Orthogonal Matching Pursuit based recovery for correlated sources with partially disjoint supports

Abstract

Compressed sensing (CS) can be applied in distributed scenarios, where the objective is to independently compress several signals that are characterized by presenting a sparse correlation. In this case, the compressed version of each signal is produced without knowledge of the other signals. The decoder has access to the compressed versions of all the signals of interest and recovers them by exploiting the signal correlations. Motivated by the idea of incorporating prior information in distributed CS we propose to study the effects of including signal support correlation information in the reconstruction process. We investigate the performance improvement obtained by jointly recovering two correlated sources, compared to single source recovery, in terms of number of samples (measurements) required to encode the signal for successful recovery. To perform recovery, we modify the OMP algorithm to jointly recover two correlated sources with partially disjoint support. The final reconstruction algorithm is an iterative process that incorporates prior information of the sources, resembling joint source channel digital coding schemes, where probabilistic information is iteratively exchanged. The study is carried out by means of numerical simulations of synthetic signals with a probabilistic model.