Single Image Blind Deconvolution with Higher-Order Texture Statistics

We present a novel method for solving blind deconvolution, i.e., the task of recovering a sharp image given a blurry one. We focus on blurry images obtained from a coded aperture camera, where both the camera and the scene are static, and allow blur to vary across the image domain. As most methods for blind deconvolution, we solve the problem in two steps: First, we estimate the coded blur scale at each pixel; second, we deconvolve the blurry image given the estimated blur. Our approach is to use linear high-order priors for texture and second-order priors for the blur scale map, i.e., constraints involving two pixels at a time. We show that by incorporating the texture priors in a least-squares energy minimization we can transform the initial blind deconvolution task in a simpler optimization problem. One of the striking features of the simplified optimization problem is that the parameters that define the functional can be learned offline directly from natural images via singular value decomposition. We also show a geometrical interpretation of image blurring and explain our method from this viewpoint. In doing so we devise a novel technique to design optimally coded apertures. Finally, our coded blur identification results in computing convolutions, rather than deconvolutions, which are stable operations. We will demonstrate in several experiments that this additional stability allows the method to deal with large blur. We also compare our method to existing algorithms in the literature and show that we achieve state-of-the-art performance with both synthetic and real data.