Sparse signal subspace decomposition based on adaptive over-complete dictionary

This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called “sparse signal subspace decomposition” (or 3SD) method. This method makes use of a novel criterion based on the occurrence frequency of atoms of the dictionary over the data set. This criterion, well adapted to subspace decomposition over a dependent basis set, adequately reflects the intrinsic characteristic of regularity of the signal. The 3SD method combines variance, sparsity, and component frequency criteria into a unified framework. It takes benefits from using an over-complete dictionary which preserves details and from subspace decomposition which rejects strong noise. The 3SD method is very simple with a linear retrieval operation. It does not require any prior knowledge on distributions or parameters. When applied to image denoising, it demonstrates high performances both at preserving fine details and suppressing strong noise.