Multigrid for Differential-Convolution Problems Arising in Image Processing

Hon Fu Raymond CHAN, Tony F. CHAN, W. L. WAN

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review


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 languageEnglish
Title of host publicationScientific Computing: Proceedings of the Workshop, 10 - 12 March 1997, Hong Kong
EditorsGene H. GOLUB, Shui-Hong LUI, T. Franklin LUK, Robert J. PLEMMONS
PublisherSpringer Singapore
Number of pages15
ISBN (Print)9789813083608
Publication statusPublished - Mar 1997
Externally publishedYes
Event6th Workshop on Scientific Computing - , Hong Kong
Duration: 10 Mar 199712 Mar 1997


Workshop6th Workshop on Scientific Computing
Country/TerritoryHong Kong


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