International audienceIn this paper, we address the problem of estimating and removing non-uniform motion blur from a single blurry image. We propose a deep learning approach to predicting the probabilistic distribution of motion blur at the patch level using a convolutional neural network (CNN). We further extend the candidate set of motion kernels predicted by the CNN using carefully designed image rotations. A Markov random field model is then used to infer a dense non-uniform motion blur field enforcing motion smoothness. Finally, motion blur is removed by a non-uniform de-blurring model using patch-level image prior. Experimental evaluations show that our approach can effectively estimate and remove complex non-uniform motion blur that is not handled well by previous approaches

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The alternating direction method with multipliers (ADMM) has been one of most powerful and successful methods for solving various composite problems. The convergence of the conventional ADMM (i.e., 2-block) for convex objective functions has been justified for a long time, and its convergence for nonconvex objective functions has, however, been established very recently. The multi-block ADMM, a natural extension of ADMM, is a widely used scheme and has also been found very useful in solving various nonconvex optimization problems. It is thus expected to establish convergence theory of the multi-block ADMM under nonconvex frameworks. In this paper we present a Bregman modification of 3-block ADMM and establish its convergence for a large family of nonconvex functions. We further extend the convergence results to the N-block case (N ≥ 3), which underlines the feasibility of multi-block ADMM applications in nonconvex settings. Finally, we present a simulation study and a real-world application to support the correctness of the obtained theoretical assertions.

Abstract-Background subtraction has been a fundamental and widely studied task in video analysis, with a wide range of applications in video surveillance, teleconferencing, and 3D modeling. Recently, motivated by compressive imaging, background subtraction from compressive measurements (BSCM) is becoming an active research task in video surveillance. In this paper, we propose a novel tensor-based robust principal component analysis (TenRPCA) approach for BSCM by decomposing video frames into backgrounds with spatial-temporal correlations and foregrounds with spatio-temporal continuity in a tensor framework. In this approach, we use 3D total variation to enhance the spatio-temporal continuity of foregrounds, and Tucker decomposition to model the spatio-temporal correlations of video background. Based on this idea, we design a basic tensor RPCA model over the video frames, dubbed as the holistic TenRPCA model. To characterize the correlations among the groups of similar 3D patches of video background, we further design a patch-group-based tensor RPCA model by joint tensor Tucker decompositions of 3D patch groups for modeling the video background. Efficient algorithms using the alternating direction method of multipliers are developed to solve the proposed models. Extensive experiments on simulated and real-world videos demonstrate the superiority of the proposed approaches over the existing state-of-the-art approaches.