Learning dictionary from signals under global sparsity constraint

A new method is proposed in this paper to learn overcomplete dictionary from signals. Differing from the current methods that enforce uniform sparsity constraint on the coefficients of each input signal, the proposed method attempts to impose global sparsity constraint on the coefficient matrix of the entire signal set. This enables the proposed method to fittingly assign the atoms of the dictionary to represent various signals and optimally adapt to the complicated structures underlying the entire signal set. By virtue of the sparse coding and sparse PCA techniques, a simple algorithm is designed for the implementation of the method. The efficiency and the convergence of the proposed algorithm are also theoretically analyzed. Based on the experimental results implemented on a series of signal and image data sets, the capability of the proposed method is substantiated in original dictionary recovering, signal reconstructing and salient signal structure revealing.