Greedy sparse reconstruction of non-negative signals using symmetric alpha-stable distributions

Abstract

An accurate representation of the acquired data, while also conserving limited resources, such as power, bandwidth and storage capacity, is a challenging task. Besides, the Gaussian assumption, which plays a predominant role in signal processing being widely used as a signal and noise model, is unrealistic for a wide range of real-world data, which can be highly sparse in appropriate orthonormal bases. In the present work, the inherent property of compressed sensing (CS) working simultaneously as a sensing and compression protocol using a small subset of random projections is exploited to reduce the total amount of data. In particular, we propose a novel iterative algorithm for sparse representation and reconstruction of nonnegative signals in highly impulsive background using the family of symmetric alpha-stable distributions. The experimental evaluation shows that our proposed method results in an increased reconstruction performance, while also achieving a higher sparsity when compared with state-of-the-art CS algorithms.