Approximated Function Based Spectral Gradient Algorithm for Sparse Signal Recovery

Numerical algorithms for the l0-norm regularized non-smooth non-convex minimization problems have recently became a topic of great interest within signal processing, compressive sensing, statistics, and machine learning. Nevertheless, the l0norm makes the problem combinatorial and generally computationally intractable. In this paper, we construct a new surrogate function to approximate l0-norm regularization, and subsequently make the discrete optimization problem continuous and smooth. Then we use the well-known spectral gradient algorithm to solve the resulting smooth optimization problem. Experiments are provided which illustrate that this method is very promising.