Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recovery

TL;DR

This paper introduces a multi-mode tensor train (MTT) factorization with spatial-spectral regularization for improved remote sensing image recovery, enhancing low-rank tensor completion by capturing mode-specific correlations.

Contribution

It generalizes tensor train factorization to mode-k tensors, proposing a novel low-MTT-rank model and an efficient algorithm for remote sensing image reconstruction.

Findings

Outperforms existing methods in visual quality

Achieves better quantitative recovery metrics

Effectively captures mode-specific low-rankness

Abstract

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.