Nonlocal Image and Movie Denoising

Abstract

Neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels. The first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes. A CCD noise model will be presented justifying the involvement of neighborhood filters. A classification of neighborhood filters will be proposed, including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter, NL-means. In order to compare denoising methods three principles will be discussed. The first principle, "method noise", specifies that only noise must be removed from an image. A second principle will be introduced, "noise to noise", according to which a denoising method must transform a white noise into a white noise. Contrarily to "method noise", this principle, which characterizes artifact-free methods, eliminates any subjectivity and can be checked by mathematical arguments and Fourier analysis. "Noise to noise" will be proven to rule out most denoising methods, with the exception of neighborhood filters. This is why a third and new comparison principle, the "statistical optimality", is needed and will be introduced to compare the performance of all 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 will be paid to the application of the statistical optimality criterion for movie denoising methods. It will be pointed out that current movie denoising methods are motion compensated neighborhood filters. This amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory. Unfortunately the aperture problem makes it impossible to estimate ground true trajectories. It will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space-time NL-means preserves more movie details.

The Imaging of Dynamic Multiphase Fluid Flow Using Synchrotron-Based X-ray Microtomography at Reservoir Conditions

“…The images were then cropped around the core so each one consisted of around 1100×1100×1100 voxels with a voxel size of 3.64 µm. The images were then passed through a 2D non-local means edge preserving filter (Buades et al 2008(Buades et al , 2005 and transformed so that any small movement between scans was corrected by the process of registration. This was done by comparing each image to the first in the sequence (the reference image) using a normalised mutual information metric (Pluim et al 2000(Pluim et al , 2003 in the process of registration.…”

From Local Kernel to Nonlocal Multiple-Model Image Denoising

“…where ρ is deÞned by the penalty function in (13). Hard and soft thresholding are particular cases of this sort of estimates (Donoho and Johnstone [22]): (1) Hard thresholding.…”

“…Note that the weights used in local algorithms can be dependent also on y s , but, nevertheless, the weights are overall dominated by the distance°°x 0 − x s°°. An important example of this speciÞc type of local Þlters is the Yaroslavsky Þlter [118], referred in Buades et al [10,13] as a precursor of the nonlocal means.…”

Image Filtering Driven by Level Curves

“…conventional kernel-based mean shift, as well as to two recent algorithms that are closely related to mean-shift: UINTA [19] and NL-Means [20]. For our algorithm, we obtain a continuous function approximation to the digital image, by means of piecewise linear interpolants fit to a triple of intensity values in half-pixels of the image (in principle, we could have used any other smooth interpolant).…”

“…Although increasing the value of W r will provide more samples for averaging, this will allow more and more intensity values to leak across edges. Moreover, in Table 1, we also compare our method to NL-means [20] and UINTA [19], again for similar parameter settings. Further empirical results with our algorithm (using W S = W r = 5) were obtained on Lansel's benchmark dataset [21].…”