Abstract: In modern signal processing,the date with large scale,high dimension and complex structure need to be stored and analyzed in more and more fields.Tensors,as a high-order extension of vectors and matrices,can more intuitively represent the structure of high-dimensional data while maintaining the inherent relationship of the original data.Tensor completion plays an important role in recovering the original tensor from the noisy or missing tensor,which can be considered as an important branch of tensor and has been widely used in collaborative filtering,image restoration,data mining and other fields.This paper focuses on the drawbacks of high time complexity in the current tensor completion technology,and proposes a new method based on coupled random projection.The essential point of the proposed method consists of two parts:coupled tensor decomposition (CPD) and random projection matrix (RPM).Through the RPM,the original high-dimensional tensor is projected into the low-dimensional space to generate alternative tensor,and the tensor completion is realized in the low-dimensional space,and thus the efficiency of our method can be improved.Then,the CPD is used to realize the reconstruction of the original tensor by mapping the completed low-dimensional tensor into the high-dimensional space.Finally,the experiments are used to analyze the effectiveness and efficiency of the proposed method.

Key words: Coupled random projection, Coupled tensor decomposition, Random projection matrix, Tensor completion, Tensors