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<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gkn2pu46ozb4tmkxczacnmtvkq" style="color: black;">IEEE Transactions on Signal Processing</a>
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 Minimum-Mean-Squared-Error (MMSE) estimator. We show that this estimator also leads to a simple formula, in the form of a plain<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/tsp.2010.2046596">doi:10.1109/tsp.2010.2046596</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a2vpi2xo5rhcjmc732gdqh5dwm">fatcat:a2vpi2xo5rhcjmc732gdqh5dwm</a> </span>
more »... expression for evaluating the contribution of every atom in the solution. An extension of the model to real-world signals is also offered, considering heterosedastic non-zero 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 re-developed for this extended model, again resulting in closed-form simple algorithms. Finally, the superiority of the MMSE estimator is demonstrated both on synthetically generated signals and on real-world signals (image patches).
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