A Survey Of The Comparison Among Different Norms Of Sparse Representation Model

Recently, sparse representation is widely applied to many fields,such as signal processing, image processing, computer vision, pattern recognition and so on. Sparse representation has relatively mature development both in theoretical research and in practical application.Scholars have proposed many algorithms to deal with sparse representation problems. The main purpose of this paper is to give a synthetical review of sparse representation and basic guidance to beginners. The algorithms of sparse representation can be divided by different points. In terms of the different norms used in the regularization of sparse representation model, sparse representation algorithms can be roughly divided into three categories: (1)l0-norm minimization based sparse representation; (2) l1-norm minimization based sparse representation; (3) Cp(0<p< 1 )-norm minimization based sparse representation. The existing algorithms of three kinds of sparse representation models are analyzed and summarized: the main classical algorithm of l0-norm minimization based sparse representation is OMP algorithm in greedy strategy; l1---norm minimization based sparse representation can be roughly divided into constrained optimization strategy, proximal algorithm and homotopy algorithm; Cp(0<p<1)-norm minimization based sparse representation can be mainly divided into IRL1, IRLS and ITM. Several representative algorithms are compared by statistical method through function technology applied in the algorithms,success rate, complexity, runtime and convergence performance: OMP uses less time and lp-norm minimization algorithms are obviously slowest; Cp-norm minimization algorithms can obtain the most sparse result if considering sparseness and they can also get the most successful result.