Multi-Dimensional Data Recovery via Feature-Based Fully-Connected Tensor Network Decomposition

Multi-dimensional data are inevitably corrupted, which hinders subsequent applications (e.g., image segmentation and classification). Recently, due to the powerful ability to characterize the correlation between any two modes of tensors, fully-connected tensor network (FCTN) decomposition has received increasing attention in multi-dimensional data recovery. However, the expressive power of FCTN decomposition in the original pixel domain has yet to be fully leveraged, which can not provide satisfactory results in the recovery of details and textures, especially for low-sampling rates or heavy noise scenarios. In this work, we suggest a feature-based FCTN decomposition model (termed as F-FCTN) for multi-dimensional data recovery, which can faithfully capture the relationship between the spatial-temporal/spectral-feature modes. Compared with the original FCTN decomposition, F-FCTN can more effectively recover the details and textures and be more suitable for the subsequent high-level applications. However, F-FCTN leads to a larger-scale feature tensor as compared with the original tensor, which brings challenges in designing the solving algorithm. To harness the resulting large-scale optimization problem, we develop an efficient leverage score sampling-based proximal alternating minimization (S-PAM) algorithm and theoretically establish its relative error guarantee. Extensive numerical experiments on real-world data illustrate that the proposed method performs favorably against compared methods in data recovery and facilitates subsequent image classification.