Research On Weighted Non-convex Regularized Low Rank Tensor Recovery Model

With the rapid development of new information technologies such as big data and artificial intelligence,the traditional sparse and low-rank recovery methods represented by compressed sensing and low-rank matrix recovery theory are no longer able to deal with the highdimensional tensor data encountered in many fields such as data mining,computer vision and pattern recognition.In this context,low-rank tensor recovery techniques with tensor data as the carrier have emerged.However,the effectiveness of its application in practical problems largely depends on the deep understanding of tensor data,and there are different low-rank tensor recovery models based on different tensor rank.At present,relying on the algebraic framework of tensor singular value decomposition,low-tubal-rank tensor recovery has rapidly become a research hotspot for scholars in the industry due to its more efficient mining and reconstruction of the potential low-rank properties of real tensor data.In this thesis,we propose and study a weighted non-convex regularized low-tubal-rank tensor recovery model by unifying many popular non-convex tubal rank relaxations in a single framework around the problem of excessive and isometric shrinkage of singular values of the most benchmark tensor convex nuclear norm parametrization minimization method in lowtubal-rank tensor recovery.First,inspired by the advantages of non-convex relaxation methods in balancing low-rank and efficient calculation,a generalized weighted non-convex non-smooth relaxation of the tensor tubal rank is proposed as a stricter regularization,which satisfies the universality of a large set of non-convex penalty functions and achieves a better approximation than convex nuclear norm regularization,leading to a weighted non-convex regularized lowtubal-rank tensor recovery model.Next,a tensor iteratively reweighted singular value threshold optimization algorithm is designed to optimize the proposed model.The algorithm uses a continuous technique,which defines the weight vector by computing the value of the supergradient and obtains the solution of the subproblem using the generalized weighted tensor singular value threshold(GWTSVT)operator.Finally,the effectiveness of the model is verified by the experiments of synthetic data and real image data.