For large-scale image reconstruction problems, the iterative regularization methods can be favorable alternatives to the direct methods. We analyze preconditioners for regularizing gradient-type iterations applied to problems with 2D band Toeplitz coefficient matrix. For problems having separable and positive definite matrices, the fit preconditioner we have introduced in a previous paper has been shown to be effective in conjunction with CG. The cost of this preconditioner is of O(n^2) operations per iteration, where n^2 is the pixels number of the image, whereas the cost of the circulant preconditioners commonly used for this type of problems is of O(n^2 log n) operations per iteration. In this paper the extension of the fit preconditioner to more general cases is proposed: namely the nonseparable positive definite case and the symmetric indefinite case. The major difficulty encountered in this extension concerns the factorization phase, where a further approximation is required. Three approximate factorizations are proposed. The preconditioners thus obtained have still a cost of O(n^2) operations per iteration. A numerical experimentation shows that the fit preconditioners Are competitive with the regularizing Chan preconditioner, both in the regularing efficiency and the computational cost.
|Autori interni:||MENCHI, ORNELLA|
|Autori:||FAVATI P; LOTTI G; MENCHI O|
|Titolo:||Preconditioners based on fit techniques for the iterative regularization in the image deconvolution problem|
|Anno del prodotto:||2005|
|Digital Object Identifier (DOI):||10.1007/s10543-005-2639-7|
|Appare nelle tipologie:||1.1 Articolo in rivista|