Matches in SemOpenAlex for { <https://semopenalex.org/work/W3120690350> ?p ?o ?g. }
- W3120690350 endingPage "1355" @default.
- W3120690350 startingPage "1332" @default.
- W3120690350 abstract "Phase retrieval refers to the problem of recovering a signal <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ {x}_{star }in mathbb {C}^{n}$ </tex-math></inline-formula> from its phaseless measurements <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$text {y}_{text {i}}=| {a}_{i}^{ mathsf {H}} {x}_{star }|$ </tex-math></inline-formula> , where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>${ {a}_{text {i}}}_{text {i}=1}^{ {m}}$ </tex-math></inline-formula> are the measurement vectors. Spectral method is widely used for initialization in many phase retrieval algorithms. The quality of spectral initialization can have a major impact on the overall algorithm. In this paper, we focus on the model where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ {A}=[ {a}_{1},ldots, {a}_{ {m}}]^{ mathsf {H}}$ </tex-math></inline-formula> has orthonormal columns, and study the spectral initialization under the asymptotic setting <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ {m}, {n}to infty $ </tex-math></inline-formula> with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$ {m}/ {n}to delta in (1,infty)$ </tex-math></inline-formula> . We use the expectation propagation framework to characterize the performance of spectral initialization for Haar distributed matrices. Our numerical results confirm that the predictions of the EP method are accurate for not-only Haar distributed matrices, but also for realistic Fourier based models (e.g. the coded diffraction model). The main findings of this paper are the following: 1) There exists a threshold on <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$delta $ </tex-math></inline-formula> (denoted as <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$delta _{ mathrm {weak}}$ </tex-math></inline-formula> ) below which the spectral method cannot produce a meaningful estimate. We show that <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$delta _{ mathrm {weak}}=2$ </tex-math></inline-formula> for the column-orthonormal model. In contrast, previous results by Mondelli and Montanari show that <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$delta _{ mathrm {weak}}=1$ </tex-math></inline-formula> for the i.i.d. Gaussian model. 2) The optimal design for the spectral method coincides with that for the i.i.d. Gaussian model, where the latter was recently introduced by Luo, Alghamdi and Lu." @default.
- W3120690350 created "2021-01-18" @default.
- W3120690350 creator A5017771205 @default.
- W3120690350 creator A5023545041 @default.
- W3120690350 creator A5040205022 @default.
- W3120690350 creator A5042980276 @default.
- W3120690350 creator A5061942819 @default.
- W3120690350 date "2021-02-01" @default.
- W3120690350 modified "2023-10-01" @default.
- W3120690350 title "Spectral Method for Phase Retrieval: An Expectation Propagation Perspective" @default.
- W3120690350 cites W1625271478 @default.
- W3120690350 cites W1934021597 @default.
- W3120690350 cites W1976078268 @default.
- W3120690350 cites W2000828982 @default.
- W3120690350 cites W2015911499 @default.
- W3120690350 cites W2044613770 @default.
- W3120690350 cites W2067125243 @default.
- W3120690350 cites W2078397124 @default.
- W3120690350 cites W2081785908 @default.
- W3120690350 cites W2082029531 @default.
- W3120690350 cites W2123202508 @default.
- W3120690350 cites W2140966562 @default.
- W3120690350 cites W2160051394 @default.
- W3120690350 cites W2399198888 @default.
- W3120690350 cites W2479365550 @default.
- W3120690350 cites W2542482481 @default.
- W3120690350 cites W2603333836 @default.
- W3120690350 cites W2776751579 @default.
- W3120690350 cites W2899900971 @default.
- W3120690350 cites W2945463326 @default.
- W3120690350 cites W2962714615 @default.
- W3120690350 cites W2962760202 @default.
- W3120690350 cites W2963050343 @default.
- W3120690350 cites W2963073572 @default.
- W3120690350 cites W2963443408 @default.
- W3120690350 cites W2963519307 @default.
- W3120690350 cites W2963521429 @default.
- W3120690350 cites W2963791198 @default.
- W3120690350 cites W2963841451 @default.
- W3120690350 cites W2963856055 @default.
- W3120690350 cites W2964130120 @default.
- W3120690350 cites W2964262188 @default.
- W3120690350 cites W2980141162 @default.
- W3120690350 cites W3012452232 @default.
- W3120690350 cites W3098848552 @default.
- W3120690350 cites W3100688274 @default.
- W3120690350 cites W3102206315 @default.
- W3120690350 cites W3106678933 @default.
- W3120690350 doi "https://doi.org/10.1109/tit.2021.3049172" @default.
- W3120690350 hasPublicationYear "2021" @default.
- W3120690350 type Work @default.
- W3120690350 sameAs 3120690350 @default.
- W3120690350 citedByCount "6" @default.
- W3120690350 countsByYear W31206903502020 @default.
- W3120690350 countsByYear W31206903502021 @default.
- W3120690350 countsByYear W31206903502022 @default.
- W3120690350 countsByYear W31206903502023 @default.
- W3120690350 crossrefType "journal-article" @default.
- W3120690350 hasAuthorship W3120690350A5017771205 @default.
- W3120690350 hasAuthorship W3120690350A5023545041 @default.
- W3120690350 hasAuthorship W3120690350A5040205022 @default.
- W3120690350 hasAuthorship W3120690350A5042980276 @default.
- W3120690350 hasAuthorship W3120690350A5061942819 @default.
- W3120690350 hasBestOaLocation W31206903501 @default.
- W3120690350 hasConcept C102519508 @default.
- W3120690350 hasConcept C11413529 @default.
- W3120690350 hasConcept C114466953 @default.
- W3120690350 hasConcept C114614502 @default.
- W3120690350 hasConcept C118615104 @default.
- W3120690350 hasConcept C134306372 @default.
- W3120690350 hasConcept C199360897 @default.
- W3120690350 hasConcept C33923547 @default.
- W3120690350 hasConcept C41008148 @default.
- W3120690350 hasConcept C45357846 @default.
- W3120690350 hasConcept C81793267 @default.
- W3120690350 hasConcept C94375191 @default.
- W3120690350 hasConceptScore W3120690350C102519508 @default.
- W3120690350 hasConceptScore W3120690350C11413529 @default.
- W3120690350 hasConceptScore W3120690350C114466953 @default.
- W3120690350 hasConceptScore W3120690350C114614502 @default.
- W3120690350 hasConceptScore W3120690350C118615104 @default.
- W3120690350 hasConceptScore W3120690350C134306372 @default.
- W3120690350 hasConceptScore W3120690350C199360897 @default.
- W3120690350 hasConceptScore W3120690350C33923547 @default.
- W3120690350 hasConceptScore W3120690350C41008148 @default.
- W3120690350 hasConceptScore W3120690350C45357846 @default.
- W3120690350 hasConceptScore W3120690350C81793267 @default.
- W3120690350 hasConceptScore W3120690350C94375191 @default.
- W3120690350 hasFunder F4320306076 @default.
- W3120690350 hasFunder F4320337345 @default.
- W3120690350 hasIssue "2" @default.
- W3120690350 hasLocation W31206903501 @default.
- W3120690350 hasLocation W31206903502 @default.
- W3120690350 hasOpenAccess W3120690350 @default.
- W3120690350 hasPrimaryLocation W31206903501 @default.
- W3120690350 hasRelatedWork W1978042415 @default.
- W3120690350 hasRelatedWork W2351355159 @default.
- W3120690350 hasRelatedWork W2358639633 @default.