# Sparse Wavelet Representations of Spatially Varying Blurring Operators

Escande, Paul and Weiss, Pierre Sparse Wavelet Representations of Spatially Varying Blurring Operators. (2015) SIAM Journal on Imaging Sciences, 8 (4). 2976-3014. ISSN 1936-4954

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Official URL: http://dx.doi.org/10.1137/151003465

## Abstract

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision, and biomedical imaging. One of the main challenges in performing this task is to design efficient numerical algorithms to approximate integral operators. We introduce a new method based on a sparse approximation of the blurring operator in the wavelet domain. This method requires $O(N\epsilon^{-d/M})$ operations to provide $\epsilon$-approximations, where N is the number of pixels of a d-dimensional image and $M \geq 1$ is a scalar describing the regularity of the blur kernel. In addition, we propose original methods to define sparsity patterns when only the operator regularity is known. Numerical experiments reveal that our algorithm provides a significant improvement compared to standard methods based on windowed convolutions.

Item Type: Article International peer-reviewed journal 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 25 Apr 2017 11:31

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