Mix-distribution modeling for overcomplete denoising

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 estimatesfor points belongingtomultiple overlapping windows are calculated as themean 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.