KMS Of Academy of mathematics and systems sciences, CAS
| Sparse Phase Retrieval Via PhaseLiftOff | |
| Xia, Yu1; Xu, Zhiqiang2,3 | |
| 2021 | |
| Source Publication | IEEE TRANSACTIONS ON SIGNAL PROCESSING
 |
| ISSN | 1053-587X |
| Volume | 69Pages:2129-2143 |
| Abstract | The aim of sparse phase retrieval is to recover a k-sparse signal x(0) is an element of C-d from quadratic measurements vertical bar < a(j), x(0)>vertical bar(2) where a(j) is an element of C-d, j = 1, ..., m. Noting vertical bar < a(j), x(0)>vertical bar(2) = Tr(A(j)X(0)) with A(j) = a(j)a(j)* is an element of C-dxd, X-0 = x(0)x(0)* is an element of C-dxd, one can recast sparse phase retrieval as a problem of recovering a rank-one sparse matrix from linear measurements. Yin and Xin introduced PhaseLiftOff which presents a proxy of rank-one condition via the difference of trace and Frobenius norm. By adding sparsity penalty to PhaseLiftOff, in this paper, we present a novel model to recover sparse signals from quadratic measurements. Theoretical analysis shows that the optimal solution to our model provides the stable recovery of x(0) under almost optimal sampling complexity m = O(k log(d/k)). We use the difference of convex function algorithm (DCA) to solve PhaseLiftOff, showing DCA converges to a stationary point. Numerical experiments demonstrate that our algorithm outperforms other state-of-the-art algorithms used for solving sparse phase retrieval. |
| Keyword | Signal recovery phase retrieval compressed sensing restricted isometry property compressed phaseless sensing |
| DOI | 10.1109/TSP.2021.3067164 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | NSFC[12025108] ; NSFC[11901143] ; NSFC[11971427] ; Zhejiang Provincial Natural Science Foundation[LQ19A010008] ; Education Department of Zhejiang Province Science Foundation[Y201840082] ; Beijing Natural Science Foundation[Z180002] |
| WOS Research Area | Engineering |
| WOS Subject | Engineering, Electrical & Electronic |
| WOS ID | WOS:000641963400004 |
| Publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58618 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Xia, Yu |
| Affiliation | 1.Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Xia, Yu,Xu, Zhiqiang. Sparse Phase Retrieval Via PhaseLiftOff[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING,2021,69:2129-2143. |
| APA | Xia, Yu,&Xu, Zhiqiang.(2021).Sparse Phase Retrieval Via PhaseLiftOff.IEEE TRANSACTIONS ON SIGNAL PROCESSING,69,2129-2143. |
| MLA | Xia, Yu,et al."Sparse Phase Retrieval Via PhaseLiftOff".IEEE TRANSACTIONS ON SIGNAL PROCESSING 69(2021):2129-2143. |
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