Dictionary Learning for Sparse Decomposition: A Novel Approach

Abstract : A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, , as the product of a dictionary, , and a sparse coefficient matrix, , as follows, . Current dictionary learning algorithmsminimize the representation error subject to a constraint on (usually having unit column-norms) and sparseness of . The resulting problem is not convex with respect to the pair . In this letter, we derive a first order series expansion formula for the factorization, . The resulting objective function is jointly convex with respect to and .We simply solve the resulting problem using alternatingminimization and apply some of the previously suggested algorithms onto our new problem. Simulation results on recovery of a known dictionary and dictionary learning for natural image patches show that our new problem considerably improves performance with a little additional computational load.
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Mostafa Sadeghi, Massoud Babaie-Zadeh, Christian Jutten. Dictionary Learning for Sparse Decomposition: A Novel Approach. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2013, 20 (12), pp.1195-1198. ⟨10.1109/LSP.2013.2285218⟩. ⟨hal-00934308⟩

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