Structural adaptive smoothing: Images, fMRI and DWI

The talk presents a class of structural adaptive smoothing methods developed at WIAS. The main focus will be on the Propagation-Separation (PS) approach proposed in Polzehl and Spokoiny (2006). The method allows to simultaneously identify regions of homogeneity with respect to a prescribed model (structural assumption) and to use this information to improve local estimates. This is achieved by an iterative procedure. The name Propagation-Separation is a synonym for the two main properties of the algorithms. In case of homogeneity, that is if the prescribed model holds with the same parameters within a large region, the algorithm essentially delivers a series of nonadaptive estimates with decreasing variance and propagates to the best estimate from this series. Separation means that, as soon as in two design points i and j significant differences are detected between estimates, observations in j will not be used to estimate the parameter in j. We establish some theoretical {nonasymptotic} results on properties of the new algorithm. We present how this approach can be adjusted to different imaging modalities, ranging from denoising of greyvalue and color images, to the analysis of data from functional Magnetic Resonance Imaging (fMRI) and Diffusion Weigted Imaging (DWI) experiments.