Low Rank and Sparse Decomposition of Ultrasound Color Flow Images for Suppressing Clutter in Real-Time

Low-rank prior-based Fast-RPCA for clutter filtering and noise suppression in non-contrast ultrasound microvascular imaging

Accurate and real-time separation of blood signal from clutter and noise signals is a critical step in clinical non-contrast ultrasound microvascular imaging. Despite the widespread adoption of singular value decomposition (SVD) and robust principal component analysis (RPCA) for clutter filtering and noise suppression, the SVD's sensitivity to threshold selection, along with the RPCA's limitations in undersampling conditions and heavy computational burden often result in suboptimal performance in complex clinical applications. To address those challenges, this study presents a novel low-rank prior-based fast RPCA (LP-fRPCA) approach to enhance the adaptability and robustness of clutter filtering and noise suppression with reduced computational cost. A low-rank prior constraint is integrated into the non-convex RPCA model to achieve a robust and efficient approximation of clutter subspace, while an accelerated alternating projection iterative algorithm is developed to improve convergence speed and computational efficiency. The performance of the LP-fRPCA method was evaluated against SVD with a tissue/blood threshold (SVD1), SVD with both tissue/blood and blood/noise thresholds (SVD2), and the classical RPCA based on the alternating direction method of multipliers algorithm through phantom and in vivo non-contrast experiments on rabbit kidneys. In the slow flow phantom experiment of 0.2 mm/s, LP-fRPCA achieved an average increase in contrast ratio (CR) of 10.68 dB, 9.37 dB, and 8.66 dB compared to SVD1, SVD2, and RPCA, respectively. In the in vivo rabbit kidney experiment, the power Doppler results demonstrate that the LP-fRPCA method achieved a superior balance in the trade-off between insufficient clutter filtering and excessive suppression of blood flow. Additionally, LP-fRPCA significantly reduced the runtime of RPCA by up to 94-fold. Consequently, the LP-fRPCA method promises to be a potential tool for clinical non-contrast ultrasound microvascular imaging.

Alternating direction method of multipliers for displacement estimation in ultrasound strain elastography

BACKGROUND

Ultrasound strain imaging, which delineates mechanical properties to detect tissue abnormalities, involves estimating the time delay between two radio-frequency (RF) frames collected before and after tissue deformation. The existing regularized optimization-based time-delay estimation (TDE) techniques suffer from at least one of the following drawbacks: (1) The regularizer is not aligned with the tissue deformation physics due to taking only the first-order displacement derivative into account; (2) TheL 2 $L2$ -norm of the displacement derivatives, which oversmooths the estimated time-delay, is utilized as the regularizer; (3) The modulus function defined mathematically should be approximated by a smooth function to facilitate the optimization ofL 1 $L1$ -norm.

PURPOSE

Our purpose is to develop a novel TDE technique that resolves the aforementioned shortcomings of the existing algorithms.

METHODS

Herein, we propose employing the alternating direction method of multipliers (ADMM) for optimizing a novel cost function consisting ofL 2 $L2$ -norm data fidelity term andL 1 $L1$ -norm first- and second-order spatial continuity terms. ADMM empowers the proposed algorithm to use different techniques for optimizing different parts of the cost function and obtain high-contrast strain images with smooth backgrounds and sharp boundaries. We name our technique ADMM for totaL variaTion RegUlarIzation in ultrasound STrain imaging (ALTRUIST). ALTRUIST's efficacy is quantified using absolute error (AE), Structural SIMilarity (SSIM), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain ratio (SR) with respect to GLUE, OVERWIND, andL 1 $L1$ -SOUL, three recently published energy-based techniques, and UMEN-Net, a state-of-the-art deep learning-based algorithm. Analysis of variance (ANOVA)-led multiple comparison tests and paired t $t$ -tests at5 % $5\%$ overall significance level were conducted to assess the statistical significance of our findings. The Bonferroni correction was taken into account in all statistical tests. Two simulated layer phantoms, three simulated resolution phantoms, one hard-inclusion simulated phantom, one multi-inclusion simulated phantom, one experimental breast phantom, and three in vivo liver cancer datasets have been used for validation experiments. We have published the ALTRUIST code at http://code.sonography.ai.

RESULTS

ALTRUIST substantially outperforms the four state-of-the-art benchmarks in all validation experiments, both qualitatively and quantitatively. ALTRUIST yields up to573 % ∗ ${573\%}^{*}$ ,41 % ∗ ${41\%}^{*}$ , and51 % ∗ ${51\%}^{*}$ SNR improvements and443 % ∗ ${443\%}^{*}$ ,53 % ∗ ${53\%}^{*}$ , and15 % ∗ ${15\%}^{*}$ CNR improvements overL 1 $L1$ -SOUL, its closest competitor, for simulated, phantom, and in vivo liver cancer datasets, respectively, where the asterisk (*) indicates statistical significance. In addition, ANOVA-led multiple comparison tests and paired t $t$ -tests indicate that ALTRUIST generally achieves statistically significant improvements over GLUE, UMEN-Net, OVERWIND, andL 1 $L1$ -SOUL in terms of AE, SSIM map, SNR, and CNR.

CONCLUSIONS

A novel ultrasonic displacement tracking algorithm named ALTRUIST has been developed. The principal novelty of ALTRUIST is incorporating ADMM for optimizing anL 1 $L1$ -norm regularization-based cost function. ALTRUIST exhibits promising performance in simulation, phantom, and in vivo experiments.

Clutter filtering of angular domain data for contrast-free ultrafast microvascular imaging

Objective. Contrast-free microvascular imaging is clinically valuable for the assessment of physiological status and the early diagnosis of diseases. Effective clutter filtering is essential for microvascular visualization without contrast enhancement. Singular value decomposition (SVD)-based spatiotemporal filter has been widely used to suppress clutter. However, clinical real-time imaging relies on short ensembles (dozens of frames), which limits the implementation of SVD filtering due to the large error of eigen-correlated estimations and high dependence on optimal threshold when used in such ensembles.Approach. To address the above challenges of imaging in short ensembles, two optimized filters of angular domain data are proposed in this paper: grouped angle SVD (GA-SVD) and angular-coherence-based higher-order SVD (AC-HOSVD). GA-SVD applies SVD to the concatenation of all angular data to improve clutter rejection performance in short ensembles, while AC-HOSVD applies HOSVD to the angular data tensor and utilizes angular coherence in addition to spatial and temporal features for filtering. Feasible threshold selection strategies in each feature space are provided. The clutter rejection performance of the proposed filters and SVD was evaluated with Doppler phantom andin vivostudies at different cases. Moreover, the robustness of the filters was explored under wrong singular value threshold estimation, and their computational complexity was studied.Main results. Qualitative and quantitative results indicated that GA-SVD and AC-HOSVD can effectively improve clutter rejection performance in short ensembles, especially AC-HOSVD. Notably, the proposed methods using 20 frames had similar image quality to SVD using 100 frames.In vivostudies showed that compared to SVD, GA-SVD increased the signal-to-noise-ratio (SNR) by 6.03 dB on average, and AC-HOSVD increased the SNR by 8.93 dB on average. Furthermore, AC-HOSVD remained better power Doppler image quality under non-optimal thresholds, followed by GA-SVD.Significance. The proposed filters can greatly enhance contrast-free microvascular visualization in short ensembles and have potential for different clinical translations due to the performance differences.

Exploiting Mechanics-Based Priors for Lateral Displacement Estimation in Ultrasound Elastography

Tracking the displacement between the pre- and post-deformed radio-frequency (RF) frames is a pivotal step of ultrasound elastography, which depicts tissue mechanical properties to identify pathologies. Due to ultrasound's poor ability to capture information pertaining to the lateral direction, the existing displacement estimation techniques fail to generate an accurate lateral displacement or strain map. The attempts made in the literature to mitigate this well-known issue suffer from one of the following limitations: 1) Sampling size is substantially increased, rendering the method computationally and memory expensive. 2) The lateral displacement estimation entirely depends on the axial one, ignoring data fidelity and creating large errors. This paper proposes exploiting the effective Poisson's ratio (EPR)-based mechanical correspondence between the axial and lateral strains along with the RF data fidelity and displacement continuity to improve the lateral displacement and strain estimation accuracies. We call our techniques MechSOUL (Mechanically-constrained Second-Order Ultrasound eLastography) and L1 -MechSOUL ( L1 -norm-based MechSOUL), which optimize L2 - and L1 -norm-based penalty functions, respectively. Extensive validation experiments with simulated, phantom, and in vivo datasets demonstrate that MechSOUL and L1 -MechSOUL's lateral strain and EPR estimation abilities are substantially superior to those of the recently-published elastography techniques. We have published the MATLAB codes of MechSOUL and L1 -MechSOUL at https://code.sonography.ai.

Custom-made flow phantoms for quantitative ultrasound microvessel imaging

Morphologically realistic flow phantoms are essential experimental tools for quantitative ultrasound-based microvessel imaging. As new quantitative flow imaging tools are developed, the need for more complex vessel-mimicking phantoms is indisputable. In this article, we propose a method for fabricating phantoms with sub-millimeter channels consisting of branches and curvatures in various shapes and sizes suitable for quantifying vessel morphological features. We used different tissue-mimicking materials (TMMs) compatible with ultrasound imaging as the base and metal wires of different diameters (0.15-1.25 mm) to create wall-less channels. The TMMs used are silicone rubber, plastisol, conventional gelatin, and medical gelatin. Mother channels in these phantoms were made in diameters of 1.25 mm or 0.3 mm and the daughter channels in diameters 0.3 mm or 0.15 mm. Bifurcations were created by soldering wires together at branch points. Quantitative parameters were assessed, and accuracy of measurements from the ground truth were determined. Channel diameters were seen to have increased (76-270%) compared to the initial state in the power Doppler images, partly due to blood mimicking fluid pressure. Amongst the microflow phantoms made from the different TMMs, the medical gelatin phantom was selected as the best option for microflow imaging, fulfilling the objective of being easy to fabricate with high transmittance while having a speed of sound and acoustic attenuation close to human tissue. A flow velocity of 0.85 ± 0.01 mm/s, comparable to physiological flow velocity was observed in the smallest diameter phantom (medical gelatin branch) presented here. We successfully constructed more complex geometries, including tortuous and multibranch channels using the medical gelatin as the TMM. We anticipate this will create new avenues for validating quantitative ultrasound microvessel imaging techniques.

Incorporating Gradient Similarity for Robust Time Delay Estimation in Ultrasound Elastography

Energy-based ultrasound elastography techniques minimize a regularized cost function consisting of data and continuity terms to obtain local displacement estimates based on the local time-delay estimation (TDE) between radio frequency (RF) frames. The data term associated with the existing techniques takes only the amplitude similarity into account and hence is not sufficiently robust to the outlier samples present in the RF frames under consideration. This drawback creates noticeable artifacts in the strain image. To resolve this issue, we propose to formulate the data function as a linear combination of the amplitude and gradient similarity constraints. We estimate the adaptive weight concerning each similarity term following an iterative scheme. Finally, we optimize the nonlinear cost function in an efficient manner to convert the problem to a sparse system of linear equations which are solved for millions of variables. We call our technique rGLUE: robust data term in GLobal Ultrasound Elastography. rGLUE has been validated using simulation, phantom, in vivo liver, and breast datasets. In all our experiments, rGLUE substantially outperforms the recent elastography methods both visually and quantitatively. For simulated, phantom, and in vivo datasets, respectively, rGLUE achieves 107%, 18%, and 23% improvements of signal-to-noise ratio (SNR) and 61%, 19%, and 25% improvements of contrast-to-noise ratio (CNR) over global ultrasound elastography (GLUE), a recently published elastography algorithm.

Second-Order Ultrasound Elastography With L1-Norm Spatial Regularization

Time delay estimation (TDE) between two radio-frequency (RF) frames is one of the major steps of quasi-static ultrasound elastography, which detects tissue pathology by estimating its mechanical properties. Regularized optimization-based techniques, a prominent class of TDE algorithms, optimize a nonlinear energy functional consisting of data constancy and spatial continuity constraints to obtain the displacement and strain maps between the time-series frames under consideration. The existing optimization-based TDE methods often consider the L2 -norm of displacement derivatives to construct the regularizer. However, such a formulation over-penalizes the displacement irregularity and poses two major issues to the estimated strain field. First, the boundaries between different tissues are blurred. Second, the visual contrast between the target and the background is suboptimal. To resolve these issues, herein, we propose a novel TDE algorithm where instead of L2 -, L1 -norms of both first- and second-order displacement derivatives are taken into account to devise the continuity functional. We handle the non-differentiability of L1 -norm by smoothing the absolute value function's sharp corner and optimize the resulting cost function in an iterative manner. We call our technique Second-Order Ultrasound eLastography (SOUL) with the L1 -norm spatial regularization ( L1 -SOUL). In terms of both sharpness and visual contrast, L1 -SOUL substantially outperforms GLobal Ultrasound Elastography (GLUE), tOtal Variation rEgulaRization and WINDow-based time delay estimation (OVERWIND), and SOUL, three recently published TDE algorithms in all validation experiments performed in this study. In cases of simulated, phantom, and in vivo datasets, respectively, L1 -SOUL achieves 67.8%, 46.81%, and 117.35% improvements of contrast-to-noise ratio (CNR) over SOUL. The L1 -SOUL code can be downloaded from http://code.sonography.ai.

Deep low-Rank plus sparse network for dynamic MR imaging

In dynamic magnetic resonance (MR) imaging, low-rank plus sparse (L+S) decomposition, or robust principal component analysis (PCA), has achieved stunning performance. However, the selection of the parameters of L+S is empirical, and the acceleration rate is limited, which are common failings of iterative compressed sensing MR imaging (CS-MRI) reconstruction methods. Many deep learning approaches have been proposed to address these issues, but few of them use a low-rank prior. In this paper, a model-based low-rank plus sparse network, dubbed L+S-Net, is proposed for dynamic MR reconstruction. In particular, we use an alternating linearized minimization method to solve the optimization problem with low-rank and sparse regularization. Learned soft singular value thresholding is introduced to ensure the clear separation of the L component and S component. Then, the iterative steps are unrolled into a network in which the regularization parameters are learnable. We prove that the proposed L+S-Net achieves global convergence under two standard assumptions. Experiments on retrospective and prospective cardiac cine datasets show that the proposed model outperforms state-of-the-art CS and existing deep learning methods and has great potential for extremely high acceleration factors (up to 24×).

Combining First- and Second-Order Continuity Constraints in Ultrasound Elastography

Ultrasound elastography is a prominent noninvasive medical imaging technique that estimates tissue elastic properties to detect abnormalities in an organ. A common approximation to tissue elastic modulus is tissue strain induced after mechanical stimulation. To compute tissue strain, ultrasound radio frequency (RF) data can be processed using energy-based algorithms. These algorithms suffer from ill-posedness to tackle. A continuity constraint along with the data amplitude similarity is imposed to obtain a unique solution to the time-delay estimation (TDE) problem. Existing energy-based methods exploit the first-order spatial derivative of the displacement field to construct a regularizer. This first-order regularization scheme alone is not fully consistent with the mechanics of tissue deformation while perturbed with an external force. As a consequence, state-of-the-art techniques suffer from two crucial drawbacks. First, the strain map is not sufficiently smooth in uniform tissue regions. Second, the edges of the hard or soft inclusions are not well-defined in the image. Herein, we address these issues by formulating a novel regularizer taking both first- and second-order derivatives of the displacement field into account. The second-order constraint, which is the principal novelty of this work, contributes both to background continuity and edge sharpness by suppressing spurious noisy edges and enhancing strong boundaries. We name the proposed technique: Second-Order Ultrasound eLastography (SOUL). Comparative assessment of qualitative and quantitative results shows that SOUL substantially outperforms three recently developed TDE algorithms called Hybrid, GLUE, and MPWC-Net++. SOUL yields 27.72%, 62.56%, and 81.37% improvements of the signal-to-noise ratio (SNR) and 72.35%, 54.03%, and 65.17% improvements of the contrast-to-noise ratio (CNR) over GLUE with data pertaining to simulation, phantom, and in vivo tissue, respectively. The SOUL code can be downloaded from code.sonography.ai.

Joint Blind Deconvolution and Robust Principal Component Analysis for Blood Flow Estimation in Medical Ultrasound Imaging

This article addresses the problem of high-resolution Doppler blood flow estimation from an ultrafast sequence of ultrasound images. Formulating the separation of clutter and blood components as an inverse problem has been shown in the literature to be a good alternative to spatio-temporal singular value decomposition (SVD)-based clutter filtering. In particular, a deconvolution step has recently been embedded in such a problem to mitigate the influence of the point spread function (PSF) of the imaging system. Deconvolution was shown in this context to improve the accuracy of the blood flow reconstruction. However, the PSF needs to be measured experimentally, and measuring it requires nontrivial experimental setups. To overcome this limitation, we propose herein a blind deconvolution method able to estimate both the blood component and the PSF from Doppler data. Numerical experiments conducted on simulated and in vivo data demonstrate qualitatively and quantitatively the effectiveness of the proposed approach in comparison with the previous method based on experimentally measured PSF and two other state-of-the-art approaches.

Automatic collateral circulation scoring in ischemic stroke using 4D CT angiography with low-rank and sparse matrix decomposition

PURPOSE

Sufficient collateral blood supply is crucial for favorable outcomes with endovascular treatment. The current practice of collateral scoring relies on visual inspection and thus can suffer from inter and intra-rater inconsistency. We present a robust and automatic method to score cerebral collateral blood supply to aid ischemic stroke treatment decision making. The developed method is based on 4D dynamic CT angiography (CTA) and the ASPECTS scoring protocol.

METHODS

The proposed method, ACCESS (Automatic Collateral Circulation Evaluation in iSchemic Stroke), estimates a target patient's unfilled cerebrovasculature in contrast-enhanced CTA using the lack of contrast agent due to clotting. To do so, the fast robust matrix completion algorithm with in-face extended Frank-Wolfe optimization is applied on a cohort of healthy subjects and a target patient, to model the patient's unfilled vessels and the estimated full vasculature as sparse and low-rank components, respectively. The collateral score is computed as the ratio of the unfilled vessels to the full vasculature, mimicking existing clinical protocols.

RESULTS

ACCESS was tested with 46 stroke patients and obtained an overall accuracy of 84.78%. The optimal threshold selection was evaluated using a receiver operating characteristics curve with the leave-one-out approach, and a mean area under the curve of 85.39% was obtained.

CONCLUSION

ACCESS automates collateral scoring to mitigate the shortcomings of the standard clinical practice. It is a robust approach, which resembles how radiologists score clinical scans, and can be used to help radiologists in clinical decisions of stroke treatment.

Clutter suppression in ultrasound: performance evaluation and review of low-rank and sparse matrix decomposition methods

Vessel diseases are often accompanied by abnormalities related to vascular shape and size. Therefore, a clear visualization of vasculature is of high clinical significance. Ultrasound color flow imaging (CFI) is one of the prominent techniques for flow visualization. However, clutter signals originating from slow-moving tissue are one of the main obstacles to obtain a clear view of the vascular network. Enhancement of the vasculature by suppressing the clutters is a significant and irreplaceable step for many applications of ultrasound CFI. Currently, this task is often performed by singular value decomposition (SVD) of the data matrix. This approach exhibits two well-known limitations. First, the performance of SVD is sensitive to the proper manual selection of the ranks corresponding to clutter and blood subspaces. Second, SVD is prone to failure in the presence of large random noise in the dataset. A potential solution to these issues is using decomposition into low-rank and sparse matrices (DLSM) framework. SVD is one of the algorithms for solving the minimization problem under the DLSM framework. Many other algorithms under DLSM avoid full SVD and use approximated SVD or SVD-free ideas which may have better performance with higher robustness and less computing time. In practice, these models separate blood from clutter based on the assumption that steady clutter represents a low-rank structure and that the moving blood component is sparse. In this paper, we present a comprehensive review of ultrasound clutter suppression techniques and exploit the feasibility of low-rank and sparse decomposition schemes in ultrasound clutter suppression. We conduct this review study by adapting 106 DLSM algorithms and validating them against simulation, phantom, and in vivo rat datasets. Two conventional quality metrics, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR), are used for performance evaluation. In addition, computation times required by different algorithms for generating clutter suppressed images are reported. Our extensive analysis shows that the DLSM framework can be successfully applied to ultrasound clutter suppression.