This paper proposes a subspace decomposition method based on an over-completedictionary in sparse representation, called "Sparse Signal SubspaceDecomposition" (or 3SD) method. This method makes use of a novel criterionbased on the occurrence frequency of atoms of the dictionary over the data set.This criterion, well adapted to subspace-decomposition over a dependent basisset, adequately re ects the intrinsic characteristic of regularity of thesignal. The 3SD method combines variance, sparsity and component frequencycriteria into an unified framework. It takes benefits from using anover-complete dictionary which preserves details and from subspacedecomposition which rejects strong noise. The 3SD method is very simple with alinear retrieval operation. It does not require any prior knowledge ondistributions or parameters. When applied to image denoising, it demonstrateshigh performances both at preserving fine details and suppressing strong noise.
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