Generalized inertial proximal deblurring

Visual signal deblurring is a challenging computational problem involving spatially invariant point spread functions, large blurring matrices and deconvolution. We formulate the visual content restoration process as an inverse convex minimization problem. We design a novel iterative multi-steps scheme incorporating an inertial term to approximate an element of the set of solutions of accretive inclusion problems. We generalize our solver for a large variety of inverse problems in imaging such as convex minimization, variational inequality and split feasibility problems. We compare the convergence rate and perceptual quality assessment with state-of-the-art algorithms on various visual input data. We demonstrate the effectiveness of our solver to deblur RGB images, HDR images, height fields, geometry images as well as motion caption data.