From relation between filter-based MRFs model and sparsity based method to the pursuit of natural images space

In the pursuit of natural image prior, responses to the specific filter bank and the character of sparse representation are of the most important clues. Based on these clues, many effective and successful algorithms are proposed and widely used in low vision tasks. Up to now, the corresponding researches with these clues are developed in relatively independent ways. In this paper, taking K-SVD as an example of sparse representation and Fields of experts (FoE) as an example of responses to the specific filter bank, we demonstrate the inherent relationship between them. The filters of FoE stand for the components that fire rarely on natural images, while the redundant dictionary of K-SVD depicts the primary components to some extent. They are two complementary pursuits of natural images space. We further bridge the gap between these two methods by proposing a method to get adaptive filters for FoE from the redundant dictionary of K-SVD. Instead of pursuing the state-of-the-art performance, our research gives a suggestive and unique view point from the essence of natural image space pursuit.