Algorithms for Toeplitz Matrices with Applications to Image Deblurring - Kimitei, Symon
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In this thesis, we present the O(n log^2 n) superfast linear least squares Schur algorithm(ssschur). The algorithm we describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This algorithm is based on the O(n^2) Schur algorithm, sped up via FFT. The algorithm solves an ill-conditioned Toeplitz-like system using Tikhonov regularization. The regularized system solved is Toeplitz-like and is of displacement rank, 4. In this thesis, we also show the effect of the choice of the regularization parameter on the quality of the images reconstructed.…mehr

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Produktbeschreibung
In this thesis, we present the O(n log^2 n) superfast linear least squares Schur algorithm(ssschur). The algorithm we describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This algorithm is based on the O(n^2) Schur algorithm, sped up via FFT. The algorithm solves an ill-conditioned Toeplitz-like system using Tikhonov regularization. The regularized system solved is Toeplitz-like and is of displacement rank, 4. In this thesis, we also show the effect of the choice of the regularization parameter on the quality of the images reconstructed.
Autorenporträt
Instructor de Matemáticas, Universidad Estatal de Kennesaw, 2008 - Presente. Instructor de Matemáticas, Universidad Estatal de Georgia, 2007-2008. Msc. Matemáticas, Universidad Estatal de Georgia, 2008. Bsc. Matemáticas, Universidad Estatal de Kennesaw, 1999. Bsc. Ciencias de la Computación, Universidad Estatal de Kennesaw, 1998.