Study On Hankel Tensor And Tensor Fitting Via QTT Method

In this paper,we mainly study two aspects.First,we give the exact QTT representation of Hankel tensor and multilayer Hankel tensor.Secondly,the tensor fitting algorithm based on QTT method is introduced.Due to the wide application of signal processing,Hankel tensor has attracted the attention of many scholars.Most applications of Hankel tensor are supported by the decomposition theory,so the QTT decomposition theory is one of the im-portant tools to study the Hankel tensor.In this paper,we define the basic Hankel tensor and derive its exact QTT representation.Then we construct the QTT representation of any Hankel tensor and any multilayer Hankel tensor.Most of the operations of the Hankel tensor can be transformed into the operation of the QTT kernel,which greatly reduces the storage and improves the computational efficiency,thus laying the theoretical foundation for the fast computation of Hankel tensor.Finally,the acceleration of the QTT method in Hankel tensor multiplica-tion is verified by numerical experiments.The method is also used to solve the problem of exponential signal fitting and the precision is very high.Tensor fitting has a good application value in real life,so it has been the concern of scholars.However,in practical applications,tensors such as color image and video,their dimension is not high while the scale is large,so most of the existing tensor fitting method does not apply.In this paper,we propose a QTT tensor fitting algorithm,which is based on the QTT method and transform a large scale low order tensor fitting problem into a small scale higher order tensor fitting problem.Finally,the algorithm is applied to the RGB color image completion.The experiments show that our method achieves good results both in the case of random deletion and continuous deletion.