David Tschumperlé

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In this paper, we focus on techniques for vector-valued image regularization, based on variational methods and PDE. 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)
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)
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 problem [2, 4, 10, 7, 33, 20, 19, 18, 22, 1, 26, 24, 9, 28, 29, 6, 30, 35, 37]. However, only few methods exist for multichannel/color images ([7, 29, 16, 36]). Here, we propose a(More)
We are interested in regularizing fields of orthonormal vector sets, using constraint-preserving anisotropic diffusion PDE's. Each point of such a field is defined by multiple orthogonal and unitary vectors and can indeed represent a lot of interesting orientation features such as direction vectors or orthogonal matrices (among other examples). We first(More)
We address three crucial issues encountered in DT-MRI (Diffusion Tensor Magnetic Resonance Imaging) : diffusion tensor Estimation, Regularization and fiber bundle Visualization. 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)
Nonlinear diffusion equations are now widely used to restore and enhance images. They allow to eliminate noise and artifacts while preserving large global features, such as object contours. In this context, we propose a differential-geometric framework to define PDEs acting on some manifold constrained datasets. We consider the case of images taking value(More)
We present a general method for the computation of PDF-based characteristics of the tissue micro-architecture in MR imaging. The approach relies on the approximation of the MR signal by a series expansion based on Spherical Harmonics and Laguerre-Gaussian functions, followed by a simple projection step that is efficiently done in a finite dimensional space.(More)