Algorithms for Toeplitz Matrices with Applications to Image Deblurring: Solving linear equations or linear least squares problems with low displacement rank using the Schur Algorithm - Symon Kimitei
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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 reg ... Full description
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Description
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.
More Information
| Author | Symon Kimitei |
|---|---|
| Publisher | LAP LAMBERT Academic Publishing |
| Release year | 2011 |
| Cover type | Softcover |
| EAN | 9783844314267 |