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Accelerating l1-l2 deblurring using wavelet expansions of operators

Escande, Paul and Weiss, Pierre Accelerating l1-l2 deblurring using wavelet expansions of operators. (2018) Journal of Computational and Applied Mathematics, 343. 373-396. ISSN 0377-0427

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Official URL: https://doi.org/10.1016/j.cam.2018.04.063

Abstract

Image deblurring is a fundamental problem in imaging, usually solved with computationally intensive optimization procedures. The goal of this paper is to provide new efficient strategies to reduce computing times for simple deblurring models regularized using orthogonal wavelet transforms. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: (i) a sparse approximation of the blur operator in wavelet bases, (ii) a diagonal preconditioner and (iii) an implementation on massively parallel architectures. Combining the three ingredients leads to acceleration factors ranging from 4 to 250 on a typical workstation. For instance, a 1024 1024 image can be deblurred in 0.15 s.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: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)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Funders:
PRES of Toulouse University and Midi-Pyrenees region
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Deposited On:26 Apr 2017 09:29

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