Preconditioning techniques for an image deblurring problem |
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| Authors: | Ke Chen Faisal Fairag Adel Al‐Mahdi |
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| Affiliation: | 1. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK;2. Department of Mathematics and statistics, KFUPM, Dhahran 31261, Saudi Arabia |
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| Abstract: | In this paper, we consider the solution of a large linear system of equations, which is obtained from discretizing the Euler–Lagrange equations associated with the image deblurring problem. The coefficient matrix of this system is of the generalized saddle point form with high condition number. One of the blocks of this matrix has the block Toeplitz with Toeplitz block structure. This system can be efficiently solved using the minimal residual iteration method with preconditioners based on the fast Fourier transform. Eigenvalue bounds for the preconditioner matrix are obtained. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | preconditioning technique saddle‐point problems image deblurring Krylov subspace method TV regularization primal dual formulation BTTB matrix FFT |
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