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
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;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2003.819006
