The focus of this research is on estimation and signal processing of multidimensional data. The work involves two main areas of research. The first deals with the development of multiscale models and estimation methods for Markov random fields (MRF) and their application to problems in image processing such as segmentation, edge detection and coding. The goal of this effort is to develop multiresolution techniques for MRF's which extend the wavelet methods introduced recently for the multiscale representation of deterministic signals. The second part of the research focusses on the development of efficient multigrid and domain decomposition methods for the solution of multidimensional estimation problems, and for inverse problems or impedance imaging. This work is part of a collaborative research effort with a group at MIT led by Professor Alan Willsky.
