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Proceedings Paper

Regularized solution of block-banded block Toeplitz systems
Author(s): Dario Andrea Bini; A. Farusi; G. Fiorentino; Beatrice Meini
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Paper Abstract

Given two n X n Toeplitz matrices T1 and T2, and a vector b (epsilon) Rn(2), consider the linear system Ax equals b - (eta) , where (eta) (epsilon) Rn(2) is an unknown vector representing the noise and A equals T1 (direct product) T2. Recovering approximations of x, given A and b, is encountered in image restoration problems. We propose a method for the approximation of the solution x that has good regularization properties. The algorithm is based on a modified version of Newton's iteration for matrix inversion and relies on the concept of approximate displacement rank. We provide a formal description of the regularization properties of Newton's iteration in terms of filters and determine bounds to the number of iterations that guarantee regularization. The method is extended to deal with more general systems where A equals (summation)i equals 1h T1(i) (direct product) T2(i). The cost of computing regularized inverses is O(n log n) operations (ops), the cost of solving the system Ax equals b is O(n2 log n) ops. Numerical experiments which show the effectiveness of our algorithm are presented.

Paper Details

Date Published: 13 November 2000
PDF: 12 pages
Proc. SPIE 4116, Advanced Signal Processing Algorithms, Architectures, and Implementations X, (13 November 2000); doi: 10.1117/12.406490
Show Author Affiliations
Dario Andrea Bini, Univ. degli Studi di Pisa (Italy)
A. Farusi, Istituto de Elaborazione dell'Informazione (Italy)
G. Fiorentino, Univ. degli Studi di Pisa (Italy)
Beatrice Meini, Univ. degli Studi di Pisa (Italy)


Published in SPIE Proceedings Vol. 4116:
Advanced Signal Processing Algorithms, Architectures, and Implementations X
Franklin T. Luk, Editor(s)

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