K-SVD with a real L0 optimization: application to image denoising
Résumé
This paper deals with sparse coding for dictionary learning in sparse representations. Because sparse coding involves an L0-norm, most, if not all, existing solutions only provide an approximate solution. Instead, in this paper, a real L0 optimization is considered for the sparse coding problem providing a global optimal solution. The proposed method reformulates the optimization problem as a Mixed-Integer Quadratic Program (MIQP), allowing then to obtain the global optimal solution by using an off-the-shelf solver. Because computing time is the main disadvantage of this approach, two techniques are proposed to improve its computational speed. One is to add suitable constraints and the other to use an appropriate initialization. The results obtained on an image denoising task demonstrate the feasibility of the MIQP approach for processing well-known benchmark images while achieving good performance compared with the most advanced methods.
Mots clés
sparse coding problem
global optimal solution
optimization problem
Mixed-Integer Quadratic Program
image denoising task
dictionary learning
sparse representations
MIQP approach
off-the-shelf solver
real L0 optimization
K-SVD
Image coding
image representation
sparsity
Image denoising
Mixed-integer quadratic programming
sparse representation
sparse coding
integer programming
quadratic programming
Optimization
Matching pursuit algorithms
Machine learning
Dictionaries
singular value decomposition
Origine : Fichiers produits par l'(les) auteur(s)
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