# A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpainting

arXiv: https://arxiv.org/abs/2009.12203 · HTML: https://mlsanity.com/paper/2009.12203/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2020.

## Built on by (most cited first, 3 of 3)

- [Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition](https://mlsanity.com/paper/2211.16739/) (2022)
- [Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition](https://mlsanity.com/paper/2408.05582/) (2024)
- [Quaternion tensor left ring decomposition and application for color image inpainting](https://mlsanity.com/paper/2307.10620/) (2023)

## Abstract (arXiv)

In this paper, we propose a lower rank quaternion decomposition algorithm and apply it to color image inpainting. We introduce a concise form for the gradient of a real function in quaternion matrix variables. The optimality conditions of our quaternion least squares problem have a simple expression with this form. The convergence and convergence rate of our algorithm are established with this tool.