# Approximation et Estimation des Opérateurs de Flou Variable

Escande, Paul and Weiss, Pierre Approximation et Estimation des Opérateurs de Flou Variable. (2016) In: GRETSI, 8 September 2015 - 11 September 2015 (Lyon, France).

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## Abstract

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision or biomedical imaging. Blurring operators are modelled using integral operators with some regularity and decrease conditions on the kernel. Recently, we studied the approximation of these operators in wavelet bases in which operators are highly compressible. They also allow to fastly compute matrix-vector products with a complexity $O(N\epsilon^{-d/M})$ for a precision $\epsilon$ in spectral norm, where N is the number of pixels of a d-dimensional image and M describes the kernel regularity. Additionnaly, we have shown that the sparsity pattern of the matrix can be pre-defined. We exploit these results to study the estimation/reconstruction of the operator from the knwoledge of few point spread functions located at arbitrary positions in the image domain. We propose an original formulation directly in the wavelet domain and a fast algorithm.

Item Type: Conference or Workshop Item (Paper) National conference proceedings French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE) PRES of Toulouse University and Midi-Pyrenees region download 24 Apr 2017 15:31

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