An explicit sharpness index related to global phase coherence

We propose a definition of a Sharpness Index that is closely related to the notion of Global Phase Coherence recently introduced for automatic image restoration and image quality assessment. Using Gaussian random fields instead of random phase images, we can estimate the probability that a random image has a given Total Variation, which leads us to an explicit formula and a fast algorithm. Theoretical arguments and numerical experiments are given to assess the similarity between the Sharpness Index and the Global Phase Coherence, and an application to non-parametric blind deconvolution is presented, that illustrates the possibilities offered by this new approach.