Image reconstruction: applications in medical sciences
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2017]
|
| Series: | De Gruyter graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 225 Seiten Illustrationen, Diagramme |
| ISBN: | 9783110500486 |
Staff View
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| 100 | 1 | |a Zeng, Gengsheng Lawrence |e Verfasser |0 (DE-588)140930612 |4 aut | |
| 245 | 1 | 0 | |a Image reconstruction |b applications in medical sciences |c Gengsheng Lawrence Zeng |
| 264 | 1 | |a Berlin |b De Gruyter |c [2017] | |
| 264 | 4 | |c © 2017 | |
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Record in the Search Index
| _version_ | 1804177473897758720 |
|---|---|
| adam_text | CONTENTS
1 BASIC PRINCIPLES OF TOMOGRAPHY * 1
1.1 TOMOGRAPHY
-----
1
1.2 PROJECTION
-----
3
1.3 IMAGE RECONSTRUCTION * 5
1.4 BACKPROJECTION * 7
1.5 MATHEMATICAL EXPRESSIONS * 9
1.5.1 PROJECTION
-----
9
1.5.2 BACKPROJECTION
-----
9
1.5.3 THE DIRAC 6-FUNCTION * 11
1.6 WORKED EXAMPLES * 13
1.7 SUMMARY
------
16
PROBLEMS * 17
BIBLIOGRAPHY
-----
18
2 PARALLEL-BEAM IMAGE RECONSTRUCTION * 19
2.1 FOURIER TRANSFORM * 19
2.2 CENTRAL SLICE THEOREM
-----
19
2.3 RECONSTRUCTION ALGORITHMS * 22
2.3.1 METHOD 1
------
22
2.3.2 METHOD 2
------
23
2.3.3 METHOD 3
------
24
2.3.4 METHOD 4
------
25
2.3.5 METHOD 5
------
25
2.3.6 METHOD 6
------
25
2.4 A COMPUTER SIMULATION
-----
27
2.5 ROI RECONSTRUCTION WITH TRUNCATED PROJECTIONS
------
28
2.6 MATHEMATICAL EXPRESSIONS * 32
2.6.1 THE FOURIER TRANSFORM AND CONVOLUTION
-----
33
2.6.2 THE HILBERT TRANSFORM AND THE FINITE HILBERT TRANSFORM
2.6.3 PROOF OF THE CENTRAL SLICE THEOREM
-----
36
2.6.4 DERIVATION OF THE FBP ALGORITHM * 37
2.6.5 EXPRESSION OF THE CONVOLUTION BACKPROJECTION
ALGORITHM * 38
2.6.6 EXPRESSION OF THE RADON INVERSION FORMULA
------
38
2.6.7 DERIVATION OF THE BACKPROJECTION-THEN-FILTERING
ALGORITHM
-----
38
2.6.8 EXPRESSION OF THE DERIVATIVE-BACKPROJECTION-HILBERT
TRANSFORM ALGORITHM * 39
2.6.9 DERIVATION OF THE BACKPROJECTION-DERIVATIVE-HILBERT
TRANSFORM ALGORITHM * 40
2.7 WORKED EXAMPLES * 40
2.8 SUMMARY
-----
47
PROBLEMS
-----
48
BIBLIOGRAPHY
-----
48
3 FAN-BEAM IMAGE RECONSTRUCTION * 50
3.1 FAN-BEAM GEOMETRY AND THE POINT SPREAD FUNCTION * 50
3.2 PARALLEL-BEAM TO FAN-BEAM ALGORITHM CONVERSION * 53
3.3 SHORT SCAN
-----
55
3.4 MATHEMATICAL EXPRESSIONS
-----
57
3.4.1 DERIVATION OF A FILTERED BACKPROJECTION FAN-BEAM
ALGORITHM * 58
3.4.2 A FAN-BEAM ALGORITHM USING THE DERIVATIVE AND THE HILBERT
TRANSFORM * 59
3.4.3 EXPRESSION FOR THE PARKER WEIGHTS
-----
61
3.4.4 ERRORS CAUSED BY FINITE BANDWIDTH IMPLEMENTATION * 62
3.5 WORKED EXAMPLES * 63
3.6 SUMMARY
-----
66
PROBLEMS
-----
67
BIBLIOGRAPHY
-----
67
4 TRANSMISSION AND EMISSION TOMOGRAPHY * 69
4.1 X-RAY COMPUTED TOMOGRAPHY * 69
4.2 POSITRON EMISSION TOMOGRAPHY AND SINGLE-PHOTON EMISSION COMPUTED
TOMOGRAPHY
-----
73
4.3 NOISE PROPAGATION IN RECONSTRUCTION * 76
4.3.1 NOISE VARIANCE OF EMISSION DATA * 76
4.3.2 NOISE VARIANCE OF TRANSMISSION DATA * 76
4.3.3 NOISE PROPAGATION IN AN FBP ALGORITHM
-----
77
4.4 ATTENUATION CORRECTION FOR EMISSION TOMOGRAPHY * 77
4.4.1 PET
-----
78
4.4.2 SPECT: TRETIAK-METZ FBP ALGORITHM FOR UNIFORM
ATTENUATION * 79
4.4.3 SPECT: INOUYE S ALGORITHM FOR UNIFORM ATTENUATION * 81
4.5 MATHEMATICAL EXPRESSIONS * 82
4.5.1 EXPRESSION FOR TRETIAK-METZ FBP ALGORITHM
-----
82
4.5.2 DERIVATION FOR INOUYE*S ALGORITHM * 83
4.5.3 RULLGAERD*S DERIVATIVE-THEN-BACKPROJECTION ALGORITHM FOR
UNIFORM ATTENUATION * 85
4.5.4 NOVIKOV-NATTERER FBP ALGORITHM FOR NONUNIFORM ATTENUATION
SPECT
-----
86
4.6 WORKED EXAMPLES * 86
4.7
5
5.1
5.1.1
5
.
1.2
5.2
5.3
5.3.1
5.3.2
5.3.3
5.4
5.4.1
5.4.2
5.4.3
5.4.4
5.4.5
5.4.6
5.4.7
5.4.8
5.5
5.6
6
6.1
6.2
6.3
6.3.1
6.3.2
6.3.3
6.4
6.5
6.6
6.6.1
6.6.2
6.6.3
SUMMARY* 88
PROBLEMS * 89
BIBLIOGRAPHY
-----
89
THREE-DIMENSIONAL IMAGE RECONSTRUCTION * 91
PARALLEL LINE-INTEGRAL DATA * 91
BACKPROJECTION-THEN-FILTERING
-----
93
FILTERED BACKPROJECTION
-----
95
PARALLEL PLANE-INTEGRAL DATA * 95
CONE-BEAM DATA * 97
FELDKAMP S ALGORITHM * 98
GRANGEAT S ALGORITHM * 99
KATSEVICH*S ALGORITHM * 101
MATHEMATICAL EXPRESSIONS * 104
BACKPROJECTION-THEN-FILTERING FOR PARALLEL LINE-INTEGRAL
DATA * 105
FBP ALGORITHM FOR PARALLEL LINE-INTEGRAL DATA * 105
THREE-DIMENSIONAL RADON INVERSION FORMULA (FBP
ALGORITHM)
-----
107
THREE-DIMENSIONAL BACKPROJECTION-THEN-FILTERING ALGORITHM
FOR RADON DATA * 107
FELDKAMP S ALGORITHM * 108
TUY S RELATIONSHIP
-----
109
GRANGEAT S RELATIONSHIP * 111
KATSEVICH*S ALGORITHM * 114
WORKED EXAMPLES * 119
SUMMARY * 122
PROBLEMS * 123
BIBLIOGRAPHY * 124
ITERATIVE RECONSTRUCTION * 127
SOLVING A SYSTEM OF LINEAR EQUATIONS * 127
ALGEBRAIC RECONSTRUCTION TECHNIQUE * 132
GRADIENT DESCENT ALGORITHMS * 133
THE GRADIENT DESCENT ALGORITHM * 133
THE LANDWEBER ALGORITHM * 135
THE CONJUGATE GRADIENT ALGORITHM * 135
ML-EM ALGORITHMS
-----
137
OS-EM ALGORITHM * 138
NOISE HANDLING * 138
ANALYTICAL METHODS - WINDOWING* 139
ITERATIVE METHODS - STOPPING EARLY * 139
ITERATIVE METHODS - CHOOSING PIXELS * 140
6.6.4
6.7
6.8
6.9
6.9.1
6.9.2
6.9.3
6.9.4
6.9.5
6.9.6
6.9.7
6.10
6.11
6.12
7
7.1
7.2
7.3
7.3.1
7.3.2
7.3.3
7.4
7.5
7.5.1
7.5.2
7.6
7.7
8
8.1
8.2
8.3
ITERATIVE METHODS - ACCURATE MODELING* 142
NOISE MODELING AS A LIKELIHOOD FUNCTION * 143
INCLUDING PRIOR KNOWLEDGE (BAYESIAN) * 145
MATHEMATICAL EXPRESSIONS * 147
ART
-----
147
THE LANDWEBER ALGORITHM * 148
CG ALGORITHM * 149
ML-EM
-----
150
OS-EM
-----
153
MAP (GREEN S ONE-STEP LATE ALGORITHM) * 154
MATCHED AND UNMATCHED PROJECTOR/BACKPROJECTOR
PAIRS
-----
154
RECONSTRUCTION USING HIGHLY UNDERSAMPLED DATA * 156
WORKED EXAMPLES * 159
SUMMARY * 171
PROBLEMS * 172
BIBLIOGRAPHY * 174
MRI RECONSTRUCTION * 178
THE *M
----
178
THE *R
-----
180
THE *I*
-----
183
TO OBTAIN ^-INFORMATION: SLICE SELECTION * 183
TO OBTAIN X-INFORMATION: FREQUENCY ENCODING
-----
185
TO OBTAIN Y-INFORMATION: PHASE ENCODING
-----
185
MATHEMATICAL EXPRESSIONS * 188
IMAGE RECONSTRUCTION FOR MRI * 191
FOURIER RECONSTRUCTION * 191
ITERATIVE RECONSTRUCTION * 192
WORKED EXAMPLES * 192
SUMMARY * 194
PROBLEMS * 195
BIBLIOGRAPHY * 195
USING FBP TO PERFORM ITERATIVE RECONSTRUCTION * 196
THE LANDWEBER ALGORITHM: FROM RECURSIVE FORM
TO NON-RECURSIVE FORM * 196
THE LANDWEBER ALGORITHM: FROM NON-RECURSIVE FORM
TO CLOSED FORM * 197
THE LANDWEBER ALGORITHM: FROM CLOSED FORM
TO BACKPROJECTION-THEN-FILTERING ALGORITHM * 198
IMPLEMENTATION OF (ARA)-1 IN THE FOURIER DOMAIN * 198
8.3.1
8.3.2 IMPLEMENTATION OF
I - (I - AATA)K
IN THE FOURIER
DOMAIN * 198
8.3.3 LANDWEBER ALGORITHM: BACKPROJECTION-THEN-FILTERING
ALGORITHM
-----
199
8.3.4 NUMERICAL EXAMPLES OF THE WINDOW FUNCTION * 199
8.4 THE LANDWEBER ALGORITHM: THE WEIGHTED FBP ALGORITHM
-----
201
8.4.1 LANDWEBER ALGORITHM: FBP WITHOUT NOISE WEIGHTING
-----
201
8.4.2 LANDWEBER ALGORITHM: FBP WITH VIEW-BASED NOISE
WEIGHTING
-----
202
8.4.3 LANDWEBER ALGORITHM: FBP WITH RAY-BASED NOISE
WEIGHTING
-----
203
8.5 FBP ALGORITHM WITH QUADRATIC CONSTRAINTS
-----
205
8.5.1 EXAMPLE OF MINIMUM NORM-CONSTRAINED FBP * 206
8.5.2 EXAMPLE OF REFERENCE IMAGE-CONSTRAINED FBP * 207
8.6 CONVOLUTION BACKPROJECTION
------
208
8.7 NON-QUADRATIC CONSTRAINTS
------
212
8.8 A VIEWPOINT FROM CALCULUS OF VARIATIONS * 214
8.9 SUMMARY
-----
217
PROBLEMS * 218
BIBLIOGRAPHY * 218
INDEX* 221
|
| any_adam_object | 1 |
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| dewey-full | 621.3 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.3 |
| dewey-search | 621.3 |
| dewey-sort | 3621.3 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik Psychologie Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV044282315 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:48:39Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110500486 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029686660 |
| oclc_num | 992510490 |
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| owner_facet | DE-1102 DE-29 DE-20 DE-M347 DE-91G DE-BY-TUM DE-634 DE-11 |
| physical | XIII, 225 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter graduate |
| spelling | Zeng, Gengsheng Lawrence Verfasser (DE-588)140930612 aut Image reconstruction applications in medical sciences Gengsheng Lawrence Zeng Berlin De Gruyter [2017] © 2017 XIII, 225 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter graduate Bildgebendes Verfahren (DE-588)4006617-4 gnd rswk-swf Bildrekonstruktion (DE-588)4145435-2 gnd rswk-swf Fachhochschul-/Hochschulausbildung Bildrekonstruktion (DE-588)4145435-2 s Bildgebendes Verfahren (DE-588)4006617-4 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-050059-2 Erscheint auch als Online-Ausgabe, ePub 978-3-11-049802-8 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029686660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zeng, Gengsheng Lawrence Image reconstruction applications in medical sciences Bildgebendes Verfahren (DE-588)4006617-4 gnd Bildrekonstruktion (DE-588)4145435-2 gnd |
| subject_GND | (DE-588)4006617-4 (DE-588)4145435-2 |
| title | Image reconstruction applications in medical sciences |
| title_auth | Image reconstruction applications in medical sciences |
| title_exact_search | Image reconstruction applications in medical sciences |
| title_full | Image reconstruction applications in medical sciences Gengsheng Lawrence Zeng |
| title_fullStr | Image reconstruction applications in medical sciences Gengsheng Lawrence Zeng |
| title_full_unstemmed | Image reconstruction applications in medical sciences Gengsheng Lawrence Zeng |
| title_short | Image reconstruction |
| title_sort | image reconstruction applications in medical sciences |
| title_sub | applications in medical sciences |
| topic | Bildgebendes Verfahren (DE-588)4006617-4 gnd Bildrekonstruktion (DE-588)4145435-2 gnd |
| topic_facet | Bildgebendes Verfahren Bildrekonstruktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029686660&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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