Blind Separation of Sparse and Smooth Signals via Approximate Message Passing Algorithm

摘要

We consider the problem to recover source signals from noisy mixed ones. This can be described as a matrix reconstruction problem. Bayesian approach enables us to utilize structural properties of a matrix such as the sparsity, but often involves computational difficulties. An approximate message passing (AMP) algorithm for matrix reconstruction avoids such difficulties by introducing some approximations. In this paper, we consider the case where the original signals are sparse and smooth. The AMP algorithm for matrix reconstruction was derived on the assumption that the values of original signals at one time instance are generated independently of those at other time instances, so one cannot consider the smoothness of original signals. We derive an AMP algorithm considering correlations of original signals at one time instance and those at adjacent time instances, and apply the proposed algorithm to signal separation problems in the case where original signals at one time instance and those at adjacent time instances are correlative.