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Anisotropic diffusion methods are well known for giving good qualitative results for image denoising. This paper gives a review of the anisotropic diffusion methodology and its application to image denoising. We propose a fixed-point iteration using a multigrid solver 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 (Brent-NCP), combining Brent's method and the normalized cumulative periodogram information of the misfit, is also introduced. We test our algorithm on several common test images with different noise levels. The experimental results demonstrate the effectiveness of the anisotropic diffusion with a multigrid approach and the broad applicability of the Brent-NCP parameter-choice algorithm. [ABSTRACT FROM AUTHOR]