  This paper describes a simple image noise removal method which combines a
preprocessing step with the Yaroslavsky filter for strong numerical, visual,
and theoretical performance on a broad class of images. The framework developed
is a two-stage approach. In the first stage the image is filtered with a
classical denoising method (e.g., wavelet or curvelet thresholding). In the
second stage a modification of the Yaroslavsky filter is performed on the
original noisy image, where the weights of the filters are governed by pixel
similarities in the denoised image from the first stage. Similar prefiltering
ideas have proved effective previously in the literature, and this paper
provides theoretical guarantees and important insight into why prefiltering can
be effective. Empirically, this simple approach achieves very good performance
for cartoon images, and can be computed much more quickly than current
patch-based denoising algorithms.
