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{\large Donghui Chen \\
{\bf Iterative Parameter-choice Algebraic Multigrid for Anisotropic Diffusion Denoising}}

Tufts University \\ Department of Mathematics \\ 503 Boston Avenue \\ Medford \\ MA 02155
\\
{\tt Donghui.Chen@tufts.edu}\\
Donghui Chen\\
Misha Kilmer\\
Scott MacLachlan\end{center}

Anisotropic diffusion methods have shown good qualitative results for
image denoising. This paper gives a review of the anisotropic diffusion
methodology and its application to image restoration. We investigate an
AMG algorithm to solve a regularized anisotropic diffusion equation,
which is not only well-posed, but also has a nontrivial steady-state
solution. A new regularization parameter-choice method, the Brent-NCP
algorithm is introduced, combining Brent's method and the normalized
cumulative periodogram (NCP) information about the residual. We test our
algorithm on three standard test images. The experimental results
demonstrate the effectiveness of the AMG approach and the broad
applications of the Brent-NCP parameter-choice algorithm.


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