# Quaternion Optimized Model with Sparse Regularization for Color Image Recovery

arXiv: https://arxiv.org/abs/2204.08629 · HTML: https://mlsanity.com/paper/2204.08629/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 33 references that are in the map.
- First posted on arXiv 19 Apr 2022.

## Builds on (most cited first, 5 of 5)

- [A Trilateral Weighted Sparse Coding Scheme for Real-World Image Denoising](https://mlsanity.com/paper/1807.04364/) (2018)
- [Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications](https://mlsanity.com/paper/1810.05186/) (2018)
- [Quaternion-based bilinear factor matrix norm minimization for color image inpainting](https://mlsanity.com/paper/2005.02886/) (2020)
- [Quaternion Fourier Transform on Quaternion Fields and Generalizations](https://mlsanity.com/paper/1306.1023/) (2013)
- [Weighted Truncated Nuclear Norm Regularization for Low-Rank Quaternion Matrix Completion](https://mlsanity.com/paper/2101.02443/) (2021)

## Built on by (most cited first, 1 of 1)

- [L2,1-Norm Regularized Quaternion Matrix Completion Using Sparse Representation and Quaternion QR Decomposition](https://mlsanity.com/paper/2309.03764/) (2023)

## Abstract (arXiv)

This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the fact that different signal types, including audio formats and images, possess structures that are inherently sparse in respect of their respective bases. Since color images can be processed as a whole in the quaternion domain, we depicted the sparsity of the color image in the quaternion discrete cosine transform (QDCT) domain. In addition, the representation of a low-rank structure that is intrinsic to the color image is a vital issue in the quaternion matrix completion problem. To achieve a more superior low-rank approximation, the quatenrion-based truncated nuclear norm (QTNN) is employed in the proposed model. Moreover, this model is facilitated by a competent alternating direction method of multipliers (ADMM) based on the algorithm. Extensive experimental results demonstrate that the proposed method can yield vastly superior completion performance in comparison with the state-of-the-art low-rank matrix/quaternion matrix approximation methods tested on color image recovery.