Combining long-range dependencies with phase information in Natural Stochastic Texture enhancement

Enhancement of Natural Stochastic Textures (NST) is of special interest in image processing. These textures are considered to be realizations of random processes, and exhibit different statistical properties than those characteristic of cartoontype natural images or of structured textures. NSTs are interesting due to their fine details, which pose a challenge to enhancement algorithms. Existing algorithms, based on models of natural images, do not produce satisfactory results on NST. The long-range dependence (LRD) property of NST is explored and substantiated in this paper. An optimization scheme, implemented in the frequency domain, is then proposed. This scheme exploits the LRD as a property of the frequency magnitude, while a desired phase, extracted from the degraded image, is imposed. The scheme is general and can be further used in other image processing tasks. Zero-phase filters are of special interest in this context.