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Mix-distribution modeling for overcomplete denoising

Vladimir Katkovnik, Alessandro Foi, Karen Egiazarian
Localized or windowed data denoising based on linear transforms equipped with some thresholding operator is a usual approach in modern signal and image processing. With overlapping windows, techniques of this kind can be
interpreted as overcomplete (redundant) data transforms (representations). In the simplest formulation, the final
estimates for points belonging to multiple overlapping windows are calculated as the mean of the estimates
independently obtained for each of the windows. In this paper we propose a general approach leading to a mix-distribution modeling of the overcomplete data and to least-squares optimal final estimates in the form of weighted
average of the least-square estimates for the windowed data. Experiments demonstrate the advanced performance of this class of the algorithms, in particular in comparison with the standard ones using the sample averaging of the
windowed estimates.
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