Phase retrieval of complex and vector-valued functions
The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vector...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Yang [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022transfer abstract |
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| Schlagwörter: |
Phase retrieval of vector-valued functions |
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| Übergeordnetes Werk: |
Enthalten in: Corrigendum to “Rifampicin resistance mutations in the rpoB gene of - Urusova, Darya V. ELSEVIER, 2022, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:283 ; year:2022 ; number:7 ; day:1 ; month:10 ; pages:0 |
| Links: |
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| DOI / URN: |
10.1016/j.jfa.2022.109593 |
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| 520 | |a The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. | ||
| 520 | |a The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. | ||
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| 650 | 7 | |a Vector field on graphs |2 Elsevier | |
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| 700 | 1 | |a Sun, Qiyu |4 oth | |
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10.1016/j.jfa.2022.109593 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001833.pica (DE-627)ELV058348018 (ELSEVIER)S0022-1236(22)00213-0 DE-627 ger DE-627 rakwb eng 570 VZ BIODIV DE-30 fid 44.00 bkl Chen, Yang verfasserin aut Phase retrieval of complex and vector-valued functions 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. Phase retrieval of vector-valued functions Elsevier Complex conjugate phase retrieval Elsevier Affine phase retrieval Elsevier Vector field on graphs Elsevier Cheng, Cheng oth Sun, Qiyu oth Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:283 year:2022 number:7 day:1 month:10 pages:0 https://doi.org/10.1016/j.jfa.2022.109593 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 283 2022 7 1 1001 0 |
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10.1016/j.jfa.2022.109593 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001833.pica (DE-627)ELV058348018 (ELSEVIER)S0022-1236(22)00213-0 DE-627 ger DE-627 rakwb eng 570 VZ BIODIV DE-30 fid 44.00 bkl Chen, Yang verfasserin aut Phase retrieval of complex and vector-valued functions 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. Phase retrieval of vector-valued functions Elsevier Complex conjugate phase retrieval Elsevier Affine phase retrieval Elsevier Vector field on graphs Elsevier Cheng, Cheng oth Sun, Qiyu oth Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:283 year:2022 number:7 day:1 month:10 pages:0 https://doi.org/10.1016/j.jfa.2022.109593 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 283 2022 7 1 1001 0 |
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10.1016/j.jfa.2022.109593 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001833.pica (DE-627)ELV058348018 (ELSEVIER)S0022-1236(22)00213-0 DE-627 ger DE-627 rakwb eng 570 VZ BIODIV DE-30 fid 44.00 bkl Chen, Yang verfasserin aut Phase retrieval of complex and vector-valued functions 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. Phase retrieval of vector-valued functions Elsevier Complex conjugate phase retrieval Elsevier Affine phase retrieval Elsevier Vector field on graphs Elsevier Cheng, Cheng oth Sun, Qiyu oth Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:283 year:2022 number:7 day:1 month:10 pages:0 https://doi.org/10.1016/j.jfa.2022.109593 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 283 2022 7 1 1001 0 |
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10.1016/j.jfa.2022.109593 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001833.pica (DE-627)ELV058348018 (ELSEVIER)S0022-1236(22)00213-0 DE-627 ger DE-627 rakwb eng 570 VZ BIODIV DE-30 fid 44.00 bkl Chen, Yang verfasserin aut Phase retrieval of complex and vector-valued functions 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. Phase retrieval of vector-valued functions Elsevier Complex conjugate phase retrieval Elsevier Affine phase retrieval Elsevier Vector field on graphs Elsevier Cheng, Cheng oth Sun, Qiyu oth Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:283 year:2022 number:7 day:1 month:10 pages:0 https://doi.org/10.1016/j.jfa.2022.109593 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 283 2022 7 1 1001 0 |
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10.1016/j.jfa.2022.109593 doi /cbs_pica/cbs_olc/import_discovery/elsevier/einzuspielen/GBV00000000001833.pica (DE-627)ELV058348018 (ELSEVIER)S0022-1236(22)00213-0 DE-627 ger DE-627 rakwb eng 570 VZ BIODIV DE-30 fid 44.00 bkl Chen, Yang verfasserin aut Phase retrieval of complex and vector-valued functions 2022transfer abstract nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. Phase retrieval of vector-valued functions Elsevier Complex conjugate phase retrieval Elsevier Affine phase retrieval Elsevier Vector field on graphs Elsevier Cheng, Cheng oth Sun, Qiyu oth Enthalten in Elsevier Urusova, Darya V. ELSEVIER Corrigendum to “Rifampicin resistance mutations in the rpoB gene of 2022 Amsterdam [u.a.] (DE-627)ELV007566018 volume:283 year:2022 number:7 day:1 month:10 pages:0 https://doi.org/10.1016/j.jfa.2022.109593 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U FID-BIODIV SSG-OLC-PHA 44.00 Medizin: Allgemeines VZ AR 283 2022 7 1 1001 0 |
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The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. |
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The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. |
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The phase retrieval problem in the classical setting is to reconstruct real/complex functions from magnitudes of their Fourier/frame measurements. In this paper, we consider a new phase retrieval paradigm in the vector-valued setting, which is motivated by complex conjugate phase retrieval of vectors in the complex range space of a real matrix and functions in the complex Paley-Wiener space, and also by determination of a vector field defined on a graph from their relative magnitudes between neighboring vertices. In this paper, we provide several characterizations to determine complex/vector-valued functions f in a linear space S of (in)finite dimensions, up to a trivial ambiguity, from the magnitudes ‖ ϕ ( f ) ‖ of their linear measurements ϕ ( f ) , ϕ ∈ Φ , and we apply the characterizations for the recovery of complex functions in a shift-invariant space from their phaseless evaluations and vector fields on a graph from their absolute magnitudes at vertices and relative magnitudes between neighboring vertices. In this paper, we also discuss the affine phase retrieval of vector-valued functions in a linear space and phase retrieval in the quaternion setting. |
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