Restricted q-Isometry Properties Adapted to Frames for Nonconvex lq-Analysis

Junhong Lin, Song Li
{"title":"Restricted q-Isometry Properties Adapted to Frames for Nonconvex lq-Analysis","authors":"Junhong Lin, Song Li","doi":"10.1109/TIT.2016.2573312","DOIUrl":null,"url":null,"abstract":"This paper discusses reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the $l_q$-analysis optimization with $0<q\\leq 1$. We first introduce a notion of restricted $q$-isometry property ($q$-RIP) adapted to a dictionary, which is a natural extension of the standard $q$-RIP, and establish a generalized $q$-RIP condition for approximate reconstruction of signals via the $l_q$-analysis optimization. We then determine how many random, Gaussian measurements are needed for the condition to hold with high probability. The resulting sufficient condition is met by fewer measurements for smaller $q$ than when $q=1$. \r\nThe introduced generalized $q$-RIP is also useful in compressed data separation. In compressed data separation, one considers the problem of reconstruction of signals' distinct subcomponents, which are (approximately) sparse in morphologically different dictionaries, from few measurements. With the notion of generalized $q$-RIP, we show that under an usual assumption that the dictionaries satisfy a mutual coherence condition, the $l_q$ split analysis with $0<q\\leq1 $ can approximately reconstruct the distinct components from fewer random Gaussian measurements with small $q$ than when $q=1$","PeriodicalId":13250,"journal":{"name":"IEEE Trans. Inf. Theory","volume":"56 1","pages":"4733-4747"},"PeriodicalIF":0.0000,"publicationDate":"2016-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"18","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Trans. Inf. Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TIT.2016.2573312","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 18

Abstract

This paper discusses reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the $l_q$-analysis optimization with $0
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
适用于非凸lq分析框架的受限q等距性质
本文通过$0
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 去求助
×
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
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1