Group iterative methods and their applications in inverse problems
Abstract
Iterative methods are preferred for solving linear systems of equations when error build-up renders exact solution methods useless. Exact methods for solving nonlinear systems of equations usually do not exist. Popular iterative methods can be classified either as simultaneous or point iterative methods. Group-iterative methods (GIMs) update a block of variables at each step. GIMs provide unified frames of study when the blocks are allowed to contain all the variables or only one variable, extending to simultaneous and point iterative methods, respectively. For certain block-size, permutation and update direction choices, GIMs are reported to obtain unexpectedly good quality solutions for linear and nonlinear problems. In some cases, the performance of GIMs surpass those of highly acclaimed methods such as Conjugate Gradient method. Block and update direction choices to accentuate this behavior has not been addressed. In this thesis, optimal block-size and permutation selection rules have been developed, and a partitioning algorithm have been designed for the linear problem. It has been shown that update direction selection is of primary interest for nonlinear problems, and optimal update direction selection strategies have been developed. These strategies have further been refined into a global search algorithm. The methods and algorithms have been illustrated on various inverse problems in signal processing, such as PET image reconstruction and segmentation, microcalcification detection using digitized X-ray mammograms, computer generated hologram design and neural network training.
Degree
Ph.D.
Advisors
Ersoy, Purdue University.
Subject Area
Electrical engineering
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.