Sparsity Based Sequential Dictionary Learning Algorithm

Abstract: The term Sparsity refered to as the number of non zero elements in sparse approximation and it can be measured by L_0 Norm. Sparse dictionary learning algorithms used to find sparse representation of the input data in the form of linear combination of basis elements. This elements are called atoms and it compose dictionary. Dictionary learning methods have been successfully used in a number of signal and image processing applications and this includes image denoising, face recognition, compression analysis. Dictionary learning algorithms consist of two stages: a sparse coding stage and a dictionary update stage. In the first stage the dictionary is kept constant and the sparsity assumption is used to produce sparse linear approximations of the observed data. In the second stage, the coefficients of the linear combination are kept constant and the dictionary is updated to minimize a certain cost function. The performance of these methods strongly depends on the dictionary update stage since most of these methods share a similar sparse coding stage. In previous dictionary learning algorithms sparsity constraint is only used in sparse coding stage but in proposed method the sparsity constraint is used both in sparse coding and dictionary update stage. Keywords: Sparsity, Dictionary learning, SVD.