Gini Index as Sparsity Measure for Signal Reconstruction from Compressive Samples

Sparsity is a fundamental concept in compressive sampling of signals/images, which is commonly measured using the l₀ norm, even though, in practice, the l₁ or the l_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.