Fast Tensor Nuclear Norm for Structured Low-Rank Visual Inpainting

Low-rank modeling has achieved great success in visual data completion. However, the low-rank assumption of original visual data may be in approximate mode, which leads to suboptimality for the recovery of underlying details, especially when the missing rate is extremely high. In this paper, we go further by providing a detailed analysis about the rank distributions in Hankel structured and clustered cases, and figure out both non-local similarity and patch-based structuralization play a positive role. This motivates us to develop a new Hankel low-rank tensor recovery method that is competent to truthfully capture the underlying details with sacrifice of slightly more computational burden. First, benefiting from the correlation of different spectral bands and the smoothness of local spatial neighborhood, we divide the visual data into overlapping 3D patches and group the similar ones into individual clusters exploring the non-local similarity. Second, the 3D patches are individually mapped to the structured Hankel tensors for better revealing low-rank property of the image. Finally, we solve the tensor completion model via the well-known alternating direction method of multiplier (ADMM) optimization algorithm. Due to the fact that size expansion happens inevitably in Hankelization operation, we further propose a fast randomized skinny tensor singular value decomposition (rst-SVD) to accelerate the per-iteration running efficiency. Extensive experimental results on real world datasets verify the superiority of our method compared to the state-of-the-art visual inpainting approaches.