BCS: Compressive sensing for binary sparse signals

Model-based compressive sensing (CS) for signal-specific applications is of particular interest in the sparse signal approximation. In this paper, we deal with a special class of sparse signals with binary entries. Unlike conventional CS approaches based on l₁ minimization, we model the CS process with a bi-partite graph. We design a novel sampling matrix with unique sum property, which can be universally applied to any binary signal. Moreover, a novel binary CS decoding algorithm (BCS) based on graph and unique sum table, which does not need complex optimization process, is proposed. Proposed method is verified and compared with existing solutions through mathematical analysis and numerical simulations.