Piecewise Constant Signal Nonlinear Filtering based on Local Center / Surround Shrinkage

The article is devoted to the synthesis of a new nonlinear filtration methods for a piecewise constant signals distorted by Poisson noise. The proposed approach to filtering assumes the principles and concepts of statistical learning, understood as learning based on input data. (cf. adaptive filtering). The synthesis is focused on a special representation of signals by samples of counts of controlled size (sampling representation). Based on the specifics of such representation, a statistical model of the signal is concretized to a parametric probabilistic model in the form of a system of receptive fields. This model allows for a very simple procedure for estimating the count probability density, which in turn is an approximation of the underling piecewise constant signal. The resulting procedure for restoring piecewise constant signals turned out to be very similar to the algorithms of wavelet-thresholding (regression shrinkage) that are actively developing today.