Scarlett, Jonathan and Evans, Jamie S. and Dey, Subhrakanti (2013) Compressed Sensing With Prior Information: Information-Theoretic Limits and Practical Decoders. IEEE Transactions on Signal Processing, 61 (2). pp. 427-439. ISSN 1053-587X

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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 ,..., xN ] T has a randomly generated sparsity pattern, where the i -th entry is non-zero with probability pi . 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.

Item Type:	Article
Keywords:	Basis pursuit; compressed sensing; compressive sampling; information-theoretic bounds; Lasso; orthogonal matching pursuit; prior information; sparsity pattern recovery; support recovery;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering
Item ID:	12704
Identification Number:	https://doi.org/10.1109/TSP.2012.2225051
Depositing User:	Subhrakanti Dey
Date Deposited:	06 Apr 2020 11:13
Journal or Publication Title:	IEEE Transactions on Signal Processing
Publisher:	Institute of Electrical and Electronics Engineers
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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