Tensorial total variation-based image and video restoration with optimized projection methods

The total variation regularization method was introduced by Rudin, Osher, and Fatemi as an efficient technique for regularizing grayscale images. In this work, we aimed to generalize the total variation method to regularize multidimensional problems such as colour image and video restoration. A degradation model in a tensor format is proposed to recover blurred and noisy colour images and videos. The alternating direction method for multipliers (ADMM) and an optimized form of projection methods have been employed to solve the tensorial total variation minimization problem. The structure of the developed approach allows the selection of the optimal parameter. We use the truncated SVD (TSVD) to reduce the size of the problem and to accelerate the convergence of the algorithm. The convergence analysis of the proposed method is proved using convex optimization. Numerical tests for image and video restoration are given showing the effectiveness of the proposed approaches.