Statistical Signal Processing and Estimation for Spatial and Multidimensional Data: Multiscale Analysis of Markov Random Fields, and Efficient Algorithms

本文的研究重点是多维数据的估计和信号处理。这项工作涉及两个主要的研究领域。第一部分讨论了马尔可夫随机场（MRF）的多尺度模型和估计方法的发展及其在图像处理中的应用，如分割、边缘检测和编码。这项工作的目标是开发多分辨率的磁振场技术，扩展了最近引入的小波方法，用于确定性信号的多尺度表示。第二部分的研究重点是开发有效的多网格和区域分解方法，用于解决多维估计问题，以及反演问题或阻抗成像。这项工作是与麻省理工学院艾伦·威尔斯基教授领导的一个小组合作研究的一部分。

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.