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Compressive sensing of digital sparse signals

This paper discusses compressive sensing with digital sparse signals. The motivation is that most existing sparse signal recovery algorithms, like matching pursuit, convex relaxation and Bayesian framework, do not fully exploit the digital nature of signals when dealing with digital sparse signals, which result in certain performance losses. In this paper, we solve this problem via a permutation-based multi-dimensional sensing matrix and an iterative recovery algorithm with maximum likelihood (ML) local detectors. The sensing matrix considered consists of several sub-matrices, each composed of a random permutation matrix and a block-diagonal matrix. The measurements generated from the same permutation matrix are referred to as a dimension. The block-diagonal matrices allow the use of the low-complexity ML detector in each dimension, which best utilizes the digital nature of signals. The multi-dimensional structure of the sensing matrix enables information exchange between dimensions through an iterative process to achieve a near global-optimal estimation. Numerical results are used to show the rate-distortion performance of the proposed technique. It is shown that it can achieve much better rate-distortion than the existing approaches based on convex relaxation and Bayesian framework with digital source signals.