Closed-form mmse estimator for denoising signals under sparse representation modelling

Matan Protter, Irad Yavneh, Michael Elad
<span title="">2008</span> <i title="IEEE"> 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel </i> &nbsp;
This paper deals with the signal denoising problem, assuming a prior based on a sparse representation with respect to a unitary dictionary. It is well known that the Maximum Aposteriori Probability (MAP) estimator in such a case has a closed-form solution based on shrinkage. The focus in this paper is on the better performing and less familiar Minimum-Mean-Squared-Error (MMSE) estimator. We show that this estimator also leads also to a simple closed-form formula, in the form of a plain
more &raquo; ... expression for evaluating the contribution of every atom in the solution. We demonstrate this formula, and compare it to the MAP and the Random-OMP method devised for approximating the MMSE result.
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