High-Order Tensor Recovery Coupling Multilayer Subspace Priori with Application in Video Restoration

In the real world, a large amount of high-order tensor data (order>3) exists, such as color videos, multispectral videos, and light-field images. However, these data often face challenges in transportation, storage, and susceptibility to damage. Meanwhile, most existing tensor-based information processing methods only concentrate on third-order tensors, which may not meet the complex requirements of high-dimensional data processing. In this paper, to better address the high-order tensor recovery issue, we propose a novel method that couples multilayer subspace priors with high-order tensor recovery techniques for tensor completion and robust tensor principal component analysis. Moreover, we provide theoretical guarantees for our approach's recovery and demonstrate that it achieves comparable performance under weaker incoherent conditions. Additionally, we develop two efficient and interpretable algorithms based on the alternating direction method of multipliers (ADMM) to solve our model. Owing to the adaptability of subspace prior information, our method demonstrates superior performance in recovering various types of data, including color videos and multispectral videos, compared with various advanced algorithms currently available.