Image and movie denoising by nonlocal means

Neighborhood filters are image and movie filters which reduce the noise by averaging similar pixels. The object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other classes of filters. First a CCD noise model will be presented justifying this class of algorithm. A classification of neighborhood filters is proposed, including classical image and movie denoising methods and a new one, the nonlocal-means (NL-means). In order to compare denoising methods three principles will be introduced. The first principle, “method noise”, specifies that only noise must be removed from an image. Second a “noise to noise” principle states that a denoising method must transform a white noise into a white noise. This principle characterizes artifact-free methods. A third principle, the “statistical optimality”, permits to compare the performance of neighborhood filters. The three principles will be applied to compare ten different image and movie denoising methods. It will be first shown that only wavelet thresholding methods and NL-means give an acceptable method noise. Second, that neighborhood filters are the only ones to satisfy the “noise to noise” principle. Third, that among them NL-means is closest to statistical optimality. A particular attention is paid to movie denoising methods. Motion compensated denoising methods turn out to be neighborhood filters where the neighborhood is constrained to stay on a single trajectory. It is demonstrated that this constraint is harmful for denoising purposes and that space-time NL-means preserves more movie details.