Generalized Tensor Total Variation minimization for visual data recovery?

In this paper, we propose a definition of Generalized Tensor Total Variation norm (GTV) that considers both the inhomogeneity and the multi-directionality of responses to derivative-like filters. More specifically, the inhomogeneity simultaneously preserves high-frequency signals and suppresses noises, while the multi-directionality ensures that, for an entry in a tensor, more information from its neighbors is taken into account. To effectively and efficiently seek the solution of the GTV minimization problem, we design a novel Augmented Lagrange Multiplier based algorithm, the convergence of which is theoretically guaranteed. Experiments are conducted to demonstrate the superior performance of our method over the state of the art alternatives on classic visual data recovery applications including completion and denoising.