Exact Transform-Domain Noise Variance for Collaborative Filtering of Stationary Correlated Noise

Abstract

Collaborative filters perform denoising through transform-domain shrinkage of a group of similar blocks extracted from an image. Existing methods for collaborative filtering of stationary correlated noise have all used simple approximations of the transform noise power spectrum adopted from methods which do not employ block grouping. We note the inaccuracies of these approximations and introduce a method for the exact computation and effective approximations of the noise power spectrum. Unlike earlier methods, the calculated noise variances are exact even when noise in one block is correlated with noise in any of the other blocks. We discuss the adoption of the exact noise power spectrum within shrinkage, in similarity testing (block matching), and in aggregation. Extensive experiments support the proposed method over earlier crude approximations used by image denoising filters such as BM3D, demonstrating dramatic improvement in many challenging conditions.