Research On Low-rank Tensor Completion Algorithm And Applications On Multi-dimension Data Completion

Recovering data from its observation with noise or even missing elements has been a challenging yet significant task in computer vision and data mining field for long period.A series of traditional methods treat the data as matrixes and solve the optimization problem with convex optimization based on nuclear norm minimization.Such approaches,failing to preserve the spatial information which is critical in data recovery tasks,have some theoretical limitation as the dimension and amount of multimedia data are increasing at the moment.Recently low-rank based tensor completion(LRTC)algorithms attract much attention in academic area for its effectiveness on preservation of spatial information and structure.Unfortunately,most of the existing LRTC algorithms treat each dimension of tensors equally,ignoring the diversity of the intrinsic structure and low-rank property along each dimension.In this paper,we make a sophisticated analysis about the distribution of rank along each dimension of real data and design a simple yet effective reweighted low-rank tensor completion model that precisely captures the essential structure correlations with reduced computational complexity.Moreover,to capture the local spatial smooth of real data,we integrate total variation into our model.Considering two formulations of LRTC,i.e.tensor unfolding and tensor decomposition,we propose corresponding two algorithms for data recovery,each of which has its rank estimation of tensor respectively.Additionally,we also introduce a nonconvex rank approximation,for its superiority on approximating the true rank of tensor.Extensive experimental results on diversified types of multi-dimensional data reveal the efficiency and effectiveness of the proposed two algorithms.