Year: 2009
Type: preprint
Abstract: In this paper we introduce deterministic $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that $\frac{\log m}{\log k}\approx \frac{\log(\log_2 n)}{\log(\log_2 k)}$. The columns of these matrices are binary BCH code vectors that their zeros are replaced with -1 (excluding the normalization factor). The samples obtained by these matrices can be easily converted to the original sparse signal; more precisely, for the noiseless samples, the simple Matching Pursuit technique, even with less than the common computational complexity, exactly reconstructs the sparse signal. In addition, using Devore's binary matrices, we expand the binary scheme to matrices with $\{0,1,-1\}$ elements.
Source: arXiv (Cornell University)
Authors: Amini, Arash, Marvasti, Farokh
Institution: Sharif University of Technology
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1672177196