用于彩色图像稀疏表示的四元数矩阵分解的对数规范最小化

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-07-19 DOI:10.1007/s11075-024-01887-9
Xiao-Min Cai, Yi-Fen Ke, Chang-Feng Ma, Ya-Jun Xie, Ri-Wei Liao
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引用次数: 0

摘要

本文结合四元数矩阵框架,利用四元数矩阵的对数规范来近似秩。与分别处理 RGB 通道的传统矩阵稀疏表示技术不同,基于四元数的方法通过在纯四元数矩阵中表示彩色图像来保持图像结构。利用对数规范,因式分解和截断技术可用于熟练的图像复原。通过另一种最小化框架,并辅以确保收敛性的细致数学审查,这些方法得以优化。最后,通过一些数值示例来证明所提算法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Logarithmic norm minimization of quaternion matrix decomposition for color image sparse representation

In this paper, incorporating the quaternion matrix framework, the logarithmic norm of quaternion matrices is employed to approximate rank. Unlike conventional sparse representation techniques for matrices, which treat RGB channels separately, quaternion-based methods maintain image structure by representing color images within a pure quaternion matrix. Leveraging the logarithmic norm, factorization and truncation techniques can be applied for proficient image recovery. Optimization of these approaches is facilitated through an alternate minimization framework, supplemented by meticulous mathematical scrutiny ensuring convergence. Finally, some numerical examples are used to demonstrate the effectiveness of the proposed algorithms.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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