Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recovery
This work addresses tensor completion for remote sensing image recovery, representing an incremental advancement in tensor factorization methods.
The paper tackles the problem of insufficient low-rankness characterization in tensor train factorization for third-order tensors by generalizing it to multi-mode tensor train factorization with spatial-spectral regularization, resulting in a method that outperforms compared methods on visual data with improved quantitative measures.
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are generally not sufficient to characterize low-rankness along each mode of third-order tensor. Inspired by this, we generalize the tensor train factorization to the mode-k tensor train factorization and introduce a corresponding multi-mode tensor train (MTT) rank. Then, we proposed a novel low-MTT-rank tensor completion model via multi-mode TT factorization and spatial-spectral smoothness regularization. To tackle the proposed model, we develop an efficient proximal alternating minimization (PAM) algorithm. Extensive numerical experiment results on visual data demonstrate that the proposed MTTD3R method outperforms compared methods in terms of visual and quantitative measures.