@article {IOPORT.05600502,
    author       = {Favati, P. and Lotti, G. and Menchi, O.},
    title        = {Regularizing inverse preconditioners for symmetric band Toeplitz matrices.},
    year         = {2007},
    journal      = {EURASIP Journal on Advances in Signal Processing [electronic only]},
    volume       = {2007},
    issn         = {1687-6180},
    pages        = {Article ID 85606, 9 p.},
    publisher    = {Springer International Publishing, Basel},
    doi          = {10.1155/2007/85606},
    abstract     = {Summary: Image restoration is a widely studied discrete ill-posed problem. Among the many regularization methods used for treating the problem, iterative methods have been shown to be effective. In this paper, we consider the case of a blurring function defined by space invariant and band-limited PSF, modeled by a linear system that has a band block Toeplitz structure with band Toeplitz blocks. In order to reduce the number of iterations required to obtain acceptable reconstructions, in 13 an inverse Toeplitz preconditioner for problems with a Toeplitz structure was proposed. The cost per iteration is of $O(n^{2}\log n)$ operations, where $n^{2}$ is the pixel number of the 2D image. In this paper, we propose inverse preconditioners with a band Toeplitz structure, which lower the cost to $O(n^{2})$ and in experiments showed the same speed of convergence and reconstruction efficiency as the inverse Toeplitz preconditioner.},
    identifier   = {05600502},
}