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.

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) The L 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 of L 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 of L 2 $L2$ -norm data fidelity term and L 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, and L 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 at 5 % $5\%$ 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 to 573 % ∗ ${573\%}^{*}$ , 41 % ∗ ${41\%}^{*}$ , and 51 % ∗ ${51\%}^{*}$ SNR improvements and 443 % ∗ ${443\%}^{*}$ , 53 % ∗ ${53\%}^{*}$ , and 15 % ∗ ${15\%}^{*}$ CNR improvements over L 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, and L 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 an L 1 $L1$ -norm regularization-based cost function. ALTRUIST exhibits promising performance in simulation, phantom, and in vivo experiments.

Displacement Tracking Techniques in Ultrasound Elastography: From Cross-Correlation to Deep Learning.

Ultrasound elastography is a non-invasive medical imaging technique that maps viscoelastic properties to characterize tissues and diseases. Elastography can be divided into two classes in a broad sense: strain elastography (SE), which relies on Hooke's law to delineate strain as a surrogate for elasticity, and shear-wave elastography (SWE), which tracks the propagation of shear waves in tissues to estimate the elasticity. As tracking the displacement field in the temporal or spatial domain is an inevitable step of both SE and SWE, the success is contingent on the displacement estimation accuracy. Recent reviews mostly focused on clinical applications of elastography, disregarding advances in displacement tracking algorithms. Herein, we comprehensively review the recently proposed displacement estimation algorithms applied to both SE and SWE. In addition to cross-correlation, block-matching (i.e., window-based), model-based, energy-based, and deep learning-based tracking techniques, we review large and lateral displacement tracking, adaptive beamforming, data enhancement, and noise-suppression algorithms facilitating better displacement estimation. We also discuss the simulation models for displacement tracking validation, clinical translation and validation of displacement tracking methods, performance evaluation metrics, and publicly available codes and data for displacement tracking in elastography. Finally, we provide experiential opinions on different tracking algorithms, list the limitations of the current state of elastographic tracking, and comment on possible future research.

ULTRA-SR Challenge: Assessment of Ultrasound Localization and TRacking Algorithms for Super-Resolution Imaging.

With the widespread interest and uptake of super-resolution ultrasound (SRUS) through localization and tracking of microbubbles, also known as ultrasound localization microscopy (ULM), many localization and tracking algorithms have been developed. ULM can image many centimeters into tissue in-vivo and track microvascular flow non-invasively with sub-diffraction resolution. In a significant community effort, we organized a challenge, Ultrasound Localization and TRacking Algorithms for Super-Resolution (ULTRA-SR). The aims of this paper are threefold: to describe the challenge organization, data generation, and winning algorithms; to present the metrics and methods for evaluating challenge entrants; and to report results and findings of the evaluation. Realistic ultrasound datasets containing microvascular flow for different clinical ultrasound frequencies were simulated, using vascular flow physics, acoustic field simulation and nonlinear bubble dynamics simulation. Based on these datasets, 38 submissions from 24 research groups were evaluated against ground truth using an evaluation framework with six metrics, three for localization and three for tracking. In-vivo mouse brain and human lymph node data were also provided, and performance assessed by an expert panel. Winning algorithms are described and discussed. The publicly available data with ground truth and the defined metrics for both localization and tracking present a valuable resource for researchers to benchmark algorithms and software, identify optimized methods/software for their data, and provide insight into the current limits of the field. In conclusion, Ultra-SR challenge has provided benchmarking data and tools as well as direct comparison and insights for a number of the state-of-the art localization and tracking algorithms.

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.

Lateral Strain Imaging Using Self-Supervised and Physically Inspired Constraints in Unsupervised Regularized Elastography.

Convolutional Neural Networks (CNN) have shown promising results for displacement estimation in UltraSound Elastography (USE). Many modifications have been proposed to improve the displacement estimation of CNNs for USE in the axial direction. However, the lateral strain, which is essential in several downstream tasks such as the inverse problem of elasticity imaging, remains a challenge. The lateral strain estimation is complicated since the motion and the sampling frequency in this direction are substantially lower than the axial one, and a lack of carrier signal in this direction. In computer vision applications, the axial and the lateral motions are independent. In contrast, the tissue motion pattern in USE is governed by laws of physics which link the axial and lateral displacements. In this paper, inspired by Hooke's law, we, first propose Physically Inspired ConsTraint for Unsupervised Regularized Elastography (PICTURE), where we impose a constraint on the Effective Poisson's ratio (EPR) to improve the lateral strain estimation. In the next step, we propose self-supervised PICTURE (sPICTURE) to further enhance the strain image estimation. Extensive experiments on simulation, experimental phantom and in vivo data demonstrate that the proposed methods estimate accurate axial and lateral strain maps.

Prevalence and factors associated with chronic school absenteeism among 207,107 in-school adolescents: Findings from cross-sectional studies in 71 low-middle and high-income countries.

BACKGROUND: Despite the negative impact of chronic school absenteeism on the psychological and physical health of adolescents, data on the burden of adolescent chronic school absenteeism (ACSA) and interventions and programs to address it are lacking. We estimated the global, regional and national level prevalence of ACSA and its correlation with violence and unintentional injury, psychosocial, protective, lifestyle, and food security-related factors among in-school adolescents across low and middle-income, and high-income countries (LMICs-HICs). OBJECTIVES: This study aimed to estimate the prevalence of chronic school absenteeism (CSA) as well as to determine its associated factors among in-school adolescents across 71 low-middle and high-income countries. METHODS: We used data from the most recent Global School-based Student Health Survey of 207,107 in-school adolescents aged 11-17 years in 71 LMICs-HICs countries across six WHO regions. We estimated the weighted prevalence of ACSA from national, regional and global perspectives. Multiple binary logistic regression analyses were used to estimate the adjusted effect of independent factors on ACSA. RESULTS: The overall population-weighted prevalence of CSA was 11·43% (95% confidence interval, CI: 11·29-11·57). Higher likelihood of CSA was associated with severe food insecurity, peer victimisation, loneliness, high level of anxiety, physically attack, physical fighting, serious injury, poor peer support, not having close friends, lack of parental support, being obese, and high levels of sedentary behaviours. Lower likelihood of CSA was associated with being female (odds ratio, OR = 0·76, 95% CI: 0·74-0·78). CONCLUSION: Our findings indicate that a combination of different socio-economic factors, peer conflict and injury factors, factors exacerbate CSA among adolescents. Interventions should be designed to focus on these risk factors and should consider the diverse cultural and socioeconomic contexts.

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.

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.

Fast and robust localization of surgical array using Kalman filter.

PROBLEM: Intraoperative tracking of surgical instruments is an inevitable task of computer-assisted surgery. An optical tracking system often fails to precisely reconstruct the dynamic location and pose of a surgical tool due to the acquisition noise and measurement variance. Embedding a Kalman filter (KF) or any of its extensions such as extended and unscented Kalman filters (EKF and UKF) with the optical tracker resolves this issue by reducing the estimation variance and regularizing the temporal behavior. However, the current KF implementations are computationally burdensome and hence takes long execution time which hinders real-time surgical tracking. AIM: This paper introduces a fast and computationally efficient implementation of linear KF to improve the measurement accuracy of an optical tracking system with high temporal resolution. METHODS: Instead of the surgical tool as a whole, our KF framework tracks each individual fiducial mounted on it using a Newtonian model. In addition to simulated dataset, we validate our technique against real data obtained from a high frame-rate commercial optical tracking system. We also perform experiments wherein a diffusive material (such as a drop of blood) blocks one of the fiducials and show that KF can substantially reduce the tracking error. RESULTS: The proposed KF framework substantially stabilizes the tracking behavior in all of our experiments and reduces the mean-squared error (MSE) by a factor of 26.84, from the order of [Formula: see text] to [Formula: see text] mm[Formula: see text]. In addition, it exhibits a similar performance to UKF, but with a much smaller computational complexity.

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.

Incorporating Multiple Observations in global Ultrasound Elastography.

In this paper, we propose a novel framework for time delay estimation in ultrasound elastography. In the presence of high acquisition noise, the state-of-the-art motion tracking techniques suffer from inaccurate estimation of displacement field. To resolve this issue, instead of one, we collect several ultrasound Radio-Frequency (RF) frames from both pre- and post-deformed scan planes to better investigate the data statistics. We formulate a non-linear cost function incorporating all observation frames from both levels of deformations. Beside data similarity, we impose axial and lateral continuity to exploit the prior information of spatial coherence. Most importantly, we consider the continuity among the displacement estimates obtained from different observation RF frames. This novel continuity constraint mainly contributes to the robustness of the proposed technique to high noise power. We efficiently optimize the aforementioned cost function to derive a sparse system of linear equations where we solve for millions of variables to estimate the displacement of all samples of all of the incorporated RF frames simultaneously. We call the proposed algorithm GLobal Ultrasound Elastography using multiple observations (mGLUE). Our primary validation of mGLUE against soft and hard inclusion simulation phantoms proves that mGLUE is capable of obtaining high quality strain map while dealing with noisy ultrasound data. In case of the soft inclusion phantom, Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) have improved by 75.37% and 57.08%, respectively. In addition, SNR and CNR improvements of 32.19% and 38.57% have been observed for the hard inclusion case.

Denoising RF Data via Robust Principal Component Analysis: Results in Ultrasound Elastography.

Ultrasound data often suffers from an excessive amount of noise especially from deep tissue or in synthetic aperture imaging where the acoustic wave is weak. Such noisy data renders Time Delay Estimation (TDE) inaccurate in the context of ultrasound elastography. Herein, a novel two-step elastography technique is presented to ensure accurate TDE while dealing with noisy ultrasound data. In the first step, instead of one, we acquire several Radio-Frequency (RF) frames from both pre- and post-deformed positions of the tissue. We stack the frames collected from pre- and post-deformed planes in separate data matrices. Since each set is collected from the same level of tissue compression, we assume that the Casorati data matrices exhibit underlying low-rank structures, which are sought by taking the low-rank and sparse decomposition framework into account. This Robust Principal Component Analysis (RPCA) approach removes the random noise from the datasets as sparse error components. In the second step, we select one frame from each denoised ensemble and employ GLobal Ultrasound Elastography (GLUE) to perform the strain elastography. We call the proposed technique RPCA-GLUE. Our preliminary validation of RPCA-GLUE against simulation phantoms containing hard and soft inclusions proves its robustness to large noise. Substantial improvement in Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) has also been observed. Simulation results show that in the presence of large noise, the proposed method substantially improves CNR from 5.0 to 22.6 in a soft inclusion and from 2.2 to 21.7 in a hard inclusion phantom.

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

In this work, a novel technique for real-time clutter rejection in ultrasound Color Flow Imaging (CFI) is proposed. Suppressing undesired clutter signal is important because clutter prohibits an unambiguous view of the vascular network. Although conventional eigen-based filters are potentially efficient in suppressing clutter signal, their performance is highly dependent on proper selection of a clutter to blood boundary which is done manually. Herein, we resolve this limitation by formulating the clutter suppression problem as a foreground-background separation problem to extract the moving blood component. To that end, we adapt the fast Robust Matrix Completion (fRMC) algorithm, and utilize the in-face extended Frank-Wolfe method to minimize the rank of the matrix of ultrasound frames. Our method automates the clutter suppression process, which is critical for clinical use. We name the method RAPID (Robust mAtrix decomPosition for suppressIng clutter in ultrasounD) since the automation step can substantially streamline clutter suppression. The technique is validated with simulation, flow phantom and two sets of in-vivo data. RAPID code as well as most of the data in this paper can be downloaded from RAPID.sonography.ai.

Factors associating different antenatal care contacts of women: A cross-sectional analysis of Bangladesh demographic and health survey 2014 data.

Antenatal care (ANC) contacts have long been considered a critical component of the continuum of care for a pregnant mother along with the newborn baby. The latest maternal mortality survey in Bangladesh suggests that progress in reducing maternal mortality has stalled as only 37% of pregnant women have attended at least four ANC contacts. This paper aims to determine what factors are associated with ANC contacts for women in Bangladesh. We analysed the data, provided by Bangladesh demographic and health survey 2014, covering a nationally representative sample of 17,863 ever married women aged 15-49 years. A two-stage stratified cluster sampling was used to collect the data. Data derived from 4,475 mothers who gave birth in the three years preceding the survey. Descriptive, inferential, and multivariate statistical techniques were used to analyse the data. An overall 78.4% of women had ANC contacts, but the WHO recommended ≥8 ANC contacts and ANC contacts by qualified doctors were only 8% for each. The logistic regression analysis revealed that division, maternal age, women's education, husband's education, wealth index and media exposure were associated with the ANC contacts. Likewise, place of residence, women's education, religion, and wealth index were also found to be associated with the WHO recommended ANC contacts. Furthermore, the husband's education, division, religion and husband's employment showed significant associations with ANC contacts by qualified doctors. However, Bangladeshi women in general revealed an unsatisfactory level of ANC contacts, the WHO recommended as well as ANC contacts by qualified doctors. In order to improve the situation, it is necessary to follow the most recent ANC contacts recommended by the WHO and to contact the qualified doctors. Moreover, an improvement in education as well as access to information along with an increase of transports, care centres and reduction of service costs would see an improvement of ANC contacts in Bangladesh.

Global Ultrasound Elastography in Spatial and Temporal Domains.

In this paper, a novel computationally efficient quasi-static ultrasound elastography technique is introduced by optimizing an energy function. Unlike conventional elastography techniques, three radio frequency (RF) frames are considered to devise a nonlinear cost function consisting of data intensity similarity term, spatial regularization terms and, most importantly, temporal continuity terms. We optimize the aforesaid cost function efficiently to obtain the time-delay estimation (TDE) of all samples between the first two and last two frames of ultrasound images simultaneously, and spatially differentiate the TDE to generate axial strain map. A novelty in our spatial and temporal regularizations is that they adaptively change based on the data, which leads to substantial improvements in TDE. We handle the computational complexity resulting from incorporation of all samples from all three frames by converting our optimization problem to a sparse linear system of equations. Consideration of both spatial and temporal continuity makes the algorithm more robust to signal decorrelation than the previous algorithms. We name the proposed method GUEST: Global Ultrasound Elastography in Spatial and Temporal directions. We validated our technique with simulation, experimental phantom, and in vivo liver data and compared the results with two recently proposed TDE methods. In all the experiments, GUEST substantially outperforms other techniques in terms of signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain ratio (SR) of the strain images.