Compressive Sensing of Digital Sparse Signals

This paper discusses the compressive sensing of digital sparse signals. An interleaver-based multi-dimensional structure is proposed for sensing matrices, along with an iterative recovery algorithm. The motivation of the proposed technique is that existing sparse signal recovery algorithms, like matching pursuit, convex relaxation and Bayesian framework, do not fully exploit the nature of digital signals, which result in certain performance loss. In the proposed technique, we solve this problem via a permutation-based multi-dimensional sensing matrix and an iterative recovery algorithm with maximum likelihood (ML) local detection. The sensing matrix considered consists of several sub-matrices, each composed of a random permutation matrix and a matrix generated by direct sum of several equal-length row vectors. The measurements generated from the same permutation matrix are referred to as a dimension. Such a matrix allows simple ML detection in each dimension, which best utilizes the digital nature of signals with reasonable complexity, while the multi-dimensional structure 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 the proposed technique can achieve much better rate-distortion performance than the conventional approach based on convex relaxation and Bayesian framework.