Deterministic sampling of sparse trigonometric polynomials
文献类型：期刊论文
| 作者 | Xu, Zhiqiang
|
| 刊名 | JOURNAL OF COMPLEXITY
 |
| 出版日期 | 2011-04-01 |
| 卷号 | 27期号:2页码:133-140 |
| 关键词 | Compressed sensing Deterministic sampling Weil sum Sparse trigonometric polynomials |
| ISSN号 | 0885-064X |
| DOI | 10.1016/j.jco.2011.01.007 |
| 英文摘要 | One 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. |
| 语种 | 英语 |
| WOS记录号 | WOS:000289135400002 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/13089]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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