A hybrid alternating proximal method for blind video restoration

International audienceOld analog television sequences suffer from a number of degradations. Some of them can be modeled through convolution with a kernel and an additive noise term. In this work, we propose a new blind deconvolution algorithm for the restoration of such sequences based on a variational formulation of the problem. Our method accounts for motion between frames, while enforcing some level of temporal continuity through the use of a novel penalty function involving optical flow operators, in addition to an edge-preserving regularization. The optimization process is performed by a proximal alternating minimization scheme benefiting from theoretical convergence guarantees. Simulation results on synthetic and real video sequences confirm the effectiveness of our method

A Distributed Strategy for Computing Proximity Operators

International audienceVarious recent iterative optimization methods require to compute the proximity operator of a sum of functions.We address this problem by proposing a new distributed algorithm for a sum of non-necessarily smooth convex functionscomposed with arbitrary linear operators. In our approach, each function is associated with a node of a graph, whichcommunicates with its neighbors. Our algorithm relies on a primal-dual splitting strategy that avoids to invert any linearoperator, thus making it suitable for processing high-dimensional datasets. The proposed algorithm has a wide array of applicationsin signal/image processing and machine learning and its convergence is established

An Alternating Proximal Approach for Blind Video Deconvolution

International audienceBlurring occurs frequently in video sequences captured by consumer devices, as a result of various factors such as lens aberrations, defocus, relative camera-scene motion, and camera shake. When it comes to the contents of archive documents such as old films and television shows, the degradations are even more serious due to several physical phenomena happening during the sensing, transmission, recording, and storing processes. We propose in this paper a versatile formulation of blind video deconvolution problems that seeks to estimate both the sharp unknown video sequence and the underlying blur kernel from an observed video. This inverse problem is severely ill-posed, and an appropriate solution can be obtained by modeling it as a nonconvex minimization problem. We provide a novel iterative algorithm to solve it, grounded on the use of recent advances in convex and nonconvex optimization techniques, and having the ability of including numerous well-known regularization strategies

Dual Block Coordinate Forward-Backward Algorithm with Application to Deconvolution and Deinterlacing of Video Sequences

International audienceOptimization methods play a central role in the solution of a wide array of problems encountered in various application fields, such as signal and image processing. Especially when the problems are highly dimensional, proximal methods have shown their efficiency through their capability to deal with composite, possibly nonsmooth objective functions. The cornerstone of these approaches is the proximity operator, which has become a quite popular tool in optimization. In this work, we propose new dual forward-backward formulations for computing the proximity operator of a sum of convex functions involving linear operators. The proposed algorithms are accelerated thanks to the introduction of a block-coordinate strategy combined with a preconditioning technique. Numerical simulations emphasize the good performance of our approach for the problem of jointly deconvoluting and deinterlacing video sequences