A Multigrid method for restoration and regularization of images with Dirichlet boundary conditions

Marco Donatelli

doi:10.1117/12.504228

24 December 2003 A Multigrid method for restoration and regularization of images with Dirichlet boundary conditions

Marco Donatelli

Author Affiliations +

Proceedings Volume 5205, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII; (2003) https://doi.org/10.1117/12.504228
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

In many 2D image restoration problems, such as image deblurring with Dirichlet boundary conditions, we deal with two-level linear systems whose coefficient matrix is a banded block Toeplitz matrix with banded Toeplitz blocks (BTTB). Usually, these matrices are ill-conditioned since they are associated to generating functions which vanish at (π, π) or in neighborhood of it. In this work, we solve such BTTB systems by applying an Algebraic Multi-Grid method (AMG). The technique we propose has an optimality property, i.e., its cost is of O(n₁ • n₂) arithmetic operations, where n₁ x n₂ is the size of the images. Unfortunately, in the case of images affected by noise, our AMG method does not provide satisfactory regularization effects. Therefore, we propose two Tikhonov-like techniques, based on a regularization parameter, which can be applied to AMG method in order to reduce the noise effects.

Citation Download Citation

Marco Donatelli "A Multigrid method for restoration and regularization of images with Dirichlet boundary conditions", Proc. SPIE 5205, Advanced Signal Processing Algorithms, Architectures, and Implementations XIII, (24 December 2003); https://doi.org/10.1117/12.504228

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