Tensor wheel completion for visual data with sparsity and smoothness on latent space

Tensor wheel decomposition has recently drawn lots of attentions in tensor completion, due to its advantages of wheel topology in exploring the intrinsic relationships. However, since the rank of tensor wheel is defined as a vector, it is very hard to select one rather-good rank for tensor completion when the model is rank-sensitive, i.e., the model is prone to overfitting due to rank selection. To solve this problem, under the tensor wheel structure, we theoretically analyze the relationship of sparsity and smoothness to the overfitting, which is expected to improve the performance by preventing the overfitting due to excessive rank selection. Then, based on the analysis of sparsity and smoothness, we proposed a novel tensor wheel completion model with sparsity and smoothness on latent space. Lastly, an efficient alternating direction method of multipliers (ADMM)-based algorithm is developed to optimize the proposed model. Experimental results show that the proposed method is superior to some existing methods in tensor completion and can maintain good results in a large range of rank selection, which enable the proposed method is not easy to overfit with the increasing of rank.