Bayesian Denoising: From MAP to MMSE Using Consistent Cycle Spinning

A. Kazerouni, U.S. Kamilov, E. Bostan, M. Unser

IEEE Signal Processing Letters, vol. 20, no. 3, pp. 249-252, March 2013.

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.

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AUTHOR="Kazerouni, A. and Kamilov, U.S. and Bostan, E. and Unser, M.",
TITLE="Bayesian Denoising: {F}rom {MAP} to {MMSE} Using Consistent Cycle
        Spinning",
JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2013",
volume="20",
number="3",
pages="249--252",
month="March",
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