Compressively sensing nonadjacent block-sparse spectra via a block discrete chirp matrix

Abstract

The block-sparse structure is shared by many types of signals, including audio, image, and radar-emitted signals. This structure can considerably improve compressive sensing (CS) performance and has attracted much attention in recent years. However, when fitting this model in practical applications, the nonzero blocks are always separated by one or more zero blocks to avoid interference between active emitters. (Generally, a block is occupied by an emitter.) In this paper, we coin a new phrase, ‘nonadjacent block sparse,’ or NBS, to describe this new structure. Our contributions are threefold. First, from a statistical probability perspective, the mean value and variance of block sparsity are evaluated and used to describe an NBS signal. Second, by employing the block discrete chirp matrix (BDCM), we propose and prove a condition that ensures the successful recovery of NBS signals from their linear measurements with high probability. Specifically, as long as a condition involved in mean value and variance of block sparsity is satisfied, an NBS signal can be successfully recovered with a high probability. Third, extensive experiments are simulated, and deep theoretical implications are discussed. The analyzed results demonstrate the progress we have made toward block-sparse CS.