Sparse reconstruction via the reed-muller sieve


Journal Article

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 N2 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 ℓ2/ℓ2 error bounds derived in this paper are tighter than the ℓ2/ℓ1 bounds arising from random ensembles and the ℓ1/ℓ1 bounds arising from expander-based ensembles. © 2010 IEEE.

Full Text

Duke Authors

Cited Authors

  • Calderbank, R; Howard, S; Jafarpour, S

Published Date

  • August 23, 2010

Published In

  • Ieee International Symposium on Information Theory Proceedings

Start / End Page

  • 1973 - 1977

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2010.5513361

Citation Source

  • Scopus