球上随机场绘制的群稀疏优化

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED
Chao Li, Xiaojun Chen
{"title":"球上随机场绘制的群稀疏优化","authors":"Chao Li, Xiaojun Chen","doi":"10.1093/imanum/drad071","DOIUrl":null,"url":null,"abstract":"Abstract We propose a group sparse optimization model for inpainting of a square-integrable isotropic random field on the unit sphere, where the field is represented by spherical harmonics with random complex coefficients. In the proposed optimization model, the variable is an infinite-dimensional complex vector and the objective function is a real-valued function defined by a hybrid of the $\\ell _2$ norm and non-Lipschitz $\\ell _p (0<p<1)$ norm that preserves rotational invariance property and group structure of the random complex coefficients. We show that the infinite-dimensional optimization problem is equivalent to a convexly-constrained finite-dimensional optimization problem. Moreover, we propose a smoothing penalty algorithm to solve the finite-dimensional problem via unconstrained optimization problems. We provide an approximation error bound of the inpainted random field defined by a scaled Karush–Kuhn–Tucker (KKT) point of the constrained optimization problem in the square-integrable space on the sphere with probability measure. Finally, we conduct numerical experiments on band-limited random fields on the sphere and images from Cosmic Microwave Background (CMB) data to show the promising performance of the smoothing penalty algorithm for inpainting of random fields on the sphere.","PeriodicalId":56295,"journal":{"name":"IMA Journal of Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Group sparse optimization for inpainting of random fields on the sphere\",\"authors\":\"Chao Li, Xiaojun Chen\",\"doi\":\"10.1093/imanum/drad071\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We propose a group sparse optimization model for inpainting of a square-integrable isotropic random field on the unit sphere, where the field is represented by spherical harmonics with random complex coefficients. In the proposed optimization model, the variable is an infinite-dimensional complex vector and the objective function is a real-valued function defined by a hybrid of the $\\\\ell _2$ norm and non-Lipschitz $\\\\ell _p (0<p<1)$ norm that preserves rotational invariance property and group structure of the random complex coefficients. We show that the infinite-dimensional optimization problem is equivalent to a convexly-constrained finite-dimensional optimization problem. Moreover, we propose a smoothing penalty algorithm to solve the finite-dimensional problem via unconstrained optimization problems. We provide an approximation error bound of the inpainted random field defined by a scaled Karush–Kuhn–Tucker (KKT) point of the constrained optimization problem in the square-integrable space on the sphere with probability measure. Finally, we conduct numerical experiments on band-limited random fields on the sphere and images from Cosmic Microwave Background (CMB) data to show the promising performance of the smoothing penalty algorithm for inpainting of random fields on the sphere.\",\"PeriodicalId\":56295,\"journal\":{\"name\":\"IMA Journal of Numerical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"IMA Journal of Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/imanum/drad071\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"IMA Journal of Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/imanum/drad071","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

摘要提出了单位球上可平方积分各向同性随机场的群稀疏优化模型,该随机场用带随机复系数的球谐波表示。在该优化模型中,变量是一个无限维的复向量,目标函数是由$\ell _2$范数和非lipschitz $\ell _p (0<p<1)$范数的混合定义的实值函数,该函数保留了随机复系数的旋转不变性和群结构。我们证明了无限维优化问题等价于凸约束有限维优化问题。此外,我们提出了一种平滑惩罚算法,通过无约束优化问题来解决有限维问题。利用概率测度给出了球面上平方可积空间中约束优化问题的缩放Karush-Kuhn-Tucker (KKT)点所定义的内涂随机场的近似误差界。最后,对球面上的带限随机场和宇宙微波背景(CMB)数据图像进行了数值实验,验证了平滑惩罚算法在球面随机场图像处理中的良好性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Group sparse optimization for inpainting of random fields on the sphere
Abstract We propose a group sparse optimization model for inpainting of a square-integrable isotropic random field on the unit sphere, where the field is represented by spherical harmonics with random complex coefficients. In the proposed optimization model, the variable is an infinite-dimensional complex vector and the objective function is a real-valued function defined by a hybrid of the $\ell _2$ norm and non-Lipschitz $\ell _p (0&lt;p&lt;1)$ norm that preserves rotational invariance property and group structure of the random complex coefficients. We show that the infinite-dimensional optimization problem is equivalent to a convexly-constrained finite-dimensional optimization problem. Moreover, we propose a smoothing penalty algorithm to solve the finite-dimensional problem via unconstrained optimization problems. We provide an approximation error bound of the inpainted random field defined by a scaled Karush–Kuhn–Tucker (KKT) point of the constrained optimization problem in the square-integrable space on the sphere with probability measure. Finally, we conduct numerical experiments on band-limited random fields on the sphere and images from Cosmic Microwave Background (CMB) data to show the promising performance of the smoothing penalty algorithm for inpainting of random fields on the sphere.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
×
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