DocumentCode
830896
Title
Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem
Author
Wohlberg, Brendt
Author_Institution
Los Alamos Nat. Lab., NM, USA
Volume
51
Issue
12
fYear
2003
Firstpage
3053
Lastpage
3060
Abstract
Certain sparse signal reconstruction problems have been shown to have unique solutions when the signal is known to have an exact sparse representation. This result is extended to provide bounds on the reconstruction error when the signal has been corrupted by noise or is not exactly sparse for some other reason. Uniqueness is found to be extremely unstable for a number of common dictionaries.
Keywords
adaptive signal processing; inverse problems; random noise; signal reconstruction; signal representation; adaptive signal decomposition; basis selection; inverse problem; noise sensitivity; signal dictionary; signal reconstruction error bounds; sparse signal representations; Dictionaries; Electroencephalography; Fourier transforms; Inverse problems; Matching pursuit algorithms; Noise generators; Signal reconstruction; Signal representations; Signal resolution; Wavelet transforms;
fLanguage
English
Journal_Title
Signal Processing, IEEE Transactions on
Publisher
ieee
ISSN
1053-587X
Type
jour
DOI
10.1109/TSP.2003.819006
Filename
1246511
Link To Document