# Deep Plug-and-play Prior for Low-rank Tensor Completion

arXiv: https://arxiv.org/abs/1905.04449 · HTML: https://mlsanity.com/paper/1905.04449/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2019.

## Built on by (most cited first, 15 of 15)

- [DeepTensor: Low-Rank Tensor Decomposition with Deep Network Priors](https://mlsanity.com/paper/2204.03145/) (2022)
- [Tensor Recovery Based on A Novel Non-convex Function Minimax Logarithmic Concave Penalty Function](https://mlsanity.com/paper/2206.13506/) (2022)
- [Unsupervised Spectral Demosaicing with Lightweight Spectral Attention Networks](https://mlsanity.com/paper/2307.01990/) (2023)
- [Two New Low Rank Tensor Completion Methods Based on Sum Nuclear Norm](https://mlsanity.com/paper/2108.03002/) (2021)
- [Salt and pepper noise removal method based on stationary Framelet transform with non-convex sparsity regularization](https://mlsanity.com/paper/2110.09113/) (2021)
- [Spherical Image Inpainting with Frame Transformation and Data-driven Prior Deep Networks](https://mlsanity.com/paper/2209.14604/) (2022)
- [DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery](https://mlsanity.com/paper/2407.05267/) (2024)
- [Tensor Full Feature Measure and Its Nonconvex Relaxation Applications to Tensor Recovery](https://mlsanity.com/paper/2109.12257/) (2021)
- ["Sparse + Low-Rank'' Tensor Completion Approach for Recovering Images and Videos](https://mlsanity.com/paper/2110.09298/) (2021)
- [Low-Rank Tensor Completion Based on Bivariate Equivalent Minimax-Concave Penalty](https://mlsanity.com/paper/2201.12709/) (2022)
- [Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recovery](https://mlsanity.com/paper/2205.03380/) (2022)
- [Under-Sampled High-Dimensional Data Recovery via Symbiotic Multi-Prior Tensor Reconstruction](https://mlsanity.com/paper/2504.05992/) (2025)
- [Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers](https://mlsanity.com/paper/2510.12425/) (2025)
- [Structure-Informed Estimation for Pilot-Limited MIMO Channels via Tensor Decomposition](https://mlsanity.com/paper/2602.04083/) (2026)
- [Bayesian Tensor Decomposition with Diffusion Model Prior](https://mlsanity.com/paper/2606.03212/) (2026)

## Abstract (arXiv)

Multi-dimensional images, such as color images and multi-spectral images, are highly correlated and contain abundant spatial and spectral information. However, real-world multi-dimensional images are usually corrupted by missing entries. By integrating deterministic low-rankness prior to the data-driven deep prior, we suggest a novel regularized tensor completion model for multi-dimensional image completion. In the objective function, we adopt the newly emerged tensor nuclear norm (TNN) to characterize the global low-rankness prior of the multi-dimensional images. We also formulate an implicit regularizer by plugging into a denoising neural network (termed as deep denoiser), which is convinced to express the deep image prior learned from a large number of natural images. The resulting model can be solved by the alternating directional method of multipliers algorithm under the plug-and-play (PnP) framework. Experimental results on color images, videos, and multi-spectral images demonstrate that the proposed method can recover both the global structure and fine details very well and achieve superior performance over competing methods in terms of quality metrics and visual effects.