A novel Bayesian Compressed Sensing algorithm using sparse tree representation

Compressed Sensing (CS) is a novel emerged theory in the last several years in the area of signal processing. CS could recover the signal correctly by sampling a sparse signal below the Nyquist rate. Bayesian Compressed Sensing (BCS) is a new framework in CS which recovery performance is proved to be close to L0-norm solution. Recent studies have recognized that in many multiscale bases such as wavelets, signals of interest have not only few significant coefficients, but also a well-organized tree structure of those significant coefficients. In this paper, we exploit the tree structure as additional prior information to the framework of the BCS, and then propose a novel BCS algorithm for signal reconstruction with limited number of measurements. Simulation results indicate that exploiting the proposed BCS algorithm using the sparse tree representation could reduce the required number of iterations greatly, and achieve better reconstruction as well as faster iteration speed compared to original BCS algorithm.