Mixing Support Detection-Based Alternating Direction Method of Multipliers for Sparse Hyperspectral Image Unmixing

IF 1.3 4区 数学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Jie Huang, Shuang Liang, Liang-Jian Deng
{"title":"Mixing Support Detection-Based Alternating Direction Method of Multipliers for Sparse Hyperspectral Image Unmixing","authors":"Jie Huang, Shuang Liang, Liang-Jian Deng","doi":"10.1007/s10851-024-01208-8","DOIUrl":null,"url":null,"abstract":"<p>Spectral unmixing is important in analyzing and processing hyperspectral images (HSIs). With the availability of large spectral signature libraries, the main task of spectral unmixing is to estimate corresponding proportions called <i>abundances</i> of pure spectral signatures called <i>endmembers</i> in mixed pixels. In this vein, only a few endmembers participate in the formation of mixed pixels in the scene and so we call them active endmembers. A plethora of sparse unmixing algorithms exploit spectral and spatial information in HSIs to enhance abundance estimation results. Many algorithms, however, treat the abundances corresponding to active and nonactive endmembers in the scene equivalently. In this article, we propose a framework named <i>mixing support detection</i> (MSD) for the spectral unmixing problem. The main idea is first to detect the active and nonactive endmembers at each iteration and then to treat the corresponding abundances differently. It follows that we only focus on the estimation of active abundances with the assumption of zero abundances corresponding to nonactive endmembers. It can be expected to reduce the computational cost, avoid the perturbations in nonactive abundances, and enhance the sparsity of the abundances. We embed the MSD framework in classic <i>alternating direction method of multipliers</i> (ADMM) updates and obtain an ADMM-MSD algorithm. In particular, five ADMM-MSD-based unmixing algorithms are provided. The residual and objective convergence results of the proposed algorithm are given under certain assumptions. Both simulated and real-data experiments demonstrate the efficacy and superiority of the proposed algorithm compared with some state-of-the-art algorithms.</p>","PeriodicalId":16196,"journal":{"name":"Journal of Mathematical Imaging and Vision","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Imaging and Vision","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10851-024-01208-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0

Abstract

Spectral unmixing is important in analyzing and processing hyperspectral images (HSIs). With the availability of large spectral signature libraries, the main task of spectral unmixing is to estimate corresponding proportions called abundances of pure spectral signatures called endmembers in mixed pixels. In this vein, only a few endmembers participate in the formation of mixed pixels in the scene and so we call them active endmembers. A plethora of sparse unmixing algorithms exploit spectral and spatial information in HSIs to enhance abundance estimation results. Many algorithms, however, treat the abundances corresponding to active and nonactive endmembers in the scene equivalently. In this article, we propose a framework named mixing support detection (MSD) for the spectral unmixing problem. The main idea is first to detect the active and nonactive endmembers at each iteration and then to treat the corresponding abundances differently. It follows that we only focus on the estimation of active abundances with the assumption of zero abundances corresponding to nonactive endmembers. It can be expected to reduce the computational cost, avoid the perturbations in nonactive abundances, and enhance the sparsity of the abundances. We embed the MSD framework in classic alternating direction method of multipliers (ADMM) updates and obtain an ADMM-MSD algorithm. In particular, five ADMM-MSD-based unmixing algorithms are provided. The residual and objective convergence results of the proposed algorithm are given under certain assumptions. Both simulated and real-data experiments demonstrate the efficacy and superiority of the proposed algorithm compared with some state-of-the-art algorithms.

Abstract Image

基于混合支持检测的交替方向乘法器法用于稀疏高光谱图像解混
光谱解混合在分析和处理高光谱图像(HSIs)中非常重要。随着大量光谱特征库的出现,光谱解混的主要任务是估算混合像素中被称为内成员的纯光谱特征的相应比例(丰度)。在这种情况下,只有少数内含物参与了场景中混合像素的形成,因此我们称之为活跃内含物。大量稀疏解混合算法利用 HSI 中的光谱和空间信息来提高丰度估算结果。然而,许多算法都将场景中活跃和非活跃内含物对应的丰度等同处理。在本文中,我们针对光谱解混合问题提出了一个名为混合支持检测(MSD)的框架。其主要思想是首先在每次迭代中检测活跃和非活跃的内含物,然后区别对待相应的丰度。因此,我们只关注活动丰度的估计,并假设非活动内含物的丰度为零。这样可以降低计算成本,避免非活动丰度的扰动,并增强丰度的稀疏性。我们将 MSD 框架嵌入经典的交替方向乘法(ADMM)更新中,得到了 ADMM-MSD 算法。具体而言,我们提供了五种基于 ADMM-MSD 的非混合算法。在某些假设条件下,给出了所提算法的残差和目标收敛结果。模拟和实际数据实验都证明了所提算法与一些最先进算法相比的有效性和优越性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision 工程技术-计算机:人工智能
CiteScore
4.30
自引率
5.00%
发文量
70
审稿时长
3.3 months
期刊介绍: The Journal of Mathematical Imaging and Vision is a technical journal publishing important new developments in mathematical imaging. The journal publishes research articles, invited papers, and expository articles. Current developments in new image processing hardware, the advent of multisensor data fusion, and rapid advances in vision research have led to an explosive growth in the interdisciplinary field of imaging science. This growth has resulted in the development of highly sophisticated mathematical models and theories. The journal emphasizes the role of mathematics as a rigorous basis for imaging science. This provides a sound alternative to present journals in this area. Contributions are judged on the basis of mathematical content. Articles may be physically speculative but need to be mathematically sound. Emphasis is placed on innovative or established mathematical techniques applied to vision and imaging problems in a novel way, as well as new developments and problems in mathematics arising from these applications. The scope of the journal includes: computational models of vision; imaging algebra and mathematical morphology mathematical methods in reconstruction, compactification, and coding filter theory probabilistic, statistical, geometric, topological, and fractal techniques and models in imaging science inverse optics wave theory. Specific application areas of interest include, but are not limited to: all aspects of image formation and representation medical, biological, industrial, geophysical, astronomical and military imaging image analysis and image understanding parallel and distributed computing computer vision architecture design.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信