|
Compressed sensing with prior Information: Strategies, geometry, and bounds This publication appears in: IEEE Transactions on Information Theory Authors: J. Mota, N. Deligiannis and M. Rodrigues Volume: 63 Issue: 7 Pages: 4472-4496 Publication Date: Jul. 2017
Abstract: We address the problem of compressed sensing (CS)with prior information: reconstruct a target CS signal with theaid of a similar signal that is known beforehand, our priorinformation. We integrate the additional knowledge of the similarsignal into CS via l1-l1 and l1-l2 minimization. We thenestablish bounds on the number of measurements required bythese problems to successfully reconstruct the original signal.Our bounds and geometrical interpretations reveal that if theprior information has good enough quality, l1-l1 minimizationimproves the performance of CS dramatically. In contrast, l1-l2 minimization has a performance very similar to classicalCS and brings no significant benefits. In addition, we use theinsight provided by our bounds to design practical schemes toimprove prior information. All our findings are illustrated withexperimental results.
|
