Compressed sensing with prior information: information-theoretic limits and practical decoders
Date
2013
Authors
Scarlett, J.
Evans, J.S.
Dey, S.
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Journal article
Citation
IEEE Transactions on Signal Processing, 2013; 61(2):427-439
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Abstract
This paper considers the problem of sparse signal recovery when the decoder has prior information on the sparsity pattern of the data. The data vector x = [x(1), ... , x(N)](T) has a randomly generated sparsity pattern, where the i-th entry is non-zero with probability p(i). Given knowledge of these probabilities, the decoder attempts to recover x based on M random noisy projections. Information-theoretic limits on the number of measurements needed to recover the support set of x perfectly are given, and it is shown that significantly fewer measurements can be used if the prior distribution is sufficiently non-uniform. Furthermore, extensions of Basis Pursuit, LASSO, and Orthogonal Matching Pursuit which exploit the prior information are presented. The improved performance of these methods over their standard counterparts is demonstrated using simulations.
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Link to a related website: http://mural.maynoothuniversity.ie/12704/1/SD_compressed.pdf, Open Access via Unpaywall
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Copyright 2012 IEEE