Algorithms for Structured Total Least Squares Problems with Applications to Blind Image Deblurring
Algorithms for Structured Total Least Squares Problems with Applications to Blind Image Deblurring
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Date
2002-08-30
Authors
Kalsi, Anoop
O'Leary, Dianne
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Abstract
Mastronardi, Lemmerling, and van Huffel presented an algorithm for solving
a total least squares problem when the matrix and its perturbations are
Toeplitz. A Toeplitz matrix is a special kind of matrix with small
displacement rank. Here we generalize the fast algorithm to any matrix
with small displacement rank. In particular, we show how to efficiently
construct the generators whenever M has small displacement rank and show
that in many important cases the Cholesky factorization of the matrix M^TM
can also be determined fast. We further extend this problem to Tikhonov
regularization of ill-posed problems and illustrate the use of the
algorithm on an image deblurring problem.
(Also UMIACS-TR-2002-70)