Iterated Nonlocal Means for Texture Restoration

The recent nonlocal means filter is a very successful technique for denoising textured images. In this paper, we formulate a variational technique that leads to an adaptive version of this filter. In particular, in an iterative manner, the filtering result is employed to redefine the similarity of patches in the next iteration. We further introduce the idea to replace the neighborhood weighting by a sorting criterion. This addresses the parameter selection problem of the original nonlocal means filter and leads to favorable denoising results of textured images, particularly in case of large noise levels. In Scale Space and Variational Methods in Computer Vision, Springer LNCS 4485, F. Sgallari et al. (Eds.), pp. 13-24, May 2007. c © Springer-Verlag Berlin Heidelberg 2007 1 From neighborhood filters to the nonlocal means filter In recent years, increasingly sophisticated filtering techniques have been developed in order to remove noise from a given input image f : (Ω ⊂ R) → R. While linear Gaussian filtering u(x) = Gρ ∗ f(x) = ∫ Gρ(x)f(x− x′) dx′ (1) with a Gaussian Gρ of width ρ > 0 is known to blur relevant image structures, more sophisticated nonlinear filtering techniques were developed, such as the total variation filtering [10], also known as the ROF model, which minimizes the cost functional: E(u) = ∫ (f − u) dx+ λ ∫ |∇u| dx. (2) The ROF model is closely related to nonlinear diffusion filters [9], in particular to the total variation flow [1]