2014/02/13 by Chao-Kai Wen, Kai‐Kit Wong, Wen, Chao-Kai +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1402.3215
openalex publication_date 2014/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.