A two-stage denoising filter: the preprocessed Yaroslavsky filter
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.