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Deterministic sampling of sparse trigonometric polynomials
Xu, Zhiqiang
2011-04-01
Source PublicationJOURNAL OF COMPLEXITY
ISSN0885-064X
Volume27Issue:2Pages:133-140
AbstractOne can recover sparse multivariate trigonometric polynomials from a few randomly taken samples with high probability (as shown by Kunis and Rauhut). We give a deterministic sampling of multivariate trigonometric polynomials inspired by Weil's exponential sum. Our sampling can produce a deterministic matrix satisfying the statistical restricted isometry property, and also nearly optimal Grassmannian frames. We show that one can exactly reconstruct every M-sparse multivariate trigonometric polynomial with fixed degree and of length D from the determinant sampling X, using the orthogonal matching pursuit, and with vertical bar X vertical bar a prime number greater than (M log D)(2). This result is optimal within the (log D)(2) factor. The simulations show that the deterministic sampling can offer reconstruction performance similar to the random sampling. (C) 2011 Elsevier Inc. All rights reserved.
KeywordCompressed sensing Deterministic sampling Weil sum Sparse trigonometric polynomials
DOI10.1016/j.jco.2011.01.007
Language英语
Funding ProjectFunds for Creative Research Groups of China[11021101] ; NSFC[10871196] ; National Basic Research Program of China (973 Program)[2010CB832702]
WOS Research AreaComputer Science ; Mathematics
WOS SubjectComputer Science, Theory & Methods ; Mathematics, Applied
WOS IDWOS:000289135400002
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/13090
Collection计算数学与科学工程计算研究所
Corresponding AuthorXu, Zhiqiang
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
Recommended Citation
GB/T 7714
Xu, Zhiqiang. Deterministic sampling of sparse trigonometric polynomials[J]. JOURNAL OF COMPLEXITY,2011,27(2):133-140.
APA Xu, Zhiqiang.(2011).Deterministic sampling of sparse trigonometric polynomials.JOURNAL OF COMPLEXITY,27(2),133-140.
MLA Xu, Zhiqiang."Deterministic sampling of sparse trigonometric polynomials".JOURNAL OF COMPLEXITY 27.2(2011):133-140.
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