# Quaternion higher-order singular value decomposition and its applications in color image processing

arXiv: https://arxiv.org/abs/2101.00364 · HTML: https://mlsanity.com/paper/2101.00364/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 56 references that are in the map.
- First posted on arXiv 2 Jan 2021.

## Builds on (most cited first, 2 of 2)

- [Color image recovery using low-rank quaternion matrix completion algorithm](https://mlsanity.com/paper/1909.06567/) (2019)
- [Quaternion-based bilinear factor matrix norm minimization for color image inpainting](https://mlsanity.com/paper/2005.02886/) (2020)

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

- [Depth-Aided Color Image Inpainting in Quaternion Domain](https://mlsanity.com/paper/2503.16818/) (2025)
- [Quaternion Infrared Visible Image Fusion](https://mlsanity.com/paper/2505.02364/) (2025)
- [Quaternion Sparse Decomposition for Multi-focus Color Image Fusion](https://mlsanity.com/paper/2505.02365/) (2025)

## Abstract (arXiv)

Higher-order singular value decomposition (HOSVD) is one of the most efficient tensor decomposition techniques. It has the salient ability to represent high_dimensional data and extract features. In more recent years, the quaternion has proven to be a very suitable tool for color pixel representation as it can well preserve cross-channel correlation of color channels. Motivated by the advantages of the HOSVD and the quaternion tool, in this paper, we generalize the HOSVD to the quaternion domain and define quaternion-based HOSVD (QHOSVD). Due to the non-commutability of quaternion multiplication, QHOSVD is not a trivial extension of the HOSVD. They have similar but different calculation procedures. The defined QHOSVD can be widely used in various visual data processing with color pixels. In this paper, we present two applications of the defined QHOSVD in color image processing: multi_focus color image fusion and color image denoising. The experimental results on the two applications respectively demonstrate the competitive performance of the proposed methods over some existing ones.