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Noise sensitivity of sparse signal representations: reconstruction error bounds for the inverse problem

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1 Author(s)
Wohlberg, B. ; Los Alamos Nat. Lab., NM, USA

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.

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Signal Processing, IEEE Transactions on  (Volume:51 ,  Issue: 12 )