Empirical study of wavelet domain image joint statistics and proposition of an efficient correlation map

This paper presents an empirical study of joint wavelet statistics for textures and other imagery to find an efficient correlation neighborhood. Since there is an established realization that modeling wavelet and other x-let coefficient relationships is crucial to any successful transform domain algorithm (such as Hidden Markov Trees), new works have been devoted to examine these dependencies from different aspects and propose an appropriate model. Because the time and computation complexity involved both in analyzing non-linear dependencies and in solving dependent models may restrict us to consider only a very small subset of contributing neighbors we focus our attention on linear dependencies (correlations) while having a squint on non-linear relations too. In this process, we study a collection of 5000 real images to corroborate our statistical analysis of the joint coefficient behavior and try to find an efficient and at the same time frugal relation map through different statistical means. The statistical observations are then certified by a coefficient significance measure and the competitiveness of the map is substantiated by plugging it into two dependent denoising frameworks.