Stacked Tucker Decomposition With Multi-Nonlinear Products for Remote Sensing Imagery Inpainting

In the field of remote sensing (RS) imaging, the occurrence of adverse meteorological conditions or sensor malfunctions can lead to missing data, posing a substantial impediment. Low-rank tensor decomposition has emerged as a promising strategy for resolving this issue, as it enables the integration of diverse data priors within a unified framework. Although various decomposition techniques, such as Tucker decomposition and tensor ring decomposition (TRD), have been developed based on multilinear products, they may not adequately capture the complex structure of RS imagery. Therefore, there is a need for tensor decompositions that incorporate nonlinear operations. To alleviate this challenge, a multi-nonlinear product is defined, which enables the construction of a nonlinear Tucker decomposition (NTD) model. To enhance the model's capability, a stacked Tucker decomposition (STD) model is formulated, by representing a tensor as the product of a core tensor and a collection of factor matrices along each mode, utilizing the multi-nonlinear product, which potentially regulates the distribution of singular values, thereby achieving a more accurate characterization of textures. The proposed model, integrated with total variation regularization, is subsequently applied to the task of RS imagery inpainting. Extensive experimental results demonstrate the superiority of the proposed model over state-of-the-art (SOTA) methods across various tasks. This validates its effectiveness and adaptability in mitigating the challenges associated with RS imagery inpainting. The code is available at https://github.com/shuangxu96/STDTV.