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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.

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