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2010

Closed-form MMSE estimation for signal denoising under sparse representation modeling over a unitary dictionary

12 years 10 months ago
Closed-form MMSE estimation for signal denoising under sparse representation modeling over a unitary dictionary
This paper deals with the Bayesian signal denoising problem, assuming a prior based on a sparse representation modeling over a unitary dictionary. It is well known that the maximum a posteriori probability (MAP) estimator in such a case has a closed-form solution based on a simple shrinkage. The focus in this paper is on the better performing and less familiar minimummean-squared-error (MMSE) estimator. We show that this estimator also leads to a simple formula, in the form of a plain recursive expression for evaluating the contribution of every atom in the solution. An extension of the model to real-world signals is also offered, considering heteroscedastic nonzero entries in the representation, and allowing varying probabilities for the chosen atoms and the overall cardinality of the sparse representation. The MAP and MMSE estimators are redeveloped for this extended model, again resulting in closed-form simple algorithms. Finally, the superiority of the MMSE estimator is demonstrate...
Matan Protter, Irad Yavneh, Michael Elad
Added 22 May 2011
Updated 22 May 2011
Type Journal
Year 2010
Where TSP
Authors Matan Protter, Irad Yavneh, Michael Elad
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