A Classic New Methods For Removing Mixed Noises

Noise can be systematically introduced into images during acquisition and transmission. A fundamental problem of image processing is to effectively remove noise from an image while keeping its features intact. The nature of the problem depends on the type of noise added to the image. Two noise models can adequately represent most noise added to images: Gaussian noise and impulse noise.There are often mixed noises (Gaussian noise and Impulse noise) in digital images, but there are few efficient methods for removing them. NL-means method makes full use of a large number of the similar phenomena in natural images filtering, have made impressive results. But these phenomena and algorithms still a lack of satisfactory theoretical basis. In this paper, we first give a mathematical justification of the non-local means method to remove Gaussian noises(Called Similarity Theorem), then give a new method by this theorem, called MNF (Mixed Noises Filter) to remove mixed noises consisting of Gaussian and uniform (random) impulse noises. Secondly, we introduce a new image statistic ROPDρ,c based power function, show theoretically ROAD and ROLD statistic are both a special case of ROPDρ,c statistic. On the basis of the MNF and the statistic, we propose a classic new methods, called ROPDρ,c Mixed Noises Filter (ROPDρ,c-MNF for short), and prove that MNF is its a special case. Our experiments show that the MNF and ROPDρ,c-MNF filter is better than the trilateral filter proposed by Garnett et al. for mixed noises, and that it is as good as the most advanced methods to remove pure Gaussian noises or pure uniform impulse noise. Finally, we introduce the notion of degree of similarity to measure the self-similarity of noisy images and answer which image is a good candidate to be restored by NL-means.