Modeling the correlation structure of images in the wavelet domain

TitleModeling the correlation structure of images in the wavelet domain
Publication TypeConference Paper
Year of Publication2001
AuthorsAzimifar, Z., P. Fieguth, and E. Jernigan
Conference Name14th Canadian Conference on Electrical and Computer Engineering
Conference LocationToronto
Keywords1-D signals, 2-D signals, across-scale statistical dependencies, Bayes methods, Bayesian approaches, correlation structure, correlation theory, Image Denoising, image enhancement, random field model, random fields, wavelet coefficients, wavelet domain, wavelet shrinkage, wavelet transforms, white noise, whitening effect, within-scale statistical dependencies

In this paper we investigate the correlation structure of the wavelet coefficients corresponding to random fields. The context of this work is the study of Bayesian approaches to wavelet shrinkage for the purposes of image denoising. This paper concentrates on both within-scale and across-scale statistical dependencies for a variety of wavelets and random fields, with examples provided for both 1-D and 2-D signals. The results show the whitening effect of the wavelet transform to be quite clear-even for particular highly correlated spatial processes the within-scale correlation decays exponentially fast, however the correlation between scales is surprisingly substantial, even for separations several scales apart. Our goal, initiated in this paper, is the development of an efficient random field model, describing these statistical correlations, and the demonstration of its effectiveness in the context of Bayesian wavelet shrinkage for signal and image denoising