The minimal measurement number for generalized conjugate phase retrieval
Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the mi...
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Gespeichert in:
| Autor*in: |
Dan, Wei [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Anmerkung: |
© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Science in China - Asheville, NC : Science in China Press, 1995, 65(2020), 3 vom: 21. Okt., Seite 655-664 |
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| Übergeordnetes Werk: |
volume:65 ; year:2020 ; number:3 ; day:21 ; month:10 ; pages:655-664 |
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| DOI / URN: |
10.1007/s11425-020-1757-6 |
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| 520 | |a Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). | ||
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10.1007/s11425-020-1757-6 doi (DE-627)SPR050460072 (SPR)s11425-020-1757-6-e DE-627 ger DE-627 rakwb eng Dan, Wei verfasserin aut The minimal measurement number for generalized conjugate phase retrieval 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). phase retrieval (dpeaa)DE-He213 measurement number (dpeaa)DE-He213 conjugate (dpeaa)DE-He213 Enthalten in Science in China Asheville, NC : Science in China Press, 1995 65(2020), 3 vom: 21. Okt., Seite 655-664 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:65 year:2020 number:3 day:21 month:10 pages:655-664 https://dx.doi.org/10.1007/s11425-020-1757-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 65 2020 3 21 10 655-664 |
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10.1007/s11425-020-1757-6 doi (DE-627)SPR050460072 (SPR)s11425-020-1757-6-e DE-627 ger DE-627 rakwb eng Dan, Wei verfasserin aut The minimal measurement number for generalized conjugate phase retrieval 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). phase retrieval (dpeaa)DE-He213 measurement number (dpeaa)DE-He213 conjugate (dpeaa)DE-He213 Enthalten in Science in China Asheville, NC : Science in China Press, 1995 65(2020), 3 vom: 21. Okt., Seite 655-664 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:65 year:2020 number:3 day:21 month:10 pages:655-664 https://dx.doi.org/10.1007/s11425-020-1757-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 65 2020 3 21 10 655-664 |
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10.1007/s11425-020-1757-6 doi (DE-627)SPR050460072 (SPR)s11425-020-1757-6-e DE-627 ger DE-627 rakwb eng Dan, Wei verfasserin aut The minimal measurement number for generalized conjugate phase retrieval 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). phase retrieval (dpeaa)DE-He213 measurement number (dpeaa)DE-He213 conjugate (dpeaa)DE-He213 Enthalten in Science in China Asheville, NC : Science in China Press, 1995 65(2020), 3 vom: 21. Okt., Seite 655-664 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:65 year:2020 number:3 day:21 month:10 pages:655-664 https://dx.doi.org/10.1007/s11425-020-1757-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 65 2020 3 21 10 655-664 |
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10.1007/s11425-020-1757-6 doi (DE-627)SPR050460072 (SPR)s11425-020-1757-6-e DE-627 ger DE-627 rakwb eng Dan, Wei verfasserin aut The minimal measurement number for generalized conjugate phase retrieval 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). phase retrieval (dpeaa)DE-He213 measurement number (dpeaa)DE-He213 conjugate (dpeaa)DE-He213 Enthalten in Science in China Asheville, NC : Science in China Press, 1995 65(2020), 3 vom: 21. Okt., Seite 655-664 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:65 year:2020 number:3 day:21 month:10 pages:655-664 https://dx.doi.org/10.1007/s11425-020-1757-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 65 2020 3 21 10 655-664 |
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10.1007/s11425-020-1757-6 doi (DE-627)SPR050460072 (SPR)s11425-020-1757-6-e DE-627 ger DE-627 rakwb eng Dan, Wei verfasserin aut The minimal measurement number for generalized conjugate phase retrieval 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). phase retrieval (dpeaa)DE-He213 measurement number (dpeaa)DE-He213 conjugate (dpeaa)DE-He213 Enthalten in Science in China Asheville, NC : Science in China Press, 1995 65(2020), 3 vom: 21. Okt., Seite 655-664 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:65 year:2020 number:3 day:21 month:10 pages:655-664 https://dx.doi.org/10.1007/s11425-020-1757-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 AR 65 2020 3 21 10 655-664 |
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Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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Abstract The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ $ ℂ^{n} $ from quadratic measurements x* A1x,…, x* Amx, where A1,…, Am ∈ $ ℝ^{n×n} $ are real symmetric matrices. The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval (up to a global phase factor as well as conjugacy) are derived in this paper. We present a set of nine vectors in $ ℝ^{4} $ and prove that it is conjugate phase retrievable on $ ℂ^{4} $. This result implies the measurement number bound 4n − 6 is not optimal for some n, which confirms a conjecture in the article by Evans and Lai (2019). © Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020 |
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