Tensor Completion via Monotone Inclusion

paper | Google Drive

Overview

In this work, we propose a novel tensor completion framework grounded in the monotone inclusion paradigm(MIP), offering rigorous convergence guarantees. The framework provides an alternative way to integrate deep denoisers as general operators with fewer constraints, rather than as proximal maps of regularizers, thereby overcoming key limitations of traditional optimization-based multi-prior methods. Moreover, it flexibly accommodates any convex tensor low-rank prior; as an example, we extend the tensor correlated total variation (TCTV) model with a weakly convex penalty to further enhance completion performance.

Motivation

Recent multi-prior tensor recovery methods have demonstrated strong empirical performance. However, most of these approaches rely on the assumption that deep denoisers serve as proximal operators of implicit regularizers, which imposes restrictive conditions such as conservativity and Lipschitz constraints [1]. To overcome these limitations, we introduce a new tensor completion framework based on MIP, which offers provable convergence and allows the incorporation of deep pseudo-contractive (DPC) denoisers [2] as general operators. The framework also supports flexible integration of any convex tensor low-rank priors. To further improve recovery quality, we generalize the tensor correlated total variation (GTCTV) with a weakly convex penalty. The following figure illustrates the motivation behind our proposed approach.

Workflow

The workflow of the proposed method is shown below, using the color video completion task as an example.

Test Dataset and Params of deep denoisers

We provide the test datasets and pretrained denoiser parameters used in our experiments at Google Drive.

Environment preparation

The required packages are listed in the TC_MIP_env.yaml file. You can run the following shell command to create a new environment named TC_MIP and install the packages by running the following command:

conda env create -f TC_MIP_env.yaml

Citation

If you find this code useful for your research, please consider citing the following paper:

@article{chen2025TC_MIP,
  title={Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers},
  author={Chen, Peng and Wei, Deliang and Yao, Jiale and Li, Fang},
  journal={arXiv preprint arXiv:2510.12425},
  year={2025}
}