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Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

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4 Author(s)
Kazerouni, A. ; Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland ; Kamilov, U.S. ; Bostan, E. ; Unser, M.

We introduce a new approach for the implementation of minimum mean-square error (MMSE) denoising for signals with decoupled derivatives. Our method casts the problem as a penalized least-squares regression in the redundant wavelet domain. It exploits the link between the discrete gradient and Haar-wavelet shrinkage with cycle spinning. The redundancy of the representation implies that some wavelet-domain estimates are inconsistent with the underlying signal model. However, by imposing additional constraints, our method finds wavelet-domain solutions that are mutually consistent. We confirm the MMSE performance of our method through statistical estimation of Lévy processes that have sparse derivatives.

Published in:

Signal Processing Letters, IEEE  (Volume:20 ,  Issue: 3 )

Date of Publication:

March 2013

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