Inner–Outer Support Set Pursuit for Distributed Compressed Sensing

We address the distributed compressed sensing problem of reconstructing a sequence of jointly sparse signals under the condition of an inaccurate and insufficient estimate of the common support set. Correlations between the jointly sparse signals are modeled by the joint sparsity model 1 (JSM-1). We propose a novel algorithm, namely inner-outer support set pursuit (IOSSP), which removes the impact of the estimated common support set, to reduce the computing time as well as the reconstruction error. The IOSSP algorithm divides the support set of each individual sparse signal into two disjoint sets: an inner support set and an outer support set. Two separate procedures, the outer support set pursuit and inner support set pursuit, are then utilized to estimate the outer and inner support sets. We provide the convergence performance of the IOSSP algorithm in both the noiseless and noisy conditions. For the noiseless case, we derive the condition on the estimated common support set, which guarantees an exact reconstruction. For the noisy case, a bound of the reconstruction error is provided, and the derivation process is inspired by the compressive sampling matching pursuit algorithm. The experimental and simulation results demonstrate that the proposed IOSSP algorithm is superior on reconstruction error and computing time over the conventional algorithms for JSM-1, e.g., the parallel pursuit with side information and joint recovery strategy algorithms.