Dictionary Learning for Sparse Representation Based on Smoothed L_0 Norm

Dictionary learning for sparse representation is a powerful and efficient tool for signal processing applications. Designing a dictionary, which can sparsely represent the training samples is the main target of this work. Most of the current dictionary learning methods minimize the representation error of the training samples, subject to the sparseness of the coefficient matrix. They use a two-steps alternating minimization approach to find the dictionary and the coefficient matrix. The first step is to sparsely approximate the training samples over the current dictionary and the second step is to update the dictionary. The first step is often time-consuming, because it is required to minimize the l_0 (or l_1) norm of the coefficient matrix. In this paper, we propose a new method for dictionary learning based on smoothed l_0 norm, which increases the speed of the sparse decomposition step. We also combine the sparse representation and the dictionary update steps, which helps us expedite convergence of the parameters. Simulation results show that, the proposed algorithm considerably increases the speed of convergence, while providing the same or better performance, particularly in the presence of noise.