Total variation blind deconvolution: The devil is in the details

In this paper we study the problem of blind deconvolu-tion. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient pri-ors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating en-ergy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. How-ever, experimentally one can observe that Chan and Wong’s algorithm converges to the desired solution even when ini