Tensor completion via tensor QR decomposition and [formula omitted]-norm minimization

Abstract

In this paper, we consider the tensor completion problem, which has been a concern for many researchers studying signal processing and computer vision. Our fast and precise method is built on extending the L2,1-norm minimization and Qatar Riyal decomposition (LNM-QR) method for the matrix completion to the tensor completion, and is different from the popular tensor completion methods that use the tensor singular value decomposition (t-SVD). In terms of shortening the computing time, t-SVD is replaced with a computing method that is approximate to t-SVD and is based on Qatar Riyal decomposition (CTSVD-QR). This can then be used to iteratively compute the largest r(r>0) singular values (tubes) and their associated singular vectors (of tubes). In addition, we use the tensor L2,1-norm instead of the tensor nuclear norm to optimize our model without tensor factorization. Then in terms of accuracy, we use the alternating direction method of multipliers (ADMM), which is a gradient-search-based method which plays a crucial role in our own method. Numerical experimental results show that our method is faster than those state-of-the-art algorithms and in addition, it has satisfactory accuracy.