Deterministic Construction of Compressed Sensing Matrices using BCH Codes
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 DOI:
 10.48550/arXiv.0908.0619
 arXiv:
 arXiv:0908.0619
 Bibcode:
 2009arXiv0908.0619A
 Keywords:

 Computer Science  Information Theory
 EPrint:
 8 pages, 2 figures, 1 table