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

## TL;DR

This paper introduces a novel tensor completion model combining low-rank tensor nuclear norm and deep denoising priors, effectively recovering multi-dimensional images with missing data, outperforming existing methods.

## Contribution

It proposes a new regularized tensor completion approach integrating low-rank tensor nuclear norm with deep denoising priors within a PnP framework.

## Key findings

- Achieves superior image recovery quality compared to competing methods.
- Effectively preserves global structure and fine details in multi-dimensional images.
- Demonstrates robustness across color images, videos, and multi-spectral images.

## Abstract

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.