Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#235960] of Robert Calderbank

Papers Published

  1. Calderbank, R; Howard, S; Jafarpour, S, Sparse reconstruction via the reed-muller sieve, IEEE International Symposium on Information Theory - Proceedings (2010), pp. 1973-1977 [doi]
    (last updated on 2018/05/23)

    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.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320