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Toward fast transform learning

Chabiron, Olivier and Malgouyres, François and Tourneret, Jean-Yves and Dobigeon, Nicolas Toward fast transform learning. (2015) International Journal of Computer Vision, 114 (2). 195-216. ISSN 0920-5691

(Document in English)

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Official URL: http://dx.doi.org/10.1007/s11263-014-0771-z


This paper introduces a new dictionary learning strategy based on atoms obtained by translating the composition of K convolutions with S-sparse kernels of known support. The dictionary update step associated with this strategy is a non-convex optimization problem. We propose a practical formulation of this problem and introduce a Gauss–Seidel type algorithm referred to as alternative least square algorithm for its resolution. The search space of the proposed algorithm is of dimension KS, which is typically smaller than the size of the target atom and much smaller than the size of the image. Moreover, the complexity of this algorithm is linear with respect to the image size, allowing larger atoms to be learned (as opposed to small patches). The conducted experiments show that we are able to accurately approximate atoms such as wavelets, curvelets, sinc functions or cosines for large values of K. The proposed experiments also indicate that the algorithm generally converges to a global minimum for large values of K and S.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://link.springer.com The original PDF of the article can be found at International Journal of Computer Vision website : http://link.springer.com/journal/11263
HAL Id:hal-01281930
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 Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (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:
Deposited On:29 Feb 2016 13:35

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