Structurally-missing Tensor Completion And Degraded Matrix Recovery

At present,most existing tensor completion methods assume that missing entries are randomly distributed in incomplete tensors,however,this could be violated in practical applications where missing entries are not only randomly but also structurally distributed.In this case,the rank minimization is unable to provide sufficient regularization to recover incomplete entries,where other priors are needed to handle this structural missing entries.Therefore,this paper proposes a novel tensor completion method to recover both randomly-missing and structurally-missing tensors,based on low rank matrix reconstruction and sparse representation.Besides,we apply this low-rank balance efficiency to matrix for 3D skeleton recovery.We derive efficient algorithms for both proposed models.The main contents and innovations of this thesis are as follows:1.We propose a novel tensor completion model equipped with double priors on the latent tensor,named tensor completion from structurally-missing entries by low tensor train(TT)rankness and fiber-wise sparsity(Tran Spa).Using two different ways of tensor matricization,the underlying tensor is regularized by a low-TT-rankness prior to exploit inter-fibers/-slices correlations,and its fibers are regularized by a sparsity prior under dictionaries to exploit intra-fibers correlations.2.A 3D skeleton motion recovery model based on a Hankel-like augmentation is proposed equipped with a sparse prior and an articulation-graph-based isometric constraint.The Hankel-like augmentation is adopted to strengthen the low-rankness and we integrate a decoupling technique to reduce the internal interferences of the data.3.We derive efficient algorithms for these two models mentioned above.The constrained models are transformed to unconstrained optimization problems by augmented Lagrangian multiplier,and a series of auxiliary variables are introduced for convenience of optimization.Then the unconstrained optimization problems are decomposed into several subproblems by alternating direction method.Experimental results demonstrate the effectiveness and superiority of the proposed models.