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

Enhancing single-element compressive ultrasound imaging through novel random aperture masking and data mixing strategy

As ultrasound techniques continue to evolve, the integration of compressed sensing technology has emerged as a pivotal advancement, offering a transformative impact on the landscape of ultrasound imaging. A key attribute of compressed sensing lies in its ability to facilitate a substantial reduction in both machinery size and power consumption. This technological synergy not only addresses crucial practical considerations in the design of ultrasound systems but also opens avenues for enhanced portability and energy efficiency. This study develops a model and introduces an aperture mask with a mixing scheme for compressive ultrasound imaging employing a single transducer, aiming to minimize the loss of information and scrutinize the variables influencing image quality while facilitating computationally efficient system simulation. A detailed procedural guide is presented for generating synthetic data, accompanied by qualitative and quantitative analyses using several sparse recovery methods under different experimental conditions. This study's analysis reveals that the proposed strategy achieves improved metrics, offering advantages for sparse recovery. Specifically, the finite element results demonstrate approximately a 10% improvement in the condition number of the measurement matrix, reflecting enhanced numerical stability.

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.

Deep-Learning Based Adaptive Ultrasound Imaging From Sub-Nyquist Channel Data

Traditional beamforming of medical ultrasound images relies on sampling rates significantly higher than the actual Nyquist rate of the received signals. This results in large amounts of data to store and process, imposing hardware and software challenges on the development of ultrasound machinery and algorithms, and impacting the resulting performance. In light of the capabilities demonstrated by deep learning methods over the past years across a variety of fields, including medical imaging, it is natural to consider their ability to recover high-quality ultrasound images from partial data. Here, we propose an approach for deep-learning-based reconstruction of B-mode images from temporally and spatially sub-sampled channel data. We begin by considering sub-Nyquist sampled data, time-aligned in the frequency domain and transformed back to the time domain. The data are further sampled spatially so that only a subset of the received signals is acquired. The partial data is used to train an encoder-decoder convolutional neural network (CNN), using as targets minimum-variance (MV) beamformed signals that were generated from the original, fully-sampled data. Our approach yields high-quality B-mode images, with up to two times higher resolution than previously proposed reconstruction approaches (NESTA) from compressed data as well as delay-and-sum (DAS) beamforming of the fully-sampled data. In terms of contrast-to- noise ratio (CNR), our results are comparable to MV beamforming of the fully-sampled data, and provide up to 2 dB higher CNR values than DAS and NESTA, thus enabling better and more efficient imaging than what is used in clinical practice today.

Slant-Stack Migration Applied to Plane-Wave Ultrasound Imaging

Ultrafast plane-wave ultrasound imaging replaces numerous focused-beam transmissions with a single emitted plane-wave pulse, insonifying the entire subsurface region of interest all at once. To improve image quality, one can employ coherent plane wave compounding (CPWC), whereby several pulses are emitted sequentially at different steering angles, and their corresponding acquired raw data frames are individually beamformed and then combined to form a final reconstructed image frame. We describe a classic geophysical reconstruction technique called slant-stack migration, adapted here to CPWC imaging. Our evaluation results, based on two public-domain datasets featuring both anechoic and hyperechoic targets, demonstrate that the presented approach compares favorably with conventional delay-and-sum beamforming.

Coherent Plane Wave Compounding Combined With Tensor Completion Applied for Ultrafast Imaging

To solve the problem of resolution and contrast in plane wave imaging (PWI), coherent plane wave compounding (CPWC) was introduced, in which scanning was performed at different angles, which can achieve the desired image quality by combining the images obtained from PWI at different angles. However, the application of this idea reduces the frame rate in proportion to the number of plane waves (PWs) or angles, so that in this modality, when dealing with some applications such as shear wave imaging (SWI) and strain imaging, there is always a compromise between the frame rate and the image quality. Tensor completion (TC) is a powerful technique to recover missing information of a low-rank tensor from limited observations based on rank minimization. In this article, we present an idea based on TC to make this compromise lighter; in other words, with a smaller number of angles, we can achieve the desired quality of the output image. To evaluate the proposed idea, plane wave imaging challenge in medical ultrasound (PICMUS) datasets was used, which were recorded at 75 different angles. The results of the resolution evaluation showed that using 20% of the coherent PWs and reconstructing other 80% by TC, compared with the situation of using only 20% of the coherent PWs provided a resolution improvement of 14.97% and 17.4% in the simulated and experimental point targets, respectively. Also, the results of the contrast investigation showed that the contrast ratio (CR) improved by 72.6%, 62.9%, and 111.4% in the simulated cyst target data, experimental cyst targets, and in vivo carotid cross section, respectively. The results confirmed that using 20% of the coherent PWs and reconstructing other 80% by TC, the image quality is very close to that obtained by considering all 75 angles, so that the difference in resolution is less than 2% and the difference in contrast to noise ratio (CNR) is less than 5 dB. Therefore, with this idea, it can be said that less compromise is needed; in other words, despite having a higher frame rate, an acceptable quality can be achieved.

Plane-Wave Ultrasound Beamforming Through Independent Component Analysis

BACKGROUND AND OBJECTIVE

Beamforming in coherent plane-wave compounding (CPWC) is an essential step in maintaining high resolution, contrast and framerate. Adaptive methods have been designed to achieve this goal by estimating the apodization weights from echo traces acquired by several transducer elements.

METHODS

Herein, we formulate plane-wave beamforming as a blind source separation problem, where the output of each transducer element is considered as a non-independent observation of the field. As such, beamforming can be formulated as the estimation of an independent component out of the observations. We then adapt the independent component analysis (ICA) algorithm to solve this problem and reconstruct the final image.

RESULTS

The proposed method is evaluated on a set of simulations, real phantom, and in vivo data available from the plane-wave imaging challenge in medical ultrasound. Moreover, the results are compared with other well-known adaptive methods.

CONCLUSIONS

Results demonstrate that the proposed method simultaneously improves the resolution and contrast.

Ultrasound image reconstruction from plane wave radio-frequency data by self-supervised deep neural network

Image reconstruction from radio-frequency (RF) data is crucial for ultrafast plane wave ultrasound (PWUS) imaging. Compared with the traditional delay-and-sum (DAS) method based on relatively imprecise assumptions, sparse regularization (SR) method directly solves the inverse problem of image reconstruction and has presented significant improvement in the image quality when the frame rate remains high. However, the computational complexity of SR is too high for practical implementation, which is inherently associated with its iterative process. In this work, a deep neural network (DNN), which is trained with an incorporated loss function including sparse regularization terms, is proposed to reconstruct PWUS images from RF data with significantly reduced computational time. It is remarkable that, a self-supervised learning scheme, in which the RF data are utilized as both the inputs and the labels during the training process, is employed to overcome the lack of the "ideal" ultrasound images as the labels for DNN. In addition, it has been also verified that the trained network can be used on the RF data obtained with steered plane waves (PWs), and thus the image quality can be further improved with coherent compounding. Using simulation data, the proposed method has significantly shorter reconstruction time (∼10 ms) than the conventional SR method (∼1-5 mins), with comparable spatial resolution and 1.5-dB higher contrast-to-noise ratio (CNR). Besides, the proposed method with single PW can achieve higher CNR than DAS with 75 PWs in reconstruction of in-vivo images of human carotid arteries.

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.

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.

Point Spread Function Formation in Plane-Wave Imaging: A Theoretical Approximation in Fourier Migration

The point spread function (PSF) is often analyzed to determine the image quality of an ultrasound system. The formation of PSF is determined by practical factors, such as transducer aperture, element directivity, apodization, pitch, imaging position, and steering angle. Conventional numerical simulations provide an iterative approach to examine those factors' effects but cannot explain the inherent mechanism of PSF formation. This article presents a theoretical approximation of PSF formation for plane-wave imaging throughout the Fourier-based reconstruction process. Aforementioned factors are incorporated in the theory. The proposed theory is used to analyze the effects of those factors and presents a high degree of consistency with numerical simulations and experiments.

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.

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.

Fourier Domain Depth Migration for Plane-Wave Ultrasound Imaging

Plane-wave (PW) ultrasound imaging allows for ultrafast image acquisition rates, thus enabling new biomedical applications, such as ultrasound-based blood flow and tissue motion characterization. We propose two novel Fourier domain techniques for PW ultrasound image reconstruction that can be used as an alternative to conventional delay-and-sum beamforming. In particular, we show how to modify two classic algorithms used for geophysical data processing (namely, Stolt's and slant-stack depth migration under zero-offset constant-velocity assumptions), so that their new versions can be used for PW ultrasound data processing. To demonstrate the merits and limitations of our approach, we provide qualitative and quantitative comparisons with other Fourier domain methods reported in the ultrasound literature. Our evaluation results are based on the image resolution, contrast, and similarity metrics obtained for several public-domain experimental benchmark data sets.

Ultrasonic Wave-Speed Diffraction Tomography With Undersampled Data Using Virtual Transducers

Ultrasonic diffraction tomography offers a way to achieve high-resolution imaging of the wave-speed map, and hence, has strong potential applications in medical diagnosis and nondestructive evaluation. Ideal images can be obtained with a complete array of sensors surrounding the scatterer, provided that the measurement data are fully sampled in space, obeying the Nyquist criterion. Spatial undersampling causes the image to be distorted and introduce unwanted circular artifacts. In this paper, we propose an iteration approach using virtual transducers to achieve high-resolution tomographic imaging with undersampled measurements. At each iteration stage, the extent constraint estimated from the shape of the object of interest is applied on the image space to obtain a regularized image, based on which the ultrasonic measurement data at virtual transducers are calculated using a forward model. The full data set composed of original and virtual measurements is then used for tomography in the next stage. A final image with sufficiently high resolution is obtained only after a few iterations. The new imaging method yields improvements in the robustness and accuracy of ultrasonic tomography with undersampled data. We present numerical results using complicated wave-speed maps from realistic corrosion profiles. In addition, an experiment using guided ultrasonic waves is performed to further evaluate the imaging method.

Phase-Shift Depth Migration for Plane-Wave Ultrasound Imaging

Plane-wave ultrasound imaging is an important modality that enables very high frame rates, which is necessary for adequate characterization of blood flow and tissue motion properties. This work describes a novel Fourier-domain method for plane-wave ultrasound image reconstruction that can be used in situations where the speed of sound varies with depth in a layered propagation medium. Our approach is based on geophysical phase-shift migration technique that has been modified to handle plane-wave ultrasound data processing. Our simulation results show that the proposed method is capable of accurately imaging point targets in a three-layer medium, mimicking tissue-bone-tissue ultrasound propagation.

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.

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.

Uncertainty quantification and sensitivity analysis of an arterial wall mechanics model for evaluation of vascular drug therapies

Quantification of the uncertainty in constitutive model predictions describing arterial wall mechanics is vital towards non-invasive assessment of vascular drug therapies. Therefore, we perform uncertainty quantification to determine uncertainty in mechanical characteristics describing the vessel wall response upon loading. Furthermore, a global variance-based sensitivity analysis is performed to pinpoint measurements that are most rewarding to be measured more precisely. We used previously published carotid diameter–pressure and intima–media thickness (IMT) data (measured in triplicate), and Holzapfel–Gasser–Ogden models. A virtual data set containing 5000 diastolic and systolic diameter–pressure points, and IMT values was generated by adding measurement error to the average of the measured data. The model was fitted to single-exponential curves calculated from the data, obtaining distributions of constitutive parameters and constituent load bearing parameters. Additionally, we (1) simulated vascular drug treatment to assess the relevance of model uncertainty and (2) evaluated how increasing the number of measurement repetitions influences model uncertainty. We found substantial uncertainty in constitutive parameters. Simulating vascular drug treatment predicted a 6% point reduction in collagen load bearing (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_\mathrm {coll}$$\end{document}Lcoll), approximately 50% of its uncertainty. Sensitivity analysis indicated that the uncertainty in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll was primarily caused by noise in distension and IMT measurements. Spread in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll could be decreased by 50% when increasing the number of measurement repetitions from 3 to 10. Model uncertainty, notably that in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\mathrm {coll}}$$\end{document}Lcoll, could conceal effects of vascular drug therapy. However, this uncertainty could be reduced by increasing the number of measurement repetitions of distension and wall thickness measurements used for model parameterisation.