Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers
Peng Chen, Deliang Wei, Jiale Yao, Fang Li
TL;DR
The paper tackles tensor completion under severe missing data by formulating the problem as a monotone-inclusion program. It introduces GTCTV, a generalized, weakly convex prior for holistic global structure, and couples it with deep pseudo-contractive (DPC) denoisers within a Davis-Yin splitting framework, yielding the GTCTV-DPC algorithm with global convergence guarantees. The authors provide detailed algorithmic derivations, including resolvents for data-fitting and GTCTV components, and prove convergence to a solution of the monotone-inclusion problem. Empirically, GTCTV-DPC consistently outperforms state-of-the-art methods on multi-dimensional images, MSIs, color videos, and spatio-temporal traffic data, especially at low sampling rates, demonstrating both superior quality and robustness. The work advances tensor completion by relaxing restrictive denoiser assumptions while preserving interpretability and convergence, with practical implications for high-dimensional data recovery in imaging and traffic analysis.
Abstract
Missing entries in multi dimensional data pose significant challenges for downstream analysis across diverse real world applications. These data are naturally represented as tensors, and recent completion methods integrating global low rank priors with plug and play denoisers have demonstrated strong empirical performance. However, these approaches often rely on empirical convergence alone or unrealistic assumptions, such as deep denoisers acting as proximal operators of implicit regularizers, which generally does not hold. To address these limitations, we propose a novel tensor completion framework grounded in the monotone inclusion paradigm. Within this framework, deep denoisers are treated as general operators that require far fewer restrictions than in classical optimization based formulations. To better capture holistic structure, we further incorporate generalized low rank priors with weakly convex penalties. Building upon the Davis Yin splitting scheme, we develop the GTCTV DPC algorithm and rigorously establish its global convergence. Extensive experiments demonstrate that GTCTV DPC consistently outperforms existing methods in both quantitative metrics and visual quality, particularly at low sampling rates. For instance, at a sampling rate of 0.05 for multi dimensional image completion, GTCTV DPC achieves an average mean peak signal to noise ratio (MPSNR) that surpasses the second best method by 0.717 dB, and 0.649 dB for multi spectral images, and color videos, respectively.