Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers

Fuente: arXiv
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Main Authors: Chen, Peng, Wei, Deliang, Yao, Jiale, Li, Fang
Format: Preprint
Published: 2025
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author Chen, Peng
Wei, Deliang
Yao, Jiale
Li, Fang
author_facet Chen, Peng
Wei, Deliang
Yao, Jiale
Li, Fang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_12425
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publishDate 2025
record_format arxiv
spellingShingle Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers
Chen, Peng
Wei, Deliang
Yao, Jiale
Li, Fang
Optimization and Control
Computer Vision and Pattern Recognition
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.
title Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers
topic Optimization and Control
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2510.12425