Convolutional Compressed Sensing Using Deterministic Sequences
Abstract
In this paper, a new class of circulant matrices built from deterministic sequences is proposed for convolution-based compressed sensing (CS). In contrast to random convolution, the coefficients of the underlying filter are given by the discrete Fourier transform of a deterministic sequence with good autocorrelation. Both uniform recovery and non-uniform recovery of sparse signals are investigated, based on the coherence parameter of the proposed sensing matrices. Many examples of the sequences are investigated, particularly the Frank-Zadoff-Chu (FZC) sequence, the \textit{m}-sequence and the Golay sequence. A salient feature of the proposed sensing matrices is that they can not only handle sparse signals in the time domain, but also those in the frequency and/or or discrete-cosine transform (DCT) domain.
Cite
@article{arxiv.1210.7506,
title = {Convolutional Compressed Sensing Using Deterministic Sequences},
author = {Kezhi Li and Lu Gan and Cong Ling},
journal= {arXiv preprint arXiv:1210.7506},
year = {2015}
}
Comments
A major overhaul of the withdrawn paper Orthogonal symmetric Toeplitz matrices for compressed sensing: Statistical isometry property