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Journal Articles IEEE Transactions on Signal Processing Year : 2010

Best Basis Compressed Sensing


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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Dates and versions

hal-00365017 , version 1 (02-03-2009)
hal-00365017 , version 2 (15-03-2009)
hal-00365017 , version 3 (10-01-2010)



Gabriel Peyré. Best Basis Compressed Sensing. IEEE Transactions on Signal Processing, 2010, 58 (5), pp.2613-2622. ⟨10.1109/TSP.2010.2042490⟩. ⟨hal-00365017v3⟩
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