Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging

Deconvolution based on sparsity and continuity improves the quality of ultrasound image

The application of ultrasound (US) image has been limited by its limited resolution, inherent speckle noise, and the impact of clutter and artifacts, especially in the miniaturized devices with restricted hardware conditions. In order to solve these problems, many researchers have explored a number of hardware modifications as well as algorithmic improvements, but further improvements in resolution, signal-to-noise ratio (SNR) and contrast are still needed. In this paper, a deconvolution algorithm based on sparsity and continuity (DBSC) is proposed to obtain the higher resolution, SNR, and, contrast. The algorithm begins with a relatively bold Wiener filtering for initial enhancement of image resolution in preprocessing, but it also introduces ringing noise and compromises the SNR. In further processing, the noise is suppressed based on the characteristic that the adjacent pixels of the US image are continuous as long as Nyquist sampling criterion is met, and the extraction of high-frequency information is balanced by using relatively sparse. Subsequently, the theory and experiments demonstrate that relative sparsity and continuity are general properties of US images. DBSC is compared with other deconvolution strategies through simulations and experiments, and US imaging under different transmission channels is also investigated. The final results show that the proposed method can greatly improve the resolution, as well as provide significant advantages in terms of contrast and SNR, and is also feasible in applications to devices with limited hardware.

A multiscale residual U-net architecture for super-resolution ultrasonic phased array imaging from full matrix capture data

Ultrasonic phased array imaging using full-matrix capture (FMC) has raised great interest among various communities, including the nondestructive testing community, as it makes full use of the echo space to provide preferable visualization performance of inhomogeneities. The conventional way of FMC data postprocessing for imaging is through beamforming approaches, such as delay-and-sum, which suffers from limited imaging resolution and contrast-to-noise ratio. To tackle these difficulties, we propose a deep learning (DL)-based image forming approach, termed FMC-Net, to reconstruct high-quality ultrasonic images directly from FMC data. Benefitting from the remarkable capability of DL to approximate nonlinear mapping, the developed FMC-Net automatically models the underlying nonlinear wave-matter interactions; thus, it is trained end-to-end to link the FMC data to the spatial distribution of the acoustic scattering coefficient of the inspected object. Specifically, the FMC-Net is an encoder-decoder architecture composed of multiscale residual modules that make local perception at different scales for the transmitter-receiver pair combinations in the FMC data. We numerically and experimentally compared the DL imaging results to the total focusing method and wavenumber algorithm and demonstrated that the proposed FMC-Net remarkably outperforms conventional methods in terms of exceeding resolution limit and visualizing subwavelength defects. It is expected that the proposed DL approach can benefit a variety of ultrasonic array imaging applications.

Ultrasound Signal Processing: From Models to Deep Learning

Medical ultrasound imaging relies heavily on high-quality signal processing to provide reliable and interpretable image reconstructions. Conventionally, reconstruction algorithms have been derived from physical principles. These algorithms rely on assumptions and approximations of the underlying measurement model, limiting image quality in settings where these assumptions break down. Conversely, more sophisticated solutions based on statistical modeling or careful parameter tuning or derived from increased model complexity can be sensitive to different environments. Recently, deep learning-based methods, which are optimized in a data-driven fashion, have gained popularity. These model-agnostic techniques often rely on generic model structures and require vast training data to converge to a robust solution. A relatively new paradigm combines the power of the two: leveraging data-driven deep learning and exploiting domain knowledge. These model-based solutions yield high robustness and require fewer parameters and training data than conventional neural networks. In this work we provide an overview of these techniques from the recent literature and discuss a wide variety of ultrasound applications. We aim to inspire the reader to perform further research in this area and to address the opportunities within the field of ultrasound signal processing. We conclude with a future perspective on model-based deep learning techniques for medical ultrasound.

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.

Dual projection generalized sidelobe canceller based on mixed signal subspace for ultrasound imaging

In this paper, we propose a dual projection generalized sidelobe canceller (DPGSC) based on mixed subspace (MS) for ultrasound imaging, which aims to improve the speckle signal-noise-ratio (sSNR) and decrease the dark-region artifacts. A mixed signal subspace based on the correlation between the desired steering vector and the eigenvectors is constructed to further optimize the desired steering vector and the final weight vector. The simulated and experimental results show that the proposed method can greatly improve the speckle uniformity. In the geabr_0 experiment, the standard deviation of background and sSNR of MS-DPGSC can be improved by 48.07% and 58.49% more than those of eigenspace-based generalized sidelobe canceller (ESGSC). Furthermore, for a hyperechoic target, the maximal improvement of contrast ratio is 95.29%. In terms of anechoic cyst, the contrast-to-noise ratio of MS-DPGSC is increased by 123.08% than that of ESGSC. The rat mammary tumor experimental data show that the proposed method has better comprehensive imaging effect than traditional generalized sidelobe cancellers and ESGSCs.

A Novel Task-Based reconstruction approach for digital breast tomosynthesis

The reconstruction of a volumetric image from Digital Breast Tomosynthesis (DBT) measurements is an ill-posed inverse problem, for which existing iterative regularized approaches can provide a good solution. However, the clinical task is somehow omitted in the derivation of those techniques, although it plays a primary role in the radiologist diagnosis. In this work, we address this issue by introducing a novel variational formulation for DBT reconstruction, tailored for a specific clinical task, namely the detection of microcalcifications. Our method aims at simultaneously enhancing the detectability performance and enabling a high-quality restoration of the background breast tissues. Our contribution is threefold. First, we introduce an original task-based reconstruction framework through the proposition of a detectability function inspired from mathematical model observers. Second, we propose a novel total-variation regularizer where the gradient field accounts for the different morphological contents of the imaged breast. Third, we integrate the two developed measures into a cost function, minimized thanks to a new form of the Majorize Minimize Memory Gradient (3MG) algorithm. We conduct a numerical comparison of the convergence speed of the proposed method with those of standard convex optimization algorithms. Experimental results show the interest of our DBT reconstruction approach, qualitatively and quantitatively.

Deep Unfolded Recovery of Sub-Nyquist Sampled Ultrasound Images

The most common technique for generating B-mode ultrasound (US) images is delay-and-sum (DAS) beamforming, where the signals received at the transducer array are sampled before an appropriate delay is applied. This necessitates sampling rates exceeding the Nyquist rate and the use of a large number of antenna elements to ensure sufficient image quality. Recently, we proposed methods to reduce the sampling rate and the array size relying on image recovery using iterative algorithms based on compressed sensing (CS) and the finite rate of innovation (FRI) frameworks. Iterative algorithms typically require a large number of iterations, making them difficult to use in real time. In this article, we propose a reconstruction method from sub-Nyquist samples in the time and spatial domain, which is based on unfolding the iterative shrinkage thresholding algorithm (ISTA), resulting in an efficient and interpretable deep network. The inputs to our network are the subsampled beamformed signals after summation and delay in the frequency domain, requiring only a subset of the US signal to be stored for recovery. Our method allows reducing the number of array elements, sampling rate, and computational time while ensuring high-quality imaging performance. Using in vivo data, we demonstrate that the proposed method yields high-quality images while reducing the data volume traditionally used up to 36 times. In terms of image resolution and contrast, our technique outperforms previously suggested methods as well as DAS and minimum-variance (MV) beamforming, paving the way to real-time applicable recovery methods.

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.

Joint Generalized Coherence Factor and Minimum Variance Beamformer for Synthetic Aperture Ultrasound Imaging

The delay-and-sum (DAS) beamformer is the most commonly used method in medical ultrasound imaging. Compared with the DAS beamformer, the minimum variance (MV) beamformer has an excellent ability to improve lateral resolution by minimizing the output of interference and noise power. However, it is hard to overcome the tradeoff between satisfactory lateral resolution and speckle preservation performance due to the fixed subarray length of covariance matrix estimation. In this study, a new approach for MV beamforming with adaptive spatial smoothing is developed to address this problem. In the new approach, the generalized coherence factor (GCF) is used as a local coherence detection tool to adaptively determine the subarray length for spatial smoothing, which is called adaptive spatial-smoothed MV (AMV). Furthermore, another adaptive regional weighting strategy based on the local signal-to-noise ratio (SNR) and GCF is devised for AMV to enhance the image contrast, which is called GCF regional weighted AMV (GAMV). To evaluate the performance of the proposed methods, we compare them with the standard MV by conducting the simulation, in vitro experiment, and the in vivo rat mammary tumor study. The results show that the proposed methods outperform MV in speckle preservation without an appreciable loss in lateral resolution. Moreover, GAMV offers excellent performance in image contrast. In particular, AMV can achieve maximal improvements of speckle signal-to-noise ratio (SNR) by 96.19% (simulation) and 62.82% (in vitro) compared with MV. GAMV achieves improvements of contrast-to-noise ratio by 27.16% (simulation) and 47.47% (in vitro) compared with GCF. Meanwhile, the losses in lateral resolution of AMV are 0.01 mm (simulation) and 0.17 mm (in vitro) compared with MV. Overall, this indicates that the proposed methods can effectively address the inherent limitation of the standard MV in order to improve the image quality.

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.

An Inverse Approach for Ultrasonic Imaging From Full Matrix Capture Data: Application to Resolution Enhancement in NDT

In the context of nondestructive testing (NDT), this article proposes an inverse problem approach for the reconstruction of high-resolution ultrasonic images from full matrix capture (FMC) data sets. We build a linear model that links the FMC data, i.e., the signals collected from all transmitter-receiver pairs of an ultrasonic array, to the discretized reflectivity map of the inspected object. In particular, this model includes the ultrasonic waveform corresponding to the response of transducers. Despite a large amount of data, the inversion problem is ill-posed. Therefore, a regularization strategy is proposed, where the reconstructed image is defined as the minimizer of a penalized least-squares cost function. A mixed penalization function is considered, which simultaneously enhances the sparsity of the image (in NDT, the reflectivity map is mostly zero except at the flaw locations) and its spatial smoothness (flaws may have some spatial extension). The proposed method is shown to outperform two well-known imaging methods: the total focusing method (TFM) and Excitelet. Numerical simulations with two close reflectors show that the proposed method improves the resolution limit defined by the Rayleigh criterion by a factor of four. Such high-resolution imaging capability is confirmed by experimental results obtained with side-drilled holes in an aluminum sample.

A unified deep network for beamforming and speckle reduction in plane wave imaging: A simulation study

Plane Wave Imaging is a fast imaging method used in ultrasound, which allows a high frame rate, but with compromised image quality when a single wave is used. In this work a learning-based approach was used to obtain improved image quality. The entire process of beamforming and speckle reduction was embedded in a single deep convolutional network, and trained with two types of simulated data. The network architecture was designed based on traditional physical considerations of the ultrasonic image formation pipe. As such, it includes beamforming with spatial matched filters, envelope detection, and a speckle reduction stage done in log-signal representation, with all stages containing trainable parameters. The approach was tested on the publicly available PICMUS datasets, achieving axial and lateral full-width-half-maximum (FWHM) resolution values of 0.22 mm and 0.35 mm respectively, and a Contrast to Noise Ratio (CNR) metric of 16.75 on the experimental datasets.

Sparsity-based beamforming to enhance two-dimensional linear-array photoacoustic tomography

In linear-array photoacoustic imaging (PAI), beamforming methods can be used to reconstruct the images. Delay-and-sum (DAS) beamformer is extensively used due to its simple implementation. However, this algorithm results in high level of sidelobes and low resolution. In this paper, it is proposed to form the photoacoustic (PA) images through a regularized inverse problem to address these limitations and improve the image quality. We define a forward/backward problem of the beamforming and solve the inverse problem using a sparse constraint added to the model which forces the sparsity of the output beamformed data. It is shown that the proposed Sparse beamforming (SB) method is robust against noise due to the sparsity nature of the problem. Numerical results show that the SB method improves the signal-to-noise ratio (SNR) for about 98.69 dB, 82.26 dB and 74.73 dB, in average, compared to DAS, delay-multiply-and-sum (DMAS) and double stage-DMAS (DS-DMAS), respectively. Also, quantitative evaluation of the experimental results shows a significant noise reduction using SB algorithm. In particular, the contrast ratio of the wire phantom at the depth of 30 mm is improved about 103.97 dB, 82.16 dB and 65.77 dB compared to DAS, DMAS and DS-DMAS algorithms, respectively, indicating a better performance of the proposed SB in terms of noise reduction.

The Effect of Dynamic Range Alterations in the Estimation of Contrast

Many adaptive beamformers claim to produce images with increased contrast, a feature that could enable a better detection of lesions and anatomical structures. Contrast is often quantified using the contrast ratio (CR) and the contrast-to-noise ratio (CNR). The estimation of CR and CNR can be affected by dynamic range alterations (DRAs), such as those produced by a trivial gray-level transformation. Thus, we can form the hypothesis that contrast improvements from adaptive beamformers can, partly, be due to DRA. In this paper, we confirm this hypothesis. We show evidence on the influence of DRA on the estimation of CR and CNR and on the fact that several methods in the state of the art do alter the DR. To study this phenomenon, we propose a DR test (DRT) to estimate the degree of DRA and we apply it to seven beamforming methods. We show that CR improvements correlate with DRT with [Formula: see text] in simulated data and [Formula: see text] in experiments. We also show that DRA may lead to increased CNR values, under some circumstances. These results suggest that claims on lesion detectability, based on CR and CNR values, should be revised.

Portable ultrasound imaging system with super-resolution capabilities

This paper discusses an ultrasound technique where the echo signals from the array of transducer elements are compressed to as few as two RF channels while still in analog domain, with a much simplified front-end electronics. The method can achieve resolutions well beyond the diffraction limit, which is set by the excitation signal wavelength and numerical aperture of the imaging system. The fundamental principle that underlies this model based imaging technique is the preservation of the spatial frequency information content of the recorded echo signals with the help of pseudo-random apodization function followed by summation. A Verasonics V1 ultrasonic scanner is used to conduct experiments using an anechoic cyst made from gel phantom, immersed in degassed water. The estimated images were compared to those obtained using traditional B-mode delay-and-sum imaging available with the Verasonics V1 ultrasound machine. The estimated images using the proposed imaging technique showed a contrast ratio of 0.96 and Full-Width-Half-Maximum (FWHM) of about half the wavelength at a depth of 9.1 cm and at 1.875 MHz center frequency while the traditional delay and sum images had a contrast ratio of 0.62 and FWHM of about 5.5 wavelengths.

Experimental evaluation of ultrasound higher-order harmonic imaging with Filtered-Delay Multiply And Sum (F-DMAS) non-linear beamforming

Tissue Harmonic Imaging (THI) mode is currently one of the preferred choices by the clinicians for its ability to provide enhanced ultrasound images, thanks to the use of the second harmonic component of backscattered echoes. This paper aims at investigating whether the combination of THI with Filtered-Delay Multiply And Sum (F-DMAS) beamforming can provide further improvements in image quality. F-DMAS is a new non-linear beamformer, which, similarly to THI, is based on the use of the second harmonics of beamformed signals and is known to increase image contrast resolution and noise rejection. Thus, we have first compared the images obtained by using F-DMAS and the standard Delay And Sum (DAS) beamformers when only the second harmonics of the received signals was selected. Moreover, possible improvements brought about by other harmonic components generated by the combined use of the fundamental plus second harmonics and F-DMAS beamforming have been explored. Experimental results demonstrate that, as compared to standard harmonic imaging with DAS, THI and F-DMAS can be joined to improve the -20 dB lateral resolution up to 1 mm, the contrast ratio up to 12 dB on a cyst-phantom and up to 9 dB on in vivo images.

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.

Inverse Problem of Ultrasound Beamforming With Sparsity Constraints and Regularization

Ultrasound (US) beamforming is the process of reconstructing an image from acquired echo traces on several transducer elements. Typical beamforming approaches, such as delay-and-sum, perform simple projection operations, while techniques using statistical information also exist, e.g., adaptive, phase coherence, delay-multiply-and-sum, and sparse coding approaches. Inspired by the feasibility and success of inverse problem (IP) formulations in several image reconstruction problems, such as computed tomography, we herein devise an IP approach for US beamforming. We define a linear forward model for the synthesis of the beamformed image, and solve its IP thanks to several intuitive and physics-based constraints and regularization terms proposed. These reflect the prior knowledge about the spectra of carrier signal and spatial coherence of modulated signal. These constraints admit effective formulation through sparse representations. Our proposed method was evaluated for plane-wave imaging (PWI) that transmits unfocused waves, enabling high frame rates with large field of view at the expense of much lower image quality with conventional beamforming techniques. Results are evaluated in numerical simulations, as well as tissue-mimicking phantoms and in vivo data provided by PWI challenge in medical US. The best results achieved by our proposed techniques are 0.39-mm full-width at half-maximum for spatial resolution and 16.3-dB contrast-to-noise ratio, using a single plane-wave transmit.

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.

Enhanced linear-array photoacoustic beamforming using modified coherence factor

Photoacoustic imaging (PAI) is a promising medical imaging modality providing the spatial resolution of ultrasound imaging and the contrast of optical imaging. For linear-array PAI, a beamformer can be used as the reconstruction algorithm. Delay-and-sum (DAS) is the most prevalent beamforming algorithm in PAI. However, using DAS beamformer leads to low-resolution images as well as high sidelobes due to nondesired contribution of off-axis signals. Coherence factor (CF) is a weighting method in which each pixel of the reconstructed image is weighted, based on the spatial spectrum of the aperture, to mainly improve the contrast. We demonstrate that the numerator of the formula of CF contains a DAS algebra and propose the use of a delay-multiply-and-sum beamformer instead of the available DAS on the numerator. The proposed weighting technique, modified CF (MCF), has been evaluated numerically and experimentally compared to CF. It was shown that MCF leads to lower sidelobes and better detectable targets. The quantitative results of the experiment (using wire targets) show that MCF leads to for about 45% and 40% improvement, in comparison with CF, in the terms of signal-to-noise ratio and full-width-half-maximum, respectively.

Double-Stage Delay Multiply and Sum Beamforming Algorithm: Application to Linear-Array Photoacoustic Imaging

Photoacoustic imaging (PAI) is an emerging medical imaging modality capable of providing high spatial resolution of Ultrasound (US) imaging and high contrast of optical imaging. Delay-and-Sum (DAS) is the most common beamforming algorithm in PAI. However, using DAS beamformer leads to low resolution images and considerable contribution of off-axis signals. A new paradigm namely delay-multiply-and-sum (DMAS), which was originally used as a reconstruction algorithm in confocal microwave imaging, was introduced to overcome the challenges in DAS. DMAS was used in PAI systems and it was shown that this algorithm results in resolution improvement and sidelobe degrading. However, DMAS is still sensitive to high levels of noise, and resolution improvement is not satisfying. Here, we propose a novel algorithm based on DAS algebra inside DMAS formula expansion, double stage DMAS (DS-DMAS), which improves the image resolution and levels of sidelobe, and is much less sensitive to high level of noise compared to DMAS. The performance of DS-DMAS algorithm is evaluated numerically and experimentally. The resulted images are evaluated qualitatively and quantitatively using established quality metrics including signal-to-noise ratio (SNR), full-width-half-maximum (FWHM) and contrast ratio (CR). It is shown that DS-DMAS outperforms DAS and DMAS at the expense of higher computational load. DS-DMAS reduces the lateral valley for about 15 dB and improves the SNR and FWHM better than 13% and 30%, respectively. Moreover, the levels of sidelobe are reduced for about 10 dB in comparison with those in DMAS.