Low-Rank Tensor Completion for Image and Video Recovery via Capped Nuclear Norm

Inspired by the robustness and efficiency of the capped nuclear norm, in this paper, we apply it to 3D tensor applications and propose a novel low-rank tensor completion method via tensor singular value decomposition (t-SVD) for image and video recovery. The proposed tensor capped nuclear norm model (TCNN) handles corrupted low-rank tensors by sparsity enhancement via truncating its partial singular values dynamically. We also develop a simple and efficient algorithm to solve the proposed nonconvex and nonsmooth optimization problem using the Majorization-Minimization (MM) framework. Since the proposed algorithm admits a closed-form solution by optimizing a well-selected approximate version of the original objective function at each iteration, it is very efficient. Experimental results on both synthetic and real-world datasets, clearly demonstrate the superior performance of the proposed method.