  Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a
low-rank tensor corrupted by sparse noise, has attracted much attention in many
real applications. This paper develops a new Global Weighted TRPCA method
(GWTRPCA), which is the first approach simultaneously considers the
significance of intra-frontal slice and inter-frontal slice singular values in
the Fourier domain. Exploiting this global information, GWTRPCA penalizes the
larger singular values less and assigns smaller weights to them. Hence, our
method can recover the low-tubal-rank components more exactly. Moreover, we
propose an effective adaptive weight learning strategy by a Modified Cauchy
Estimator (MCE) since the weight setting plays a crucial role in the success of
GWTRPCA. To implement the GWTRPCA method, we devise an optimization algorithm
using an Alternating Direction Method of Multipliers (ADMM) method. Experiments
on real-world datasets validate the effectiveness of our proposed method.
