Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

A computational framework for elliptic inverse problems with uncertain boundary conditions

This project concerns the computational solution of inverse problems formulated as partial differential equation (PDE)-constrained optimization problems with interior data. The areas addressed are twofold. First, we present a novel software architecture designed to solve inverse problems constrained by an elliptic system of PDEs. These generally require the solution of forward and adjoint problems, evaluation of the objective function, and computation of its gradient, all of which are approximated numerically using finite elements. The creation of specialized "layered"' elements to perform these tasks leads to a modular software structure that improves code maintainability and promotes functional interoperability between different software components. Second, we address issues related to forward model definition in the presence of boundary condition (BC) uncertainty. We propose two variational formulations to accommodate that uncertainty: (a) a Bayesian formulation that assumes Gaussian measurement noise and a minimum strain energy prior, and (b) a Lagrangian formulation that is completely free of displacement and traction BCs. This work is motivated by applications in the field of biomechanical imaging, where the mechanical properties within soft tissues are inferred from observations of tissue motion. In this context, the constraint PDE is well accepted, but considerable uncertainty exists in the BCs. The approaches developed here are demonstrated on a variety of applications, including simulated and experimental data. We present modulus reconstructions of individual cells, tissue-mimicking phantoms, and breast tumors

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 http://code.sonography.ai.Comment: Link to the Supplemental Video: https://drive.google.com/file/d/1uOmt-T4i9MwR98jUoMsu-eOhQ2mgjrBd/view?usp=sharin

Characterization of carotid artery plaques using noninvasive vascular ultrasound elastography

L'athérosclérose est une maladie vasculaire complexe qui affecte la paroi des artères (par l'épaississement) et les lumières (par la formation de plaques). La rupture d'une plaque de l'artère carotide peut également provoquer un accident vasculaire cérébral ischémique et des complications. Bien que plusieurs modalités d'imagerie médicale soient actuellement utilisées pour évaluer la stabilité d'une plaque, elles présentent des limitations telles que l'irradiation, les propriétés invasives, une faible disponibilité clinique et un coût élevé. L'échographie est une méthode d'imagerie sûre qui permet une analyse en temps réel pour l'évaluation des tissus biologiques. Il est intéressant et prometteur d’appliquer une échographie vasculaire pour le dépistage et le diagnostic précoces des plaques d’artère carotide. Cependant, les ultrasons vasculaires actuels identifient uniquement la morphologie d'une plaque en termes de luminosité d'écho ou l’impact de cette plaque sur les caractéristiques de l’écoulement sanguin, ce qui peut ne pas être suffisant pour diagnostiquer l’importance de la plaque. La technique d’élastographie vasculaire non-intrusive (« noninvasive vascular elastography (NIVE) ») a montré le potentiel de détermination de la stabilité d'une plaque. NIVE peut déterminer le champ de déformation de la paroi vasculaire en mouvement d’une artère carotide provoqué par la pulsation cardiaque naturelle. En raison des différences de module de Young entre les différents tissus des vaisseaux, différents composants d’une plaque devraient présenter différentes déformations, caractérisant ainsi la stabilité de la plaque. Actuellement, les performances et l’efficacité numérique sous-optimales limitent l’acceptation clinique de NIVE en tant que méthode rapide et efficace pour le diagnostic précoce des plaques vulnérables. Par conséquent, il est nécessaire de développer NIVE en tant qu’outil d’imagerie non invasif, rapide et économique afin de mieux caractériser la vulnérabilité liée à la plaque. La procédure à suivre pour effectuer l’analyse NIVE consiste en des étapes de formation et de post-traitement d’images. Cette thèse vise à améliorer systématiquement la précision de ces deux aspects de NIVE afin de faciliter la prédiction de la vulnérabilité de la plaque carotidienne. Le premier effort de cette thèse a été dédié à la formation d'images (Chapitre 5). L'imagerie par oscillations transversales a été introduite dans NIVE. Les performances de l’imagerie par oscillations transversales couplées à deux estimateurs de contrainte fondés sur un modèle de déformation fine, soit l’ « affine phase-based estimator (APBE) » et le « Lagrangian speckle model estimator (LSME) », ont été évaluées. Pour toutes les études de simulation et in vitro de ce travail, le LSME sans imagerie par oscillation transversale a surperformé par rapport à l'APBE avec imagerie par oscillations transversales. Néanmoins, des estimations de contrainte principales comparables ou meilleures pourraient être obtenues avec le LSME en utilisant une imagerie par oscillations transversales dans le cas de structures tissulaires complexes et hétérogènes. Lors de l'acquisition de signaux ultrasonores pour la formation d'images, des mouvements hors du plan perpendiculaire au plan de balayage bidimensionnel (2-D) existent. Le deuxième objectif de cette thèse était d'évaluer l'influence des mouvements hors plan sur les performances du NIVE 2-D (Chapitre 6). À cette fin, nous avons conçu un dispositif expérimental in vitro permettant de simuler des mouvements hors plan de 1 mm, 2 mm et 3 mm. Les résultats in vitro ont montré plus d'artefacts d'estimation de contrainte pour le LSME avec des amplitudes croissantes de mouvements hors du plan principal de l’image. Malgré tout, nous avons néanmoins obtenu des estimations de déformations robustes avec un mouvement hors plan de 2.0 mm (coefficients de corrélation supérieurs à 0.85). Pour un jeu de données cliniques de 18 participants présentant une sténose de l'artère carotide, nous avons proposé d'utiliser deux jeux de données d'analyses sur la même plaque carotidienne, soit des images transversales et longitudinales, afin de déduire les mouvements hors plan (qui se sont avérés de 0.25 mm à 1.04 mm). Les résultats cliniques ont montré que les estimations de déformations restaient reproductibles pour toutes les amplitudes de mouvement, puisque les coefficients de corrélation inter-images étaient supérieurs à 0.70 et que les corrélations croisées normalisées entre les images radiofréquences étaient supérieures à 0.93, ce qui a permis de démontrer une plus grande confiance lors de l'analyse de jeu de données cliniques de plaques carotides à l'aide du LSME. Enfin, en ce qui concerne le post-traitement des images, les algorithmes NIVE doivent estimer les déformations des parois des vaisseaux à partir d’images reconstituées dans le but d’identifier les tissus mous et durs. Ainsi, le dernier objectif de cette thèse était de développer un algorithme d'estimation de contrainte avec une résolution de la taille d’un pixel ainsi qu'une efficacité de calcul élevée pour l'amélioration de la précision de NIVE (Chapitre 7). Nous avons proposé un estimateur de déformation de modèle fragmenté (SMSE) avec lequel le champ de déformation dense est paramétré avec des descriptions de transformées en cosinus discret, générant ainsi des composantes de déformations affines (déformations axiales et latérales et en cisaillement) sans opération mathématique de dérivées. En comparant avec le LSME, le SMSE a réduit les erreurs d'estimation lors des tests de simulations, ainsi que pour les mesures in vitro et in vivo. De plus, la faible mise en oeuvre de la méthode SMSE réduit de 4 à 25 fois le temps de traitement par rapport à la méthode LSME pour les simulations, les études in vitro et in vivo, ce qui pourrait permettre une implémentation possible de NIVE en temps réel.Atherosclerosis is a complex vascular disease that affects artery walls (by thickening) and lumens (by plaque formation). The rupture of a carotid artery plaque may also induce ischemic stroke and complications. Despite the use of several medical imaging modalities to evaluate the stability of a plaque, they present limitations such as irradiation, invasive property, low clinical availability and high cost. Ultrasound is a safe imaging method with a real time capability for assessment of biological tissues. It is clinically used for early screening and diagnosis of carotid artery plaques. However, current vascular ultrasound technologies only identify the morphology of a plaque in terms of echo brightness or the impact of the vessel narrowing on flow properties, which may not be sufficient for optimum diagnosis. Noninvasive vascular elastography (NIVE) has been shown of interest for determining the stability of a plaque. Specifically, NIVE can determine the strain field of the moving vessel wall of a carotid artery caused by the natural cardiac pulsation. Due to Young’s modulus differences among different vessel tissues, different components of a plaque can be detected as they present different strains thereby potentially helping in characterizing the plaque stability. Currently, sub-optimum performance and computational efficiency limit the clinical acceptance of NIVE as a fast and efficient method for the early diagnosis of vulnerable plaques. Therefore, there is a need to further develop NIVE as a non-invasive, fast and low computational cost imaging tool to better characterize the plaque vulnerability. The procedure to perform NIVE analysis consists in image formation and image post-processing steps. This thesis aimed to systematically improve the accuracy of these two aspects of NIVE to facilitate predicting carotid plaque vulnerability. The first effort of this thesis has been targeted on improving the image formation (Chapter 5). Transverse oscillation beamforming was introduced into NIVE. The performance of transverse oscillation imaging coupled with two model-based strain estimators, the affine phase-based estimator (APBE) and the Lagrangian speckle model estimator (LSME), were evaluated. For all simulations and in vitro studies, the LSME without transverse oscillation imaging outperformed the APBE with transverse oscillation imaging. Nonetheless, comparable or better principal strain estimates could be obtained with the LSME using transverse oscillation imaging in the case of complex and heterogeneous tissue structures. During the acquisition of ultrasound signals for image formation, out-of-plane motions which are perpendicular to the two-dimensional (2-D) scan plane are existing. The second objective of this thesis was to evaluate the influence of out-of-plane motions on the performance of 2-D NIVE (Chapter 6). For this purpose, we designed an in vitro experimental setup to simulate out-of-plane motions of 1 mm, 2 mm and 3 mm. The in vitro results showed more strain estimation artifacts for the LSME with increasing magnitudes of out-of-plane motions. Even so, robust strain estimations were nevertheless obtained with 2.0 mm out-of-plane motion (correlation coefficients higher than 0.85). For a clinical dataset of 18 participants with carotid artery stenosis, we proposed to use two datasets of scans on the same carotid plaque, one cross-sectional and the other in a longitudinal view, to deduce the out-of-plane motions (estimated to be ranging from 0.25 mm to 1.04 mm). Clinical results showed that strain estimations remained reproducible for all motion magnitudes since inter-frame correlation coefficients were higher than 0.70, and normalized cross-correlations between radiofrequency images were above 0.93, which indicated that confident motion estimations can be obtained when analyzing clinical dataset of carotid plaques using the LSME. Finally, regarding the image post-processing component of NIVE algorithms to estimate strains of vessel walls from reconstructed images with the objective of identifying soft and hard tissues, we developed a strain estimation method with a pixel-wise resolution as well as a high computation efficiency for improving NIVE (Chapter 7). We proposed a sparse model strain estimator (SMSE) for which the dense strain field is parameterized with Discrete Cosine Transform descriptions, thereby deriving affine strain components (axial and lateral strains and shears) without mathematical derivative operations. Compared with the LSME, the SMSE reduced estimation errors in simulations, in vitro and in vivo tests. Moreover, the sparse implementation of the SMSE reduced the processing time by a factor of 4 to 25 compared with the LSME based on simulations, in vitro and in vivo results, which is suggesting a possible implementation of NIVE in real time

Real-time Regularized Tracking of Shear-Wave in Ultrasound Elastography

Elastography is a convenient and affordable method for imaging mechanical properties of tissue, which are often correlated with pathologies. An emerging novel elastography technique applies an external acoustic radiation force (ARF) to generate shear-wave in the tissue which are then tracked using ultrasound imaging. Accurate tracking of the small tissue motion (referred to as tissue displacement) is a critical step in shear-wave elastography, but is challenging due to various sources of noise in the ultrasound data. I formulate tissue displacement estimation as an optimization problem and propose two computationally efficient approaches to estimate the displacement field. The first algorithm is referred to as dynamic programming analytic minimization (DPAM), which utilizes first order Taylor series expansion of the highly nonlinear cost function to allow for its efficient optimization. DPAM was previously proposed for quasi-static elastography and I extend the approach to shear-wave elastography. The second algorithm is a novel technique that exploits second-order Taylor expansion of the non-linear cost function. I call the new algorithm as second-order analytic minimization elastography (SESAME). I compare DMAP and SESAME to the standard normalized Cross Correlation (NCC) approach in the context of estimating displacement and elasticity of the medium for shear-wave elastography (SWE). The results of micrometer-order displacement estimation in a uniform simulation phantom illustrate that SESAME outperforms DPAM, which in turn outperforms NCC in terms of signal to noise ratio (SNR) and jitter. In addition, the relative difference between true and reconstructed shear modulus (averaged over several excitations focusing at different focal depths with different scatterers realizations at each depth) is approximately 3.41%, 1.12% and 1.01%, respectively, for NCC, DPAM and SESAME. The performance of the proposed methods is also assessed with real data acquired using a tissue-mimicking phantom, wherein, in comparison to NCC, DPAM and SESAME improve the SNR of displacement by 7.6 dB and 9.5 dB, respectively. Experimental results on a tissue-mimicking phantom also show that shear modulus reconstruction is more accurate with DPAM and SESAME in comparison with NCC