Title :
Sparse signal recovery in Hilbert spaces
Author :
Pope, G. ; Bolcskei, Helmut
Author_Institution :
Dept. of IT & EE, ETH Zurich, Zurich, Switzerland
Abstract :
This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the number of (possibly infinite-dimensional) subspaces participating in the signal´s representation. Our general results recover uncertainty relations and coherence-based recovery thresholds for sparse signals, block-sparse signals, multi-band signals, signals in shift-invariant spaces, and signals in finite unions of (possibly infinite-dimensional) subspaces. Moreover, we improve upon and generalize several of the existing results and, in many cases, we find shortened and simplified proofs.
Keywords :
Hilbert spaces; signal representation; Hilbert spaces; block-sparse signals; coherence-based recovery thresholds; coherence-based sparse signal recovery; infinite-dimensional subspaces; multiband signals; signal representation; Coherence; Hilbert space; Kernel; Matching pursuit algorithms; Sparks; Uncertainty; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
978-1-4673-2580-6
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2012.6283506