Distributed compressed sensing of non-negative signals using symmetric alpha-stable distributions

Sensor networks gather an enormous amount of data over space and time to derive an estimate of a parameter or function. Several constraints, such as limited power, bandwidth, and storage capacity, motivate the need for a new paradigm for sensor data processing in order to extend the network´s lifetime, while also obtaining accurate estimates. In a companion paper [1], we proposed a novel iterative algorithm for reconstructing non-negative sparse signals in highly impulsive background by modeling their prior distribution using symmetric alpha-stable distributions. In the present work, we extend this algorithm in the framework of distributed compressed sensing using duality theory and the method of subgradients for the optimization of the associated cost function. The experimental results show that our proposed distributed method maintains the reconstruction performance of its centralized counterpart, while also achieving a highly sparse basis configuration, thus reducing the total amount of data handled by each sensor.