Sparse Reconstruction via The Reed-Muller Sieve

Details Sparse Reconstruction via The Reed-Muller Sieve Sparse Reconstruction via The Reed-Muller Sieve

2010-04-16

arxiv.org/abs/1004.2926v1

Computer Science

Information Theory

To appear in ISIT 2010

Scientific paper

This paper introduces the Reed Muller Sieve, a deterministic measurement matrix for compressed sensing. The columns of this matrix are obtained by exponentiating codewords in the quaternary second order Reed Muller code of length $N$. For $k=O(N)$, the Reed Muller Sieve improves upon prior methods for identifying the support of a $k$-sparse vector by removing the requirement that the signal entries be independent. The Sieve also enables local detection; an algorithm is presented with complexity $N^2 \log N$ that detects the presence or absence of a signal at any given position in the data domain without explicitly reconstructing the entire signal. Reconstruction is shown to be resilient to noise in both the measurement and data domains; the $\ell_2 / \ell_2$ error bounds derived in this paper are tighter than the $\ell_2 / \ell_1$ bounds arising from random ensembles and the $\ell_1 /\ell_1$ bounds arising from expander-based ensembles.

Affiliated with

Also associated with

No associations

Rating

Sparse Reconstruction via The Reed-Muller Sieve does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sparse Reconstruction via The Reed-Muller Sieve, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sparse Reconstruction via The Reed-Muller Sieve will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69440