Randomized Algorithm on Tensor Singular Value Decomposition for Image and Video Reconstructions

Abstract

In this work, we introduce a randomized algorithm for analyzing and capturing multi-linear data structure. Tensor singular value decomposition (T-SVD) is a useful method to extract the most dominant features of a given tensor data and to compute a low multi-linear rank basis. However, computing T-SVD can be time-consuming for large-scale data. The randomized algorithm is therefore employed on T-SVD, so called randomized T-SVD, to reduce the computational complexity on large-scale problems. We proposed a method that employs the randomized T-SVD to construct an efficient tensor basis used in  the least-squares approximation for estimating the missing values on data recovery applications. Numerical experiments on data recovery are performed for image and video reconstructions. These results show that the proposed method is considerably faster than the traditional tensor  approach while achieving a comparable peak signal-to-noise ratio.