Smoothers for Discontinuous Signals

We discuss the interplay between local M -smoothers, Bayes smoothers and some nonlinear filters for edge-preserving signal reconstruction. We prove that all smoothers in question are nonlinear filters in a precise sense and characterize their fixed points. Then a Potts model is adopted for segmentation. For 1-d signals, an exact algorithm for the computation of maximum posterior modes is derived and applied to a phantom and to 1-d fMRI-data.