Istituto di Informatica e Telematica     
Menchi O., Lotti G., Favati P. Regularizing inverse preconditioners for symmetric band Toeplitz matrices. In: Numerical Linear Algebra in Signals and Systems (Monopoli, 2006).
The image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem efficiently the iterative methods have been shown to be effective. We consider here the case of a blurring function defined by space invariant and band limited PSF, which is modelled by a linear system having a band block Toeplitz structure with band Toeplitz blocks. In order to reduce the number of iterations required to obtain acceptable reconstruction, an Inverse Toeplitz preconditioner for problems with Toeplitz structure has been proposed by Hanke and Nagy. The cost per iteration of their method is of O(n2 log n) operations, where n2 is the pixels number of the 2D image, regardless of the band structure of the original matrix. We propose inverse preconditioners with band Toeplitz structure, which lower the cost to O(n2) and show experimentally the same speed of convergence and reconstruction efficiency of the Inverse Toeplitz preconditioner.
DOI: 10.1155/2007/85606
Subject image restoration
Toeplitz blocks
G.1.3 Numerical Linear Algebra

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