Collaborative Filtering of Correlated Noise: Exact Transform-Domain Variance for Improved Shrinkage and Patch Matching

Collaborative filters perform denoising through transform-domain shrinkage of a group of similar patches extracted from an image. Existing collaborative filters of stationary correlated noise have all used simple approximations of the transform noise power spectrum adopted from methods which do not employ patch grouping and instead operate on a single patch. We note the inaccuracies of these approximations and introduce a method for the exact computation of the noise power spectrum. Unlike earlier methods, the calculated noise variances are exact even when noise in one patch is correlated with noise in any of the other patches. We discuss the adoption of the exact noise power spectrum within shrinkage, in similarity testing (patch matching), and in aggregation. We also introduce effective approximations of the spectrum for faster computation. Extensive experiments support the proposed method over earlier crude approximations used by image denoising filters such as Block-Matching and 3D-filtering (BM3D), demonstrating dramatic improvement in many challenging conditions.