Analysis of Compressed Sensing with Spatially-Coupled Orthogonal Matrices

Abstract

Recent development in compressed sensing (CS) has revealed that the use of a special design of measurement matrix, namely the spatially-coupled matrix, can achieve the information-theoretic limit of CS. In this paper, we consider the measurement matrix which consists of the spatially-coupled \emph{orthogonal} matrices. One example of such matrices are the randomly selected discrete Fourier transform (DFT) matrices. Such selection enjoys a less memory complexity and a faster multiplication procedure. Our contributions are the replica calculations to find the mean-square-error (MSE) of the Bayes-optimal reconstruction for such setup. We illustrate that the reconstruction thresholds under the spatially-coupled orthogonal and Gaussian ensembles are quite different especially in the noisy cases. In particular, the spatially coupled orthogonal matrices achieve the faster convergence rate, the lower measurement rate, and the reduced MSE.

References in corpus (1)

• Analysis of CDMA systems that are characterized by eigenvalue spectrum

Cited by in corpus (5)

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• Approximate message-passing decoder and capacity-achieving sparse superposition codes
• On the Performance of Turbo Signal Recovery with Partial DFT Sensing Matrices
• Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes
• Compressed Coding, AMP Based Decoding and Analog Spatial Coupling