Adaptively robust high-order tensor factorization for low-rank tensor reconstruction

Abstract

Recently, various approaches have been proposed for tensor reconstruction from incomplete and contaminated data. However, most algorithms focus on third-order tensors, neglecting higher-order tensors that are common in real-world applications. Additionally, many studies use LASSO-type penalties or second-order statistics to capture noise patterns, which may not perform well with dense and gross outliers. To address these challenges, we propose a novel robust high-order tensor recovery model that simultaneously removes complex noise and completes missing entries. We introduce a factor Frobenius norm for the low-rank structures of high-order tensors and derive a nonconvex function via the $L_2$ criterion. An estimation algorithm is developed using the alternating minimization method. Our method jointly estimates tensor terms of interest and precision parameters, adapting to noise patterns for data-driven robustness. We analyze the convergence properties of our algorithm, and numerical experiments validate its superiority in natural image reconstruction, video restoration, and background modeling compared to state-of-the-art methods.