Abstract
We consider the use of multigrid methods for solving certain differential-convolution equations which arise in regularized image deconvolution problems. We first point out that the usual smoothing procedures (e.g. relaxation smoothers) do not work well for these types of problems because the high frequency error components are not smoothed out. To overcome this problem, we propose to use optimal fast-transform preconditioned conjugate gradient smoothers. The motivation is to combine the advantages of multigrid (mesh independence) and fast transform based methods (clustering of eigenvalues for the convolution operator). Numerical results for Tikhonov regularization with the identity and the Laplacian operators show that the resulting method is effective. However, preliminary results for total variation regularization show that this case is much more difficult and further analysis is required.
Original language | English |
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Title of host publication | Scientific Computing: Proceedings of the Workshop, 10 - 12 March 1997, Hong Kong |
Editors | Gene H. GOLUB, Shui-Hong LUI, T. Franklin LUK, Robert J. PLEMMONS |
Publisher | Springer Singapore |
Pages | 58-72 |
Number of pages | 15 |
ISBN (Print) | 9789813083608 |
Publication status | Published - Mar 1997 |
Externally published | Yes |
Event | 6th Workshop on Scientific Computing - , Hong Kong Duration: 10 Mar 1997 → 12 Mar 1997 |
Workshop
Workshop | 6th Workshop on Scientific Computing |
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Country/Territory | Hong Kong |
Period | 10/03/97 → 12/03/97 |