Coupled Compressive Sensing : Sequential Reinforcement Approach

Abstract

We consider multiple Compressive Sensing (CS) problems wherein the supports of signal vectors of CS problems are restricted to satisfy a collection of joint logical constraints, which we refer to as coupling constraints. We consider a case where the coupling constraints are encoded in a graph and present a sequential reinforcement approach to solve the multiple CS problems efficiently. In the sequential reinforcement approach, we iteratively select and solve one CS problem that we can solve with the highest confidence level and use the recovered signal supports to reinforce the correct support recovery of remaining CS problems. The efficacy of the proposed approach is validated using the experiments with a synthetic problem and power network topology identification of IEEE 14 bus network.