# Quaternion-based bilinear factor matrix norm minimization for color image inpainting

arXiv: https://arxiv.org/abs/2005.02886 · HTML: https://mlsanity.com/paper/2005.02886/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2020.

## Built on by (most cited first, 12 of 12)

- [Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss](https://mlsanity.com/paper/2202.02063/) (2022)
- [Quaternion higher-order singular value decomposition and its applications in color image processing](https://mlsanity.com/paper/2101.00364/) (2021)
- [Quaternion-based dynamic mode decomposition for background modeling in color videos](https://mlsanity.com/paper/2112.13982/) (2021)
- [Approximation of Images via Generalized Higher Order Singular Value Decomposition over Finite-dimensional Commutative Semisimple Algebra](https://mlsanity.com/paper/2202.00450/) (2022)
- [Quaternion Optimized Model with Sparse Regularization for Color Image Recovery](https://mlsanity.com/paper/2204.08629/) (2022)
- [Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition](https://mlsanity.com/paper/2408.05582/) (2024)
- [Quaternion Nuclear Norms Over Frobenius Norms Minimization for Robust Matrix Completion](https://mlsanity.com/paper/2504.21468/) (2025)
- [Quaternion tensor left ring decomposition and application for color image inpainting](https://mlsanity.com/paper/2307.10620/) (2023)
- [L2,1-Norm Regularized Quaternion Matrix Completion Using Sparse Representation and Quaternion QR Decomposition](https://mlsanity.com/paper/2309.03764/) (2023)
- [Quaternion Infrared Visible Image Fusion](https://mlsanity.com/paper/2505.02364/) (2025)
- [Color Image Set Recognition Based on Quaternionic Grassmannians](https://mlsanity.com/paper/2505.23629/) (2025)
- [Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition](https://mlsanity.com/paper/2606.03654/) (2026)

## Abstract (arXiv)

As a new color image representation tool, quaternion has achieved excellent results in the color image processing, because it treats the color image as a whole rather than as a separate color space component, thus it can make full use of the high correlation among RGB channels. Recently, low-rank quaternion matrix completion (LRQMC) methods have proven very useful for color image inpainting. In this paper, we propose three novel LRQMC methods based on three quaternion-based bilinear factor (QBF) matrix norm minimization models. Specifically, we define quaternion double Frobenius norm (Q-DFN), quaternion double nuclear norm (Q-DNN) and quaternion Frobenius/nuclear norm (Q-FNN), and then show their relationship with quaternion-based matrix Schatten-p (Q- Schatten-p ) norm for certain p values. The proposed methods can avoid computing quaternion singular value decompositions (QSVD) for large quaternion matrices, and thus can effectively reduce the calculation time compared with existing (LRQMC) methods. The experimental results demonstrate the superior performance of the proposed methods over some state-of-the-art low-rank (quaternion) matrix completion methods.