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 1.7 3区 数学 Q2 MATHEMATICS, APPLIED Numerical Algorithms 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
Numerical Algorithms
Numerical Algorithms 数学-应用数学
CiteScore
4.00
自引率
9.50%
发文量
201
审稿时长
9 months
期刊介绍: The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.
期刊最新文献
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