volumetric Ultrasound Imaging

A key step in ultrasound image formation is digital beamforming of signals sampled by several transducer elements placed upon an array. High-resolution digital beamforming introduces the demand for sampling rates significantly higher than the signals' Nyquist rate, which greatly increases the volume of data that must be transmitted from the system's front end. In 3-D ultrasound imaging, 2-D transducer arrays rather than 1-D arrays are used, and more scan lines are needed. This implies that the amount of sampled data is vastly increased with respect to 2-D imaging. In this work, we show that a considerable reduction in data rate can be achieved by applying the ideas of Xampling and frequency domain beamforming (FDBF), leading to a sub-Nyquist sampling rate, which uses only a portion of the bandwidth of the ultrasound signals to reconstruct the image. We extend previous work on FDBF for 2-D ultrasound imaging to accommodate the geometry imposed by volumetric scanning and a 2-D grid of transducer elements. High image quality from low-rate samples is demonstrated by simulation of a phantom image composed of several small reflectors. Our technique is then applied to raw data of a heart ventricle phantom obtained by a commercial 3-D ultrasound system. We show that by performing 3-D beamforming in the frequency domain, sub-Nyquist sampling and low processing rate are achievable, while maintaining adequate image quality.

Compressed Sensing Doppler Ultrasound Reconstruction Using Block Sparse Bayesian Learning

In this paper we propose a framework for using duplex Doppler ultrasound systems. These type of systems need to interleave the acquisition and display of a B-mode image and of the pulsed Doppler spectrogram. In a recent study (Richy , 2013), we have shown that compressed sensing-based reconstruction of Doppler signal allowed reducing the number of Doppler emissions and yielded better results than traditional interpolation and at least equivalent or even better depending on the configuration than the study estimating the signal from sparse data sets given in Jensen, 2006. We propose here to improve over this study by using a novel framework for randomly interleaving Doppler and US emissions. The proposed method reconstructs the Doppler signal segment by segment using a block sparse Bayesian learning (BSBL) algorithm based CS reconstruction. The interest of using such framework in the context of duplex Doppler is linked to the unique ability of BSBL to exploit block-correlated signals and to recover non-sparse signals. The performance of the technique is evaluated from simulated data as well as experimental in vivo data and compared to the recent results in Richy , 2013.

Compressive Deconvolution in Medical Ultrasound Imaging

The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small number of measurements and/or using a reduced number of ultrasound pulse emissions. Nevertheless, RF image spatial resolution, contrast and signal to noise ratio are affected by the limited bandwidth of the imaging transducer and the physical phenomenon related to US wave propagation. To overcome these limitations, several deconvolution-based image processing techniques have been proposed to enhance the ultrasound images. In this paper, we propose a novel framework, named compressive deconvolution, that reconstructs enhanced RF images from compressed measurements. Exploiting an unified formulation of the direct acquisition model, combining random projections and 2D convolution with a spatially invariant point spread function, the benefit of our approach is the joint data volume reduction and image quality improvement. The proposed optimization method, based on the Alternating Direction Method of Multipliers, is evaluated on both simulated and in vivo data.