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Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices


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 operations, where 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 and in experiments showed the same speed of convergence and reconstruction efficiency as the inverse Toeplitz preconditioner.


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Favati, P., Lotti, G. & Menchi, O. Regularizing Inverse Preconditioners for Symmetric Band Toeplitz Matrices. EURASIP J. Adv. Signal Process. 2007, 085606 (2007).

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  • Information Technology
  • Linear System
  • Iterative Method
  • Quantum Information
  • Regularization Method