Calderbank, R; Howard, S; Jafarpour, S, *Sparse reconstruction via the reed-muller sieve*,
Ieee International Symposium on Information Theory Proceedings
(August, 2010),
pp. 1973-1977 [doi] .
**Abstract:**

*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 N2log 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/ℓ2error bounds derived in this paper are tighter than the ℓ2/ℓ1bounds arising from random ensembles and the ℓ1/ℓ1bounds arising from expander-based ensembles. © 2010 IEEE.*