Robust Low-Rank and Sparse Tensor Decomposition for Low-Rank Tensor Completion

Low-rank tensor completion (LRTC) is a hot research direction in computer vision and machine learning because it can effectively recover the missing entries of tensor. However, most of the existing LRTC methods not only need to repeatedly calculate the time-consuming SVD decomposition, but also only consider a noise distribution in the model. To overcome the above shortcomings, based on the tensor-tensor product (t-product), we propose a new LRTC method-the robust low-rank and sparse tensor decomposition model (RLRST) for tensor completion. Firstly, in order to estimate the unknown entries in tensor data more accurately, two kinds of noise: sparse noise and Gaussian noise are considered simultaneously in RLRST. Secondly, the low-rank recovery tensor is equivalently decomposed into two smaller tensor t-products, which effectively saves the running time of the algorithm. Then, based on the alternate direction method of multipliers (ADMM), an efficient iterative updated algorithm is presented for our RLRST optimization. Finally, numerical experiments on image inpainting tasks demonstrate the effectiveness of our method over other related state-of-the-art tensor completion methods.