Research On Data Recovery Method Based On Tensor

Recently, with the superiority of higher order tensor in data analysis and processing, and the development of Compressed Sensing, tensor completion problem, i.e., tensor missing values recovery problem, has win a lot of attention. This problem arises in many fields such as computer vision, image processing and recommendation system.In the familiar with the knowledge of tensor, after analyzing the related works of tensor completion both on board and at home, find that the existing tensor completion methods have problems in the use of observed tensor data, have low recovery accuracy and low convergence rate, and can only be assured of obtaining a local minimizer. The purpose of this paper is to find the best way to decomposition tensor data in order to extract the potential low rank structure, then finally recovery the unknown elements of tensor. We present a tensor completion mode based on tensor Tucker decomposition which is the extension version of matrix singular value decomposition, which has the advantage in making full use of multi-dimensional relation of tensor elements. Experiments on both synthesis data and real images show the good performance of our method which combines tensor Tucker decomposition and soft threshold operator. The contributions of this paper include:1. We propose an iterative tensor Tucker method in recovery tensor missing values. This method makes use of the fact that tensor Tucker is the high dimension extension of matrix SVD. Given the n-rank of recovery tensor, the method combines both the known elements and recovered elements during the iterative process to fill the empty elements. And the results of test show this method is easy process and have good recovery ability.2. We propose a tensor Tucker thresholding method. This operator absorbs matrix singular thresholding operator in the processing of tensor Tucker decomposition. This operator has the advantage in both keeping multi-dimensional relation among tensor elements and using the soft threshold extract tensor n-vank number. As a result, the operator can improve the recovery accuracy of tensor completion methods.3. We use both the N-Mode Dimensionality Reduction method and tensor Tucker thresholding method to find the best n-rank approximation tensor to recovery missing values, for N-Mode Dimensionality Reduction method has good quality in finding the approximation tensor when given the values of tensor n-rank. Then we present an alternating direction method of multiplier method and the extended gradient mode to solve tensor completion problem, for the reason that the alternating direction method of multiplier has great advantage in solve convex optimization function. By combining our Tucker thresholding method this new method has higher recovery accuracy than other methods while the extend the classical gradient method has excellent convergence property of gradient based methods in solving optimization problems...