Math @ Duke

Publications [#235960] of Robert Calderbank
Papers Published
 Calderbank, R; Howard, S; Jafarpour, S, Sparse reconstruction via the reedmuller sieve,
IEEE International Symposium on Information Theory  Proceedings
(2010),
pp. 19731977 [doi]
(last updated on 2018/02/17)
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 ksparse 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 expanderbased ensembles. © 2010 IEEE.


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