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Cleaning of noise from signals is a classical and long-studied problem in signal processing. Algorithms for this task necessarily rely on an apriori knowledge about the signal characteristics, along with information about the noise properties. For signals that admit sparse representations over a known dictionary, a commonly used denoising technique is to seek the sparsest representation that synthesizes...
We consider the problem of signal separation, where the observation y = x1 +x2 +v is composed of the signals x1 and x2 to be separated, along with additive noise v. We further assume that x1 and x2 have sparse representations with respect to two different dictionaries D1 and D2, respectively. Exploiting sparse representations for signal separation has been introduced recently under the name Morphological...
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 a posteriori 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...
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