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Thursday, September 8, 9:30 am in room MTH 3206, University of Maryland, College Park

Preconditioned Iterative Regularization

Dr. J. Nagy, Dept. of Computer Science, UMCP

nagy@cs.umd.edu

A preconditioned iterative regularization scheme is examined for solving large scale structured linear systems g = Hf + eta, arising from the discretization of ill-posed inverse problems in the presence of noise. The case where H is a block Toeplitz matrix with Toeplitz blocks is considered. The preconditioned conjugate gradient method is applied, where H is approximated by a block circulant matrix with circulant blocks, resulting in a fast 2-D FFT-based iterative scheme. It is shown how the iterations can be effectively and efficiently regularized for solving ill-posed problems by using the spectral decomposition of the preconditioner. An application to image restoration is presented. Sept. 8, Numerical Analysis Seminar, U. of MD, College Park