Compressed Sensing with Prior Information: Strategies, Geometry, and Bounds

João F. C. Mota, Nikos Deligiannis, Miguel Raul Dias Rodrigues

Research output: Contribution to journalArticle

38 Citations (Scopus)
30 Downloads (Pure)

Abstract

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via L1-L1and L1-L2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, L1-L1 minimization improves the performance of CS dramatically. In contrast, L1-L2 minimization has a performance very similar to classical CS and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results.
Original languageEnglish
Pages (from-to)4472-4496
Number of pages25
JournalIEEE Transactions on Information Theory
Volume63
Issue number7
Early online date19 Apr 2017
DOIs
Publication statusPublished - Jul 2017

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