A Gradient-Enhanced l(1) Approach for the Recovery of Sparse Trigonometric Polynomials

doi:10.4208/cicp.OA-2018-0006

	A Gradient-Enhanced l(1) Approach for the Recovery of Sparse Trigonometric Polynomials
	Xu, Zhiqiang; Zhou, Tao
	2018-07-01
发表期刊	COMMUNICATIONS IN COMPUTATIONAL PHYSICS
ISSN	1815-2406
卷号	24 期号:1 页码:286-308
摘要	In this paper, we discuss a gradient-enhanced l(1) approach for the recovery of sparse Fourier expansions. By gradient-enhanced approaches we mean that the directional derivatives along given vectors are utilized to improve the sparse approximations. We first consider the case where both the function values and the directional derivatives at sampling points are known. We show that, under some mild conditions, the inclusion of the derivatives information can indeed decrease the coherence of measurement matrix, and thus leads to the improved the sparse recovery conditions of the l(1) minimization. We also consider the case where either the function values or the directional derivatives are known at the sampling points, in which we present a sufficient condition under which the measurement matrix satisfies RIP, provided that the samples are distributed according to the uniform measure. This result shows that the derivatives information plays a similar role as that of the function values. Several numerical examples are presented to support the theoretical statements. Potential applications to function (Hermite-type) interpolations and uncertainty quantification are also discussed.
关键词	Gradient-enhanced l(1) minimization compressed sensing sparse Fourier expansions restricted isometry property mutual incoherence
DOI	10.4208/cicp.OA-2018-0006
语种	英语
资助项目	NSFC[91630203] ; NSFC[11422113] ; NSFC[11331012] ; NSFC[11688101] ; National Basic Research Program of China (973 Program)[2015CB856000] ; NSF of China[91630203] ; NSF of China[11688101] ; NSF of China[91630312] ; NSF of China[11571351] ; NSF of China[11731006] ; science challenge project[TZ2018001] ; NCMIS ; youth innovation promotion association (CAS)
WOS研究方向	Physics
WOS类目	Physics, Mathematical
WOS记录号	WOS:000455953800014
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32280
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Tao
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Xu, Zhiqiang,Zhou, Tao. A Gradient-Enhanced l(1) Approach for the Recovery of Sparse Trigonometric Polynomials[J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS,2018,24(1):286-308.
APA	Xu, Zhiqiang,&Zhou, Tao.(2018).A Gradient-Enhanced l(1) Approach for the Recovery of Sparse Trigonometric Polynomials.COMMUNICATIONS IN COMPUTATIONAL PHYSICS,24(1),286-308.
MLA	Xu, Zhiqiang,et al."A Gradient-Enhanced l(1) Approach for the Recovery of Sparse Trigonometric Polynomials".COMMUNICATIONS IN COMPUTATIONAL PHYSICS 24.1(2018):286-308.