Gini index as sparsity measure for signal reconstruction from compressive samples

Abstract

Sparsity is a fundamental concept in compressive sampling of signals/images, which is commonly measured using the 0 norm, even though, in practice, the 1 or the p (0< p< 1) (pseudo-) norm is preferred. In this paper, we explore the use of the Gini index (GI), of a discrete signal, as a more effective measure of its sparsity for a significantly improved performance in its reconstruction from compressive samples. We also successfully incorporate the GI into a stochastic optimization algorithm for signal reconstruction from compressive samples and illustrate our approach with both synthetic and real signals/images. © 2011 IEEE.