Spatially Regularized Low Rank Tensor Optimization for Visual Data Completion

Low-rank tensor completion is a recent method for estimating the values of the missing elements in tensor data by minimizing the tensor rank. However, with only the low rank prior, the local piecewise smooth structure that is important for visual data is not used effectively. To address this problem, we define a new spatial regularization S-norm for tensor completion in order to exploit the local spatial smoothness structure of visual data. More specifically, we introduce the S-norm to the tensor completion model based on a non-convex LogDet function. The S-norm helps to drive the neighborhood elements towards similar values. We utilize the Alternating Direction Method of Multiplier (ADMM) to optimize the proposed model. Experimental results in visual data demonstrate that our method outperforms the state-of-the-art tensor completion models.