Signal recovery on the sphere from compressive and phaseless measurements:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Aachen
Apprimus Verlag
2020
|
| Ausgabe: | 1. Auflage |
| Schriftenreihe: | Elektro- und Informationstechnik
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | ix, 133 Seiten Illustrationen, Diagramme 21 cm |
| ISBN: | 9783863598365 |
Internformat
MARC
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| 245 | 1 | 0 | |a Signal recovery on the sphere from compressive and phaseless measurements |c vorgelegt von Arya Bangun, M.Sc. |
| 250 | |a 1. Auflage | ||
| 264 | 1 | |a Aachen |b Apprimus Verlag |c 2020 | |
| 300 | |a ix, 133 Seiten |b Illustrationen, Diagramme |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Elektro- und Informationstechnik | |
| 502 | |b Dissertation |c Rheinisch-Westfälische Technische Hochschule Aachen |d 2020 | ||
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CONTENTS
1.
INTRODUCTION
1
1.1.
MOTIVATION
.
1
1.2.
THESIS
OUTLINE
AND
CONTRIBUTIONS
.
3
2.
BACKGROUND
7
2.1.
NOTATION
.
7
2.2.
COMPRESSED
SENSING
.
8
2.3.
PHASELESS
MEASUREMENTS
.
11
2.4.
SIGNAL
PROCESSING
ON
THE
SPHERE
AND
THE
ROTATION
GROUP
.
14
2.4.1.
SPHERICAL
HARMONICS
AND
WIGNER
D-FUNCTIONS
.
14
2.4.2.
SPARSE
EXPANSIONS
OF
BAND-LIMITED
FUNCTIONS
.
17
2.4.3.
PRODUCT
AND
ADDITION
THEOREMS
.
18
2.5.
SPHERICAL
NEAR-FIELD
ANTENNA
MEASUREMENTS
(SNF)
.
20
3.
SPARSE
SIGNAL
RECOVERY
FROM
RANDOM
SAMPLINGS
23
3.1.
PROBLEM
FORMULATION
.
25
3.2.
BOUNDED
ORTHONORMAL
SYSTEMS
(BOS)
.
26
3.2.1.
RESTRICTED
ISOMETRY
PROPERTY
(RIP)
FOR
BOS
.
26
3.2.2.
SPARSE
RECOVERY
GUARANTEES
.
27
3.3.
RIP-BOS
FOR
SENSING
MATRICES
FROM
WIGNER
D-FUNCTIONS
.
27
3.4.
NUMERICAL
EXPERIMENTS
.
30
3.4.1.
PHASE
TRANSITION
DIAGRAMS
.
30
3.4.2.
APPLICATION
TO
SNF
.
31
3.5.
CONCLUSION
.
34
4.
CONSTRUCTION
OF
LOW-COHERENCE
DETERMINISTIC
SENSING
MATRICES
37
4.1.
PROBLEM
FORMULATION
.
40
4.2.
MODULARLY
SYMMETRIC
PATTERNS
OVER
THE
AZIMUTH
AND
THE
POLARIZATION
.
41
4.3.
COHERENCE
ANALYSIS
BY
USING
WIGNER
3J
SYMBOLS
.
42
4.4.
SAMPLING
PATTERN
DESIGN
FROM
EQUISPACED
ELEVATION
POINTS
.
44
4.5.
NUMERICAL
EXPERIMENTS
.
49
4.5.1.
COHERENCE
EVALUATIONS
.
50
CONTENTS
4.5.2.
PHASE
TRANSITION
DIAGRAMS
.
51
4.5.3.
APPLICATION
TO
SNF
.
52
4.6.
CONCLUSION
.
56
5. COHERENCE
BOUNDS
FOR
DETERMINISTIC
SENSING
MATRICES
57
5.1.
PROBLEM
FORMULATION
.
59
5.2.
SUM
OF
SAMPLED
LEGENDRE
POLYNOMIALS
.
60
5.2.1.
CLOSED-FORM
EXPRESSION
.
60
5.2.2.
PROPERTIES
OF
THE
RESIDUAL
.
63
5.2.3.
NON-NEGATIVE
AND
INCREASING
PROPERTIES
.
64
5.3.
INEQUALITIES
OF
WIGNER
3J
SYMBOLS
.
67
5.3.1.
DECREASING
PROPERTIES
OF
WIGNER
3J
SYMBOLS
.
67
5.3.2.
SUM
OF
ODD
AND
EVEN
DEGREES
OF
WIGNER
3J
SYMBOLS
.
68
5.3.3.
SUM
OF
THE
PRODUCTS
OF
WIGNER
3J
SYMBOLS
AND
INTEGERS
.
70
5.4.
ESTIMATION
OF
THE
L
2
-NORM
.
72
5.5.
MAXIMUM
OF
THE
NORMALIZED
INNER
PRODUCTS
.
74
5.6.
NUMERICAL
RESULTS
.
79
5.7.
CONCLUSION
.
80
6.
SIGNAL
RECOVERY
FROM
PHASELESS
MEASUREMENTS
83
6.1.
PROBLEM
FORMULATION
.
85
6.2.
AMBIGUITIES
IN
PHASELESS
MEASUREMENTS
.
86
6.2.1.
COMPLEX
SPHERICAL
HARMONICS
.
86
6.2.2.
REAL
SPHERICAL
HARMONICS
.
86
6.3.
NUMERICAL
RESULTS
.
88
6.3.1.
PHASE
TRANSITION
DIAGRAMS
.
90
6.3.2.
APPLICATION
TO
SNF
.
93
6.4.
CONCLUSION
.
94
7.
CONCLUSION
97
7.1.
SUMMARY
.
98
7.2.
OUTLOOK
AND
FUTURE
WORKS
.
99
LIST
OF
FIGURES
102
LIST
OF
SYMBOLS
103
LIST
OF
ABBREVIATIONS
105
A.
EIGENFUNCTIONS
ON
THE
SPHERE
AND
THE
ROTATION
GROUP
107
A.L.
SPHERICAL
HARMONICS
AND
WIGNER
D-FUNCTIONS
.
107
A.2.
HYPERGEOMETRIC
POLYNOMIALS
.
110
VIII
CONTENTS
B.
MATHEMATICAL
PRELIMINARIES
115
B.L.
SUMMATION
.
115
B.1.1.
BERNOULLI
SUMMATION
.
115
B.L.
2.
ABEL
PARTIAL
SUMMATION
.
116
B.L.
3.
RIEMANN
TRAPEZOIDAL
RULE
.
116
C.
PROPERTIES
OF
WIGNER
3J
SYMBOLS
119
BIBLIOGRAPHY
121
CURRICULUM
VITAE
133
IX |
| adam_txt |
CONTENTS
1.
INTRODUCTION
1
1.1.
MOTIVATION
.
1
1.2.
THESIS
OUTLINE
AND
CONTRIBUTIONS
.
3
2.
BACKGROUND
7
2.1.
NOTATION
.
7
2.2.
COMPRESSED
SENSING
.
8
2.3.
PHASELESS
MEASUREMENTS
.
11
2.4.
SIGNAL
PROCESSING
ON
THE
SPHERE
AND
THE
ROTATION
GROUP
.
14
2.4.1.
SPHERICAL
HARMONICS
AND
WIGNER
D-FUNCTIONS
.
14
2.4.2.
SPARSE
EXPANSIONS
OF
BAND-LIMITED
FUNCTIONS
.
17
2.4.3.
PRODUCT
AND
ADDITION
THEOREMS
.
18
2.5.
SPHERICAL
NEAR-FIELD
ANTENNA
MEASUREMENTS
(SNF)
.
20
3.
SPARSE
SIGNAL
RECOVERY
FROM
RANDOM
SAMPLINGS
23
3.1.
PROBLEM
FORMULATION
.
25
3.2.
BOUNDED
ORTHONORMAL
SYSTEMS
(BOS)
.
26
3.2.1.
RESTRICTED
ISOMETRY
PROPERTY
(RIP)
FOR
BOS
.
26
3.2.2.
SPARSE
RECOVERY
GUARANTEES
.
27
3.3.
RIP-BOS
FOR
SENSING
MATRICES
FROM
WIGNER
D-FUNCTIONS
.
27
3.4.
NUMERICAL
EXPERIMENTS
.
30
3.4.1.
PHASE
TRANSITION
DIAGRAMS
.
30
3.4.2.
APPLICATION
TO
SNF
.
31
3.5.
CONCLUSION
.
34
4.
CONSTRUCTION
OF
LOW-COHERENCE
DETERMINISTIC
SENSING
MATRICES
37
4.1.
PROBLEM
FORMULATION
.
40
4.2.
MODULARLY
SYMMETRIC
PATTERNS
OVER
THE
AZIMUTH
AND
THE
POLARIZATION
.
41
4.3.
COHERENCE
ANALYSIS
BY
USING
WIGNER
3J
SYMBOLS
.
42
4.4.
SAMPLING
PATTERN
DESIGN
FROM
EQUISPACED
ELEVATION
POINTS
.
44
4.5.
NUMERICAL
EXPERIMENTS
.
49
4.5.1.
COHERENCE
EVALUATIONS
.
50
CONTENTS
4.5.2.
PHASE
TRANSITION
DIAGRAMS
.
51
4.5.3.
APPLICATION
TO
SNF
.
52
4.6.
CONCLUSION
.
56
5. COHERENCE
BOUNDS
FOR
DETERMINISTIC
SENSING
MATRICES
57
5.1.
PROBLEM
FORMULATION
.
59
5.2.
SUM
OF
SAMPLED
LEGENDRE
POLYNOMIALS
.
60
5.2.1.
CLOSED-FORM
EXPRESSION
.
60
5.2.2.
PROPERTIES
OF
THE
RESIDUAL
.
63
5.2.3.
NON-NEGATIVE
AND
INCREASING
PROPERTIES
.
64
5.3.
INEQUALITIES
OF
WIGNER
3J
SYMBOLS
.
67
5.3.1.
DECREASING
PROPERTIES
OF
WIGNER
3J
SYMBOLS
.
67
5.3.2.
SUM
OF
ODD
AND
EVEN
DEGREES
OF
WIGNER
3J
SYMBOLS
.
68
5.3.3.
SUM
OF
THE
PRODUCTS
OF
WIGNER
3J
SYMBOLS
AND
INTEGERS
.
70
5.4.
ESTIMATION
OF
THE
L
2
-NORM
.
72
5.5.
MAXIMUM
OF
THE
NORMALIZED
INNER
PRODUCTS
.
74
5.6.
NUMERICAL
RESULTS
.
79
5.7.
CONCLUSION
.
80
6.
SIGNAL
RECOVERY
FROM
PHASELESS
MEASUREMENTS
83
6.1.
PROBLEM
FORMULATION
.
85
6.2.
AMBIGUITIES
IN
PHASELESS
MEASUREMENTS
.
86
6.2.1.
COMPLEX
SPHERICAL
HARMONICS
.
86
6.2.2.
REAL
SPHERICAL
HARMONICS
.
86
6.3.
NUMERICAL
RESULTS
.
88
6.3.1.
PHASE
TRANSITION
DIAGRAMS
.
90
6.3.2.
APPLICATION
TO
SNF
.
93
6.4.
CONCLUSION
.
94
7.
CONCLUSION
97
7.1.
SUMMARY
.
98
7.2.
OUTLOOK
AND
FUTURE
WORKS
.
99
LIST
OF
FIGURES
102
LIST
OF
SYMBOLS
103
LIST
OF
ABBREVIATIONS
105
A.
EIGENFUNCTIONS
ON
THE
SPHERE
AND
THE
ROTATION
GROUP
107
A.L.
SPHERICAL
HARMONICS
AND
WIGNER
D-FUNCTIONS
.
107
A.2.
HYPERGEOMETRIC
POLYNOMIALS
.
110
VIII
CONTENTS
B.
MATHEMATICAL
PRELIMINARIES
115
B.L.
SUMMATION
.
115
B.1.1.
BERNOULLI
SUMMATION
.
115
B.L.
2.
ABEL
PARTIAL
SUMMATION
.
116
B.L.
3.
RIEMANN
TRAPEZOIDAL
RULE
.
116
C.
PROPERTIES
OF
WIGNER
3J
SYMBOLS
119
BIBLIOGRAPHY
121
CURRICULUM
VITAE
133
IX |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bangun, Arya 1988- |
| author_GND | (DE-588)120637960X |
| author_facet | Bangun, Arya 1988- |
| author_role | aut |
| author_sort | Bangun, Arya 1988- |
| author_variant | a b ab |
| building | Verbundindex |
| bvnumber | BV046777827 |
| ctrlnum | (OCoLC)1164627337 (DE-599)DNB1207415006 |
| edition | 1. Auflage |
| format | Thesis Book |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV046777827 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:48:57Z |
| indexdate | 2024-07-20T05:48:52Z |
| institution | BVB |
| isbn | 9783863598365 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032187097 |
| oclc_num | 1164627337 |
| open_access_boolean | |
| owner | DE-29T |
| owner_facet | DE-29T |
| physical | ix, 133 Seiten Illustrationen, Diagramme 21 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Apprimus Verlag |
| record_format | marc |
| series2 | Elektro- und Informationstechnik |
| spelling | Bangun, Arya 1988- Verfasser (DE-588)120637960X aut Signal recovery on the sphere from compressive and phaseless measurements vorgelegt von Arya Bangun, M.Sc. 1. Auflage Aachen Apprimus Verlag 2020 ix, 133 Seiten Illustrationen, Diagramme 21 cm txt rdacontent n rdamedia nc rdacarrier Elektro- und Informationstechnik Dissertation Rheinisch-Westfälische Technische Hochschule Aachen 2020 Komprimierte Abtastung (DE-588)1036377245 gnd rswk-swf Messunsicherheit (DE-588)4210374-5 gnd rswk-swf Fernfeld (DE-588)4154023-2 gnd rswk-swf Signalregenerierung (DE-588)4181274-8 gnd rswk-swf Antennenmesstechnik (DE-588)4142613-7 gnd rswk-swf Sphäre (DE-588)4182221-3 gnd rswk-swf Abtastung (DE-588)4140375-7 gnd rswk-swf Strahlungscharakteristik (DE-588)4057852-5 gnd rswk-swf Antennennahfeld (DE-588)4142615-0 gnd rswk-swf Transformation Mathematik (DE-588)4060637-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Signalregenerierung (DE-588)4181274-8 s Komprimierte Abtastung (DE-588)1036377245 s Sphäre (DE-588)4182221-3 s Strahlungscharakteristik (DE-588)4057852-5 s Antennenmesstechnik (DE-588)4142613-7 s Antennennahfeld (DE-588)4142615-0 s Transformation Mathematik (DE-588)4060637-5 s Fernfeld (DE-588)4154023-2 s Abtastung (DE-588)4140375-7 s Messunsicherheit (DE-588)4210374-5 s DE-604 B:DE-101 application/pdf https://d-nb.info/1207415006/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032187097&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bangun, Arya 1988- Signal recovery on the sphere from compressive and phaseless measurements Komprimierte Abtastung (DE-588)1036377245 gnd Messunsicherheit (DE-588)4210374-5 gnd Fernfeld (DE-588)4154023-2 gnd Signalregenerierung (DE-588)4181274-8 gnd Antennenmesstechnik (DE-588)4142613-7 gnd Sphäre (DE-588)4182221-3 gnd Abtastung (DE-588)4140375-7 gnd Strahlungscharakteristik (DE-588)4057852-5 gnd Antennennahfeld (DE-588)4142615-0 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| subject_GND | (DE-588)1036377245 (DE-588)4210374-5 (DE-588)4154023-2 (DE-588)4181274-8 (DE-588)4142613-7 (DE-588)4182221-3 (DE-588)4140375-7 (DE-588)4057852-5 (DE-588)4142615-0 (DE-588)4060637-5 (DE-588)4113937-9 |
| title | Signal recovery on the sphere from compressive and phaseless measurements |
| title_auth | Signal recovery on the sphere from compressive and phaseless measurements |
| title_exact_search | Signal recovery on the sphere from compressive and phaseless measurements |
| title_exact_search_txtP | Signal recovery on the sphere from compressive and phaseless measurements |
| title_full | Signal recovery on the sphere from compressive and phaseless measurements vorgelegt von Arya Bangun, M.Sc. |
| title_fullStr | Signal recovery on the sphere from compressive and phaseless measurements vorgelegt von Arya Bangun, M.Sc. |
| title_full_unstemmed | Signal recovery on the sphere from compressive and phaseless measurements vorgelegt von Arya Bangun, M.Sc. |
| title_short | Signal recovery on the sphere from compressive and phaseless measurements |
| title_sort | signal recovery on the sphere from compressive and phaseless measurements |
| topic | Komprimierte Abtastung (DE-588)1036377245 gnd Messunsicherheit (DE-588)4210374-5 gnd Fernfeld (DE-588)4154023-2 gnd Signalregenerierung (DE-588)4181274-8 gnd Antennenmesstechnik (DE-588)4142613-7 gnd Sphäre (DE-588)4182221-3 gnd Abtastung (DE-588)4140375-7 gnd Strahlungscharakteristik (DE-588)4057852-5 gnd Antennennahfeld (DE-588)4142615-0 gnd Transformation Mathematik (DE-588)4060637-5 gnd |
| topic_facet | Komprimierte Abtastung Messunsicherheit Fernfeld Signalregenerierung Antennenmesstechnik Sphäre Abtastung Strahlungscharakteristik Antennennahfeld Transformation Mathematik Hochschulschrift |
| url | https://d-nb.info/1207415006/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032187097&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bangunarya signalrecoveryonthespherefromcompressiveandphaselessmeasurements |
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Inhaltsverzeichnis