Optimal filter based on scale-invariance generation of natural images

One of the most striking properties of natural image statistics is the scale invariance. Some earlier studies have assumed that the kurtosis of marginal band pass filter response to be constant throughout scales for a natural image. In our study, this assumption is loosened by adaptively estimating an optimal filter computation whose response distributions through scales have the least Kullback-Leibler divergence. The adaptive filter and its responses characterize the scale-invariance property more accurately and effectively and are further utilized to model the statistics scale-invariance prior in this paper. Extensive experiments on image super-resolution and de-noising manifest that the explored natural images scale-invariance prior model achieves significant performance improvements over the current state-of-the-art schemes.