Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 58, Issue 5, Pages 2613-2622Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2010.2042490
Keywords
Bandlets; best basis; compressed sensing; cosine packets; sparsity; wavelet packets
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This paper proposes a best basis extension of compressed sensing recovery. Instead of regularizing the compressed sensing inverse problem with a sparsity prior in a fixed basis, our framework makes use of sparsity in a tree-structured dictionary of orthogonal bases. A new iterative thresholding algorithm performs both the recovery of the signal and the estimation of the best basis. The resulting reconstruction from compressive measurements optimizes the basis to the structure of the sensed signal. Adaptivity is crucial to capture the regularity of complex natural signals. Numerical experiments on sounds and geometrical images indeed show that this best basis search improves the recovery with respect to fixed sparsity priors.
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