2016/07/18 by Dongcai Su, Su, Dongcai
Engineering · #Electrical and Bioimpedance Tomography #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.1607.04926
openalex publication_date 2016/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies a data recovery problem in compressed sensing (CS), given a measurement vector b with corruptions: b=Ax0+f0, can we recover x0 and f0 via the reweighted l1 minimization: minimize |x| + lambda*|f| subject to Ax+f=b? Here the m by n measurement matrix A is a partial Fourier matrix, x0 denotes the n dimensional ground true signal vector, f0 denotes the m-dimensional corrupted noise vector, it is assumed that a positive fraction of entries in the measurement vector b are corrupted by the non-zero entries of f0. This problem had been studied in literatures [1-3], unfortunately, certain random assumptions (which are often hard to meet in practice) are required for the signal x0 in these papers. In this paper, we show that x0 and f0 can be recovered exactly by the solution of the above reweighted l1 minimization with high probability provided that m>O(card(x0)log(n)log(n)) and n is prime, here card(x0) denotes the cardinality (number of non-zero entries) of x0. Except the sparsity, no extra assumption is needed for x0.