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Dictionary learning for sparse representation: A novel approach

Sadeghi, M ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1109/LSP.2013.2285218
  3. Publisher: 2013
  4. Abstract:
  5. A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, Y, as the product of a dictionary, D, and a sparse coefficient matrix, X, as follows, Y ≈ DX. Current dictionary learning algorithms minimize the representation error subject to a constraint on D (usually having unit column-norms) and sparseness of X. The resulting problem is not convex with respect to the pair (D, X). In this letter, we derive a first order series expansion formula for the factorization, DX. The resulting objective function is jointly convex with respect to D and X. We simply solve the resulting problem using alternating minimization 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
  6. Keywords:
  7. Dictionary learning ; Sparse representation ; Alternating minimization ; Computational loads ; Dictionary learning algorithms ; K-SVD,MOD ; Matrix factorizations ; Objective functions ; Algorithms ; Matrix algebra ; Problem solving
  8. Source: IEEE Signal Processing Letters ; Volume 20, Issue 12 , 2013 , Pages 1195-1198 ; 10709908 (ISSN)
  9. URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6626561