Sparse Phase Retrieval Via PhaseLiftOff
Xia, Yu1; Xu, Zhiqiang2,3
AbstractThe 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.
KeywordSignal recovery phase retrieval compressed sensing restricted isometry property compressed phaseless sensing
Indexed BySCI
Funding ProjectNSFC[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 AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000641963400004
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Document Type期刊论文
Corresponding AuthorXia, Yu
Affiliation1.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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