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In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDEs. Starting from the study of PDE-based formalisms previously proposed in the literature for the regularization of scalar and vector-valued data, we propose a unifying expression that gathers the majority of these previous frameworks into a(More)
We are interested in PDE's (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE's, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensor-driven PDE,(More)
The restoration of noisy and blurred scalar images has been widely studied, and many algorithms based on variational or stochastic formulations have tried to solve this ill-posed Here, we propose a new vector image restoration PDE which removes the noise and enhances blurred vector contours, thanks to a vector generalisation of scalar¨-function diffusions(More)
This paper deals with the problem of regularizing noisy fields of diffusion tensors, considered as symmetric and semi-positive definite Ò ¢ Ò matrices (as for instance 2D structure tensors or DT-MRI medical images). We first propose a simple anisotropic PDE-based scheme that acts directly on the matrix coefficients and preserve the semi-positive constraint(More)
We present a method for the estimation of various features of the tissue micro-architecture using the diffusion magnetic resonance imaging. The considered features are designed from the displacement probability density function (PDF). The estimation is based on two steps: first the approximation of the signal by a series expansion made of Gaussian-Laguerre(More)
3 4 Résumé Nous nous intéressons aux approches par EDP pour la régularisation d'images multivaluées, et leurs applicationsà une large classe deprobì emes d'intérêts. L'´ etude et la comparaison des méthodes existantes nous permetà la fois de proposer un cadre mathématique commun mieux adapté aux interprétations géométriques locales de ces EDP, mais aussi de(More)
We present a robust method to retrieve neuronal fibers in human brain white matter from High-Angular Resolution MRI (HARDI datasets). Contrary to classical fiber-tracking techniques done on the traditional 2nd-order tensor model (DTI) which may lead to truncated or biased estimated diffusion directions in case of fiber crossing configurations, we propose(More)
We address the problem of efficient sampling of the diffusion space for the Diffusion Magnetic Resonance Imaging (dMRI) modality. While recent scanner improvements enable the acquisition of more and more detailed images, it is still unclear which q-space sampling strategy gives the best performance. We evaluate several q-space sampling distributions by an(More)
We address three crucial issues encountered in DT-MRI (Diffusion Tensor Magnetic Resonance Imaging) : diffusion tensor Estimation, Regularization and fiber bundle Vi-sualization. We first review related algorithms existing in the literature and propose then alternative variational formalisms that lead to new and improved schemes, thanks to the preservation(More)