Tensor Completion for Multidimensional Inverse Problems with Applications to Magnetic Resonance Relaxometry

This thesis deals with tensor completion for the solution of multidimensional inverse problems. We study the problem of reconstructing an approximately low rank tensor from a small number of noisy linear measurements. New recovery guarantees, numerical algorithms, non-uniform sampling strategies, and parameter selection algorithms are developed. We derive a fixed point continuation algorithm for tensor completion and prove its convergence. A restricted isometry property (RIP) based tensor recovery guarantee is proved. Probabilistic recovery guarantees are obtained for sub-Gaussian measurement operators and for measurements obtained by non-uniform sampling from a Parseval tight frame. We show how tensor completion can be used to solve multidimensional inverse problems arising in NMR relaxometry. Algorithms are developed for regularization parameter selection, including accelerated k-fold cross-validation and generalized cross-validation. These methods are validated on experimental and simulated data. We also derive condition number estimates for nonnegative least squares problems. Tensor recovery promises to significantly accelerate N-dimensional NMR relaxometry and related experiments, enabling previously impractical experiments. Our methods could also be applied to other inverse problems arising in machine learning, image processing, signal processing, computer vision, and other fields.

Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.

Utilisation d’un modèle de co-culture cellulaire pour l’évaluation in vitro du transport inverse du cholestérol

De nouveaux modèles cellulaires in vitro par transfert de milieu et par coculture ont été mis au point afin d’évaluer la capacité des HDL à éliminer l’excès de cholestérol des tissus périphériques et de le transporter vers le foie afin d’être excrété par le foie, un processus nommé le transport inverse du cholestérol (TIC). Le système cellulaire par transfert in vitro où des macrophages J774 sont gorgés de LDL acétylées et marqués au 3H-cholestérol a été préalablement établi afin de mesurer par scintillation l’efflux de cholestérol marqué vers le milieu de culture contenant des accepteurs de cholestérol. Ce milieu conditionné est transféré sur des cellules HepG2 afin d’étudier l’influx du cholestérol marqué. Ce dernier nous permet d’observer un transport de cholestérol de 25 % hors des J774 et un transport de 39 000 cpm dans les HepG2 en utilisant un milieu contenant 2 % de sérums humains mis en commun. Une stimulation des cellules J774 par l’AMPc augmente l’efflux et l’influx d’environ 45 %. Des tests de preuve de concept ont été effectués sur le système cellulaire par co-culture qui utilise des chambres de Boyden où les J774 sont localisées au fond d’un puits et les HepG2 dans un insert, et où le milieu est partagé entre les deux types cellulaires. On a déterminé qu’une confluence densité de 60 000 cellules/cm2 sur un insert constitué d’une membrane de polyester avec des pores de 3,0 μm, sans autre revêtement, permet d’observer un influx spécifique au sérum d’environ 6 000 cpm associés aux cellules HepG2, où 50 % des comptes radioactifs sont dans les cellules et l’autre moitié présente à la surface cellulaire.

Inverse identification of the bending stiffness of a braided polyethylene twine subject to large deformation: application to the identification of the mesh opening rigidity of fishing nets.

The evaluation of the mesh opening stiffness of fishing nets is an important issue in assessing the selectivity of trawls. It appeared that a larger bending rigidity of twines decreases the mesh opening and could reduce the escapement of fish. Nevertheless, netting structure is complex. A netting is made up of braided twines made of polyethylene or polyamide. These twines are tied with non-symmetrical knots. Thus, these assemblies develop contact-friction interactions. Moreover, the netting can be subject to large deformation. In this study, we investigate the responses of netting samples to different types of solicitations. Samples are loaded and unloaded with creep and relaxation stages, with different boundary conditions. Then, two models have been developed: an analytical model and a finite element model. The last one was used to assess, with an inverse identification algorithm, the bending stiffness of twines. In this paper, experimental results and a model for netting structures made up of braided twines are presented. During dry forming of a composite, for example, the matrix is not present or not active, and relative sliding can occur between constitutive fibres. So an accurate modelling of the mechanical behaviour of fibrous material is necessary. This study offers experimental data which could permit to improve current models of contact-friction interactions [4], to validate models for large deformation analysis of fibrous materials [1] on a new experimental case, then to improve the evaluation of the mesh opening stiffness of a fishing net

Inverse kinematics for upper limb compound movement estimation in exoskeleton-assisted rehabilitation

Robot-Assisted Rehabilitation (RAR) is relevant for treating patients affected by nervous system injuries (e.g., stroke and spinal cord injury) -- The accurate estimation of the joint angles of the patient limbs in RAR is critical to assess the patient improvement -- The economical prevalent method to estimate the patient posture in Exoskeleton-based RAR is to approximate the limb joint angles with the ones of the Exoskeleton -- This approximation is rough since their kinematic structures differ -- Motion capture systems (MOCAPs) can improve the estimations, at the expenses of a considerable overload of the therapy setup -- Alternatively, the Extended Inverse Kinematics Posture Estimation (EIKPE) computational method models the limb and Exoskeleton as differing parallel kinematic chains -- EIKPE has been tested with single DOFmovements of the wrist and elbow joints -- This paper presents the assessment of EIKPEwith elbow-shoulder compoundmovements (i.e., object prehension) -- Ground-truth for estimation assessment is obtained from an optical MOCAP (not intended for the treatment stage) -- The assessment shows EIKPE rendering a good numerical approximation of the actual posture during the compoundmovement execution, especially for the shoulder joint angles -- This work opens the horizon for clinical studies with patient groups, Exoskeleton models, and movements types --

Geological realism in hydrogeological and geophysical inverse modeling: A review

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydrogeological data. Modern geostatistical simulation algorithms can produce multiple subsurface realizations that are in agreement with conceptual geological models and statistical rock physics can be used to map these realizations into physical properties that are sensed by the geophysical or hydrogeological data. The inverse problem consists of finding one or an ensemble of such subsurface realizations that are in agreement with the data. The most general inversion frameworks are presently often computationally intractable when applied to large-scale problems and it is necessary to better understand the implications of simplifying (1) the conceptual geological model (e.g., using model compression); (2) the physical forward problem (e.g., using proxy models); and (3) the algorithm used to solve the inverse problem (e.g., Markov chain Monte Carlo or local optimization methods) to reach practical and robust solutions given today's computer resources and knowledge. We also highlight the need to not only use geophysical and hydrogeological data for parameter estimation purposes, but also to use them to falsify or corroborate alternative geological scenarios.

Effect of hamstring injuries on kicking in soccer using inverse dynamics

Las lesiones musculares del muslo tienen una gran incidencia en el fútbol. El objetivo del estudio ha sido desarrollar un nuevo procedimiento para evaluar el efecto de las lesiones de isquiotibiales en los golpeos con el pie s en el fútbol utilizando los principios de la dinámica inversa. El trabajo se ha centrado en la evaluación de la diferencia entre sujetos que habían sufrido la lesión en los últimos 5 años y los que no. Se analizaron 17 jugadores de fútbol profesionales realizando cinco tiros con el empeine y cinco con el interior del pie. Los movimientos se registraron mediante una plataforma de fuerza y un sistema de captura de movimiento Vicon funcionando a 500Hz. Los participantes también tomaron parte en una prueba de isocinético en la que se midió el torque isocinético en 60 º/s y 120 º/s. Se observaron diferencias significativas en los parámetros cinemáticos y cinéticos entre los dos grupos (lesionados y no lesionados) en la fase posterior del golpeo y en el instante de máxima flexión de cadera. No se encontraron diferencias significativas entre los dos grupos en la prueba isocinética tradicional. Estos resultados indican que el procedimiento empleado probablemente podría ser muy útil en la evaluación del efecto de las lesiones de isquiotibiales en el fútbol.

Inverse Spectral Methods in Acoustic Normal Mode Velocimetry of High Reynolds Number Spherical Couette Flows

Experimental geophysical fluid dynamics often examines regimes of fluid flow infeasible for computer simulations. Velocimetry of zonal flows present in these regimes brings many challenges when the fluid is opaque and vigorously rotating; spherical Couette flows with molten metals are one such example. The fine structure of the acoustic spectrum can be related to the fluid’s velocity field, and inverse spectral methods can be used to predict and, with sufficient acoustic data, mathematically reconstruct the velocity field. The methods are to some extent inherited from helioseismology. This work develops a Finite Element Method suitable to matching the geometries of experimental setups, as well as modelling the acoustics based on that geometry and zonal flows therein. As an application, this work uses the 60-cm setup Dynamo 3.5 at the University of Maryland Nonlinear Dynamics Laboratory. Additionally, results obtained using a small acoustic data set from recent experiments in air are provided.

Large national series of patients with Xq28 duplication involving MECP2: Delineation of brain MRI abnormalities in 30 affected patients.

Xq28 duplications encompassing MECP2 have been described in male patients with a severe neurodevelopmental disorder associated with hypotonia and spasticity, severe learning disability, stereotyped movements, and recurrent pulmonary infections. We report on standardized brain magnetic resonance imaging (MRI) data of 30 affected patients carrying an Xq28 duplication involving MECP2 of various sizes (228 kb to 11.7 Mb). The aim of this study was to seek recurrent malformations and attempt to determine whether variations in imaging features could be explained by differences in the size of the duplications. We showed that 93% of patients had brain MRI abnormalities such as corpus callosum abnormalities (n = 20), reduced volume of the white matter (WM) (n = 12), ventricular dilatation (n = 9), abnormal increased hyperintensities on T2-weighted images involving posterior periventricular WM (n = 6), and vermis hypoplasia (n = 5). The occipitofrontal circumference varied considerably between >+2SD in five patients and <-2SD in four patients. Among the nine patients with dilatation of the lateral ventricles, six had a duplication involving L1CAM. The only patient harboring bilateral posterior subependymal nodular heterotopia also carried an FLNA gene duplication. We could not demonstrate a correlation between periventricular WM hyperintensities/delayed myelination and duplication of the IKBKG gene. We thus conclude that patients with an Xq28 duplication involving MECP2 share some similar but non-specific brain abnormalities. These imaging features, therefore, could not constitute a diagnostic clue. The genotype-phenotype correlation failed to demonstrate a relationship between the presence of nodular heterotopia, ventricular dilatation, WM abnormalities, and the presence of FLNA, L1CAM, or IKBKG, respectively, in the duplicated segment.

Distance and overcurrent relay coordination considering non standardized inverse time curves

Protective relaying comprehends several procedures and techniques focused on maintaining the power system working safely during and after undesired and abnormal network conditions, mostly caused by faulty events. Overcurrent relay is one of the oldest protective relays, its operation principle is straightforward: when the measured current is greater than a specified magnitude the protection trips; less variables are required from the system in comparison with other protections, causing the overcurrent relay to be the simplest and also the most difficult protection to coordinate; its simplicity is reflected in low implementation, operation, and maintenance cost. The counterpart consists in the increased tripping times offered by this kind of relays mostly before faults located far from their location; this problem can be particularly accentuated when standardized inverse-time curves are used or when only maximum faults are considered to carry out relay coordination. These limitations have caused overcurrent relay to be slowly relegated and replaced by more sophisticated protection principles, it is still widely applied in subtransmission, distribution, and industrial systems. In this work, the use of non standardized inverse-time curves, the model and implementation of optimization algorithms capable to carry out the coordination process, the use of different levels of short circuit currents, and the inclusion of distance relays to replace insensitive overcurrent ones are proposed methodologies focused on the overcurrent relay performance improvement. These techniques may transform the typical overcurrent relay into a more sophisticated one without changing its fundamental principles and advantages. Consequently a more secure and still economical alternative can be obtained, increasing its implementation area

Complete Urethral Duplication in Children: A Case Report

Introduction: Urethral duplication (UD) is a rare congenital anomaly with multiple anatomical variants. Case Presentation: In this article we present a four year-old child with complete UD. The patient was admitted for hypospadias repair, in evaluation we found type IIA1 UD according to Effmann classification. Patient underwent hypospadias repair saving complete UD. Conclusions: After one year follow-up he has normal and continent urination.

STUDY OF A DIRECT SAMPLING METHOD FOR THE INVERSE MEDIUM SCATTERING PROBLEM

Direct sampling methods are increasingly being used to solve the inverse medium scattering problem to estimate the shape of the scattering object. A simple direct method using one incident wave and multiple measurements was proposed by Ito, Jin and Zou. In this report, we performed some analytic and numerical studies of the direct sampling method. The method was found to be effective in general. However, there are a few exceptions exposed in the investigation. Analytic solutions in different situations were studied to verify the viability of the method while numerical tests were used to validate the effectiveness of the method.