Medical image reconstruction: from analytical and iterative methods to machine learning
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| Previous Title: | Medical image reconstruction : a conceptual tutorial |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Berlin
De Gruyter
[2023]
|
| Edition: | 2nd edition |
| Series: | De Gruyter Graduate
|
| Subjects: | |
| Online Access: | Beschreibung für Marketing Inhaltsverzeichnis |
| Physical Description: | XIV, 273 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| ISBN: | 9783111055039 |
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MARC
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| 100 | 1 | |a Zeng, Gengsheng Lawrence |e Verfasser |0 (DE-588)140930612 |4 aut | |
| 245 | 1 | 0 | |a Medical image reconstruction |b from analytical and iterative methods to machine learning |c Gengsheng Lawrence Zeng |
| 250 | |a 2nd edition | ||
| 264 | 1 | |a Berlin |b De Gruyter |c [2023] | |
| 264 | 4 | |c © 2023 | |
| 300 | |a XIV, 273 Seiten |b Illustrationen, Diagramme |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Graduate | |
| 650 | 0 | 7 | |a Bildrekonstruktion |0 (DE-588)4145435-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Tomografie |0 (DE-588)4078351-0 |2 gnd |9 rswk-swf |
| 653 | |a 2-dimensional Image Reconstruction | ||
| 653 | |a 2-dimensionale Bildrekonstruktion | ||
| 653 | |a 3-dimensional Image Reconstruction | ||
| 653 | |a 3-dimensionale Bildrekonstruktion | ||
| 653 | |a Einzelphotonen-Emissions-Computertomographie | ||
| 653 | |a Magnetic Resonance Imaging | ||
| 653 | |a Magnetresonanztomographie | ||
| 653 | |a Single Photon Emission Computed Tomography | ||
| 689 | 0 | 0 | |a Tomografie |0 (DE-588)4078351-0 |D s |
| 689 | 0 | 1 | |a Bildrekonstruktion |0 (DE-588)4145435-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-105540-4 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-105570-1 |
| 780 | 0 | 0 | |i Vorangegangen ist |t Medical image reconstruction : a conceptual tutorial |z 978-3-642-05367-2 |w (DE-604)BV036117275 |
| 856 | 4 | 2 | |m X:MVB |u https://www.degruyter.com/isbn/9783111055039 |3 Beschreibung für Marketing |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034312400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034312400 | ||
| 883 | 1 | |8 1\p |a vlb |d 20230125 |q DE-101 |u https://d-nb.info/provenance/plan#vlb | |
Record in the Search Index
| _version_ | 1804185349164892160 |
|---|---|
| adam_text | CONTENTS
PREFACE
-
VII
1
1.1
1.2
1.3
1.4
1.5
1.5.1
1.5.2
1.5.3
1.6
1.7
BASIC
PRINCIPLES
OF
TOMOGRAPHY
-
1
TOMOGRAPHY
-
1
PROJECTION
-
3
IMAGE
RECONSTRUCTION
-
6
BACKPROJECTION
----
8
MATHEMATICAL
EXPRESSIONS
----
9
PROJECTION
-
9
BACKPROJECTION
----
10
THE
DIRAC
8-FUNCTION
----
12
WORKED
EXAMPLES
-
14
SUMMARY
----
18
PROBLEMS
-
18
BIBLIOGRAPHY
----
19
2
2.1
2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.4
2.5
2.6
2.6.1
2.6.2
2.6.3
2.6.4
2.6.5
2.6.6
2.6.7
2.6.8
PARALLEL-BEAM
IMAGE
RECONSTRUCTION
-
20
FOURIER
TRANSFORM
-
20
CENTRAL
SLICE
THEOREM
-
21
RECONSTRUCTION
ALGORITHMS
-
23
METHODI
-----24
METHOD
2
----
24
METHODS
----
26
METHOD
4
----
26
METHODS
----
26
METHOD
6
----
27
A
COMPUTER
SIMULATION
-
28
ROI
RECONSTRUCTION
WITH
TRUNCATED
PROJECTIONS
-
29
MATHEMATICAL
EXPRESSIONS
-
34
THE
FOURIER
TRANSFORM
AND
CONVOLUTION
-
34
THE
HILBERT
TRANSFORM
AND
THE
FINITE
HILBERT
TRANSFORM
-
35
PROOF
OF
THE
CENTRAL
SLICE
THEOREM
-
37
DERIVATION
OF
THE
FBP
ALGORITHM
----
38
EXPRESSION
OF
THE
CONVOLUTION
BACKPROJECTION
ALGORITHM
-
39
EXPRESSION
OF
THE
RADON
INVERSION
FORMULA
-
40
DERIVATION
OF
THE
BACKPROJECTION-THEN-FILTERING
ALGORITHM
-
40
EXPRESSION
OF
THE
DERIVATIVE-BACKPROJECTION-HILBERT
TRANSFORM
ALGORITHM
-
41
2.6.9
DERIVATION
OF
THE
BACKPROJECTION-DERIVATIVE-HILBERT
TRANSFORM
ALGORITHM
-
42
X
-
CONTENTS
2.7
WORKED
EXAMPLES
-
42
2.8
SUMMARY
-
49
PROBLEMS
-
50
BIBLIOGRAPHY
-
50
3
FAN-BEAM
IMAGE
RECONSTRUCTION
-
52
3.1
FAN-BEAM
GEOMETRY
AND
THE
POINT
SPREAD
FUNCTION
-
52
3.2
PARALLEL-BEAM
TO
FAN-BEAM
ALGORITHM
CONVERSION
-
55
3.3
SHORT
SCAN
-
57
3.4
MATHEMATICAL
EXPRESSIONS
-
59
3.4.1
DERIVATION
OF
A
FILTERED
BACKPROJECTION
FAN-BEAM
ALGORITHM
-
60
3.4.2
A
FAN-BEAM
ALGORITHM
USING
THE
DERIVATIVE
AND
THE
HILBERT
TRANSFORM
-
61
3.4.3
EXPRESSION
FOR
THE
PARKER
WEIGHTS
-
63
3.4.4
ERRORS
CAUSED
BY
FINITE
BANDWIDTH
IMPLEMENTATION
-
64
3.5
WORKED
EXAMPLES
-
65
3.6
SUMMARY
-
68
PROBLEMS
-
69
BIBLIOGRAPHY
-
69
4
TRANSMISSION
AND
EMISSION
TOMOGRAPHY
-
71
4.1
X-RAY
COMPUTED
TOMOGRAPHY
-
71
4.2
POSITRON
EMISSION
TOMOGRAPHY
AND
SINGLE-PHOTON
EMISSION
COMPUTED
TOMOGRAPHY
-
75
4.3
NOISE
PROPAGATION
IN
RECONSTRUCTION
-
78
4.3.1
NOISE
VARIANCE
OF
EMISSION
DATA
-
78
4.3.2
NOISE
VARIANCE
OF
TRANSMISSION
DATA
-
79
4.3.3
NOISE
PROPAGATION
IN
AN
FBP
ALGORITHM
-
79
4.4
ATTENUATION
CORRECTION
FOR
EMISSION
TOMOGRAPHY
-
80
4.4.1
PET
------
80
4.4.2
SPECT:
TRETIAK-METZ
FBP
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
81
4.4.3
SPECT:
INOUYE
S
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
83
4.5
MATHEMATICAL
EXPRESSIONS
-
85
4.5.1
EXPRESSION
FOR
TRETIAK-METZ
FBP
ALGORITHM
-
85
4.5.2
DERIVATION
FOR
INOUYE
S
ALGORITHM
-
85
4.5.3
RULLGARD
S
DERIVATIVE-THEN-BACKPROJECTION
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
87
4.5.4
NOVIKOV-NATTERER
FBP
ALGORITHM
FOR
NONUNIFORM
ATTENUATION
SPECT
------88
4.6
WORKED
EXAMPLES
-
89
CONTENTS
-
XI
4.7
SUMMARY
-
91
PROBLEMS
-
91
BIBLIOGRAPHY
-
92
5
THREE-DIMENSIONAL
IMAGE
RECONSTRUCTION
-
94
5.1
PARALLEL
LINE-INTEGRAL
DATA
-
94
5.1.1
BACKPROJECTION-THEN-FILTERING
-
96
5.1.2
FILTERED
BACKPROJECTION
-
98
5.2
PARALLEL
PLANE-INTEGRAL
DATA
-
98
5.3
CONE-BEAM
DATA
-
100
5.3.1
FELDKAMP
S
ALGORITHM
-
101
5.3.2
GRANGEAT
S
ALGORITHM
-
102
5.3.3
KATSEVICH
S
ALGORITHM
-
104
5.4
MATHEMATICAL
EXPRESSIONS
-
108
5.4.1
BACKPROJECTION-THEN-FILTERING
FOR
PARALLEL
LINE-INTEGRAL
DATA
-
108
5.4.2
FBP
ALGORITHM
FOR
PARALLEL
LINE-INTEGRAL
DATA
-
109
5.4.3
THREE-DIMENSIONAL
RADON
INVERSION
FORMULA
(FBP
ALGORITHM)
-
112
5.4.4
THREE-DIMENSIONAL
BACKPROJECTION-THEN-FILTERING
ALGORITHM
FOR
RADON
DATA
-
113
5.4.5
FELDKAMP
S
ALGORITHM
-
113
5.4.6
TUY S
RELATIONSHIP
-
114
5.4.7
GRANGEAT
S
RELATIONSHIP
-
117
5.4.8
KATSEVICH
S
ALGORITHM
-
119
5.5
RADON
TRANSFORM
AND
RAY
TRANSFORM
IN
N
DIMENSIONS
-
125
5.6
WORKED
EXAMPLES
-
126
5.7
SUMMARY
-
129
PROBLEMS
-
130
BIBLIOGRAPHY
-
130
6
ITERATIVE
RECONSTRUCTION
-
133
6.1
SOLVING
A
SYSTEM
OF
LINEAR
EQUATIONS
-
133
6.2
ALGEBRAIC
RECONSTRUCTION
TECHNIQUE
-
138
6.3
GRADIENT
DESCENT
ALGORITHMS
-
139
6.3.1
THE
GRADIENT
DESCENT
ALGORITHM
-
139
6.3.2
THE
LANDWEBER
ALGORITHM
-
141
6.3.3
THE
CONJUGATE
GRADIENT
ALGORITHM
-
142
6.4
ML-EM
ALGORITHMS
-
143
6.5
OS-EM
ALGORITHM
--------
144
6.6
NOISE
HANDLING
--------
144
6.6.1
ANALYTICAL
METHODS:
WINDOWING
-
145
6.6.2
ITERATIVE
METHODS:
STOPPING
EARLY
-
145
6.6.3
ITERATIVE
METHODS:
CHOOSING
PIXELS
-
146
XII
-
CONTENTS
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
ITERATIVE
METHODS:
ACCURATE
MODELING
-
148
NOISE
MODELING
AS
A
LIKELIHOOD
FUNCTION
-
149
INCLUDING
PRIOR
KNOWLEDGE
(BAYESIAN)
-
152
MATHEMATICAL
EXPRESSIONS
-
153
ART
----
153
THE
LANDWEBER
ALGORITHM
-
154
CG
ALGORITHM
----
155
ML-EM
----
157
OS-EM
----
159
MAP
(GREEN
S
ONE-STEP-LATE
ALGORITHM)
-
160
MATCHED
AND
UNMATCHED
PROJECTOR/BACKPROJECTOR
PAIRS
-
162
RECONSTRUCTION
USING
HIGHLY
UNDERSAMPLED
DATA
-
164
WORKED
EXAMPLES
-
167
SUMMARY
-
179
PROBLEMS
-
180
BIBLIOGRAPHY
-
182
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
MRI
RECONSTRUCTION
-
185
THE
M
----
185
THE
R
---
187
THE
I
-----190
TO
OBTAIN
Z-INFORMATION:
SLICE
SELECTION
-
190
TO
OBTAIN
X-INFORMATION:
FREQUENCY
ENCODING
-
191
TO
OBTAIN
Y-INFORMATION:
PHASE
ENCODING
-
192
MATHEMATICAL
EXPRESSIONS
-
195
IMAGE
RECONSTRUCTION
FOR
MRI
-
198
FOURIER
RECONSTRUCTION
-
198
ITERATIVE
RECONSTRUCTION
-
199
WORKED
EXAMPLES
-
200
SUMMARY
-
201
PROBLEMS
-----202
BIBLIOGRAPHY
----
202
8
8.1
USING
FBP
TO
PERFORM
ITERATIVE
RECONSTRUCTION
-
204
THE
LANDWEBER
ALGORITHM:
FROM
RECURSIVE
FORM
TO
NONRECURSIVE
FORM
----
204
8.2
THE
LANDWEBER
ALGORITHM:
FROM
NONRECURSIVE
FORM
TO
CLOSED
FORM
-
205
8.3
THE
LANDWEBER
ALGORITHM:
FROM
CLOSED
FORM
TO
BACKPROJECTION-THEN
FILTERING
ALGORITHM
-
206
8.3.1
IMPLEMENTATION
OF
(ATA)1
IN
THE
FOURIER
DOMAIN
-
206
CONTENTS
-
XIII
8.3.2
8.3.3
8.3.4
8.4
8.4.1
8.4.2
8.4.3
8.5
8.5.1
8.5.2
8.6
8.7
8.8
8.9
IMPLEMENTATION
OF
I
(I
AA
T
A}
K
IN
THE
FOURIER
DOMAIN
-
207
LANDWEBER
ALGORITHM:
BACKPROJECTION-THEN-FILTERING
ALGORITHM
-
207
NUMERICAL
EXAMPLES
OF
THE
WINDOW
FUNCTION
-
207
THE
LANDWEBER
ALGORITHM:
THE
WEIGHTED
FBP
ALGORITHM
-
209
LANDWEBER
ALGORITHM:
FBP
WITHOUT
NOISE
WEIGHTING
-
209
LANDWEBER
ALGORITHM:
FBP
WITH
VIEW-BASED
NOISE
WEIGHTING
-
210
LANDWEBER
ALGORITHM:
FBP
WITH
RAY-BASED
NOISE
WEIGHTING
-
211
FBP
ALGORITHM
WITH
QUADRATIC
CONSTRAINTS
----
213
EXAMPLE
OF
MINIMUM-NORM
CONSTRAINED
FBP
-
214
EXAMPLE
OF
REFERENCE-IMAGE
CONSTRAINED
FBP
-
216
CONVOLUTION
BACKPROJECTION
-
217
NONQUADRATIC
CONSTRAINTS
-
220
A
VIEWPOINT
FROM
CALCULUS
OF
VARIATIONS
-
223
NOISE-WEIGHTED
FBP
ALGORITHM
FOR
UNIFORMLY
ATTENUATED
SPECT
PROJECTIONS
----
226
8.10
8.10.1
8.10.2
OTHER
APPLICATIONS
OF
THE
LANDWEVER-FBP
ALGORITHM
-
227
THE
LANDWEBER-FBP
VERSION
OF
THE
ITERATIVE
FBP
ALGORITHM
-
227
ESTIMATION
OF
THE
INITIAL
IMAGE
S
CONTRIBUTIONS
TO
THE
ITERATIVE
LANDWEBER
RECONSTRUCTION
-
228
8.10.3
FBP
IMPLEMENTATION
OF
THE
IMMEDIATELY
AFTER-BACKPROJECTION
FILTERING
-
229
8.10.4
8.11
REAL-TIME
SELECTION
OF
ITERATION
NUMBER
-
230
SUMMARY
-
230
PROBLEMS
----
231
BIBLIOGRAPHY
----
231
9
9.1
MACHINE
LEARNING
-
233
ANALYTIC
ALGORITHMS
VERSUS
ITERATIVE
ALGORITHMS
VERSUS
MACHINE
LEARNING
ALGORITHMS
-
233
9.2
9.2.1
9.2.2
9.2.3
9.2.4
9.2.5
9.3
9.4
BASIC
PRINCIPLES
OF
MACHINE
LEARNING
-
234
ADAPTIVE
LINEAR
NEURON
(ADALINE)
----
235
UNIVERSAL
APPROXIMATION
-
236
A
DEEP
MODEL
FOR
A
CONTINUOUS
UNIVARIATE
FUNCTION
-
242
WHEN
THE
INPUT
IS
AN
N-TUPLE
-
245
AN
N-TUPLE
TO
M-TUPLE
MAPPING
----
246
IMAGE
RECONSTRUCTION
AS
AN
N-TUPLE
TO
M-TUPLE
MAPPING
-
249
CONVOLUTIONAL
NEURAL
NETWORK
(CNN)
AS
A
MATCHED
FILTER
FOR
IDENTIFICATION
-
250
9.5
9.6
9.7
CONVOLUTIONAL
NEURAL
NETWORK
(CNN)
AS
A
NONLINEAR
DENOISE
FILTER
-
255
SUPER-RESOLUTION
-
258
TRAINING
----
260
XIV
-
CONTENTS
9.8
ATTENTION
----
261
9.9
9.10
PERSPECTIVES
-
262
SUMMARY
-
265
PROBLEM
----
266
BIBLIOGRAPHY
-
267
INDEX
-
269
|
| adam_txt |
CONTENTS
PREFACE
-
VII
1
1.1
1.2
1.3
1.4
1.5
1.5.1
1.5.2
1.5.3
1.6
1.7
BASIC
PRINCIPLES
OF
TOMOGRAPHY
-
1
TOMOGRAPHY
-
1
PROJECTION
-
3
IMAGE
RECONSTRUCTION
-
6
BACKPROJECTION
----
8
MATHEMATICAL
EXPRESSIONS
----
9
PROJECTION
-
9
BACKPROJECTION
----
10
THE
DIRAC
8-FUNCTION
----
12
WORKED
EXAMPLES
-
14
SUMMARY
----
18
PROBLEMS
-
18
BIBLIOGRAPHY
----
19
2
2.1
2.2
2.3
2.3.1
2.3.2
2.3.3
2.3.4
2.3.5
2.3.6
2.4
2.5
2.6
2.6.1
2.6.2
2.6.3
2.6.4
2.6.5
2.6.6
2.6.7
2.6.8
PARALLEL-BEAM
IMAGE
RECONSTRUCTION
-
20
FOURIER
TRANSFORM
-
20
CENTRAL
SLICE
THEOREM
-
21
RECONSTRUCTION
ALGORITHMS
-
23
METHODI
-----24
METHOD
2
----
24
METHODS
----
26
METHOD
4
----
26
METHODS
----
26
METHOD
6
----
27
A
COMPUTER
SIMULATION
-
28
ROI
RECONSTRUCTION
WITH
TRUNCATED
PROJECTIONS
-
29
MATHEMATICAL
EXPRESSIONS
-
34
THE
FOURIER
TRANSFORM
AND
CONVOLUTION
-
34
THE
HILBERT
TRANSFORM
AND
THE
FINITE
HILBERT
TRANSFORM
-
35
PROOF
OF
THE
CENTRAL
SLICE
THEOREM
-
37
DERIVATION
OF
THE
FBP
ALGORITHM
----
38
EXPRESSION
OF
THE
CONVOLUTION
BACKPROJECTION
ALGORITHM
-
39
EXPRESSION
OF
THE
RADON
INVERSION
FORMULA
-
40
DERIVATION
OF
THE
BACKPROJECTION-THEN-FILTERING
ALGORITHM
-
40
EXPRESSION
OF
THE
DERIVATIVE-BACKPROJECTION-HILBERT
TRANSFORM
ALGORITHM
-
41
2.6.9
DERIVATION
OF
THE
BACKPROJECTION-DERIVATIVE-HILBERT
TRANSFORM
ALGORITHM
-
42
X
-
CONTENTS
2.7
WORKED
EXAMPLES
-
42
2.8
SUMMARY
-
49
PROBLEMS
-
50
BIBLIOGRAPHY
-
50
3
FAN-BEAM
IMAGE
RECONSTRUCTION
-
52
3.1
FAN-BEAM
GEOMETRY
AND
THE
POINT
SPREAD
FUNCTION
-
52
3.2
PARALLEL-BEAM
TO
FAN-BEAM
ALGORITHM
CONVERSION
-
55
3.3
SHORT
SCAN
-
57
3.4
MATHEMATICAL
EXPRESSIONS
-
59
3.4.1
DERIVATION
OF
A
FILTERED
BACKPROJECTION
FAN-BEAM
ALGORITHM
-
60
3.4.2
A
FAN-BEAM
ALGORITHM
USING
THE
DERIVATIVE
AND
THE
HILBERT
TRANSFORM
-
61
3.4.3
EXPRESSION
FOR
THE
PARKER
WEIGHTS
-
63
3.4.4
ERRORS
CAUSED
BY
FINITE
BANDWIDTH
IMPLEMENTATION
-
64
3.5
WORKED
EXAMPLES
-
65
3.6
SUMMARY
-
68
PROBLEMS
-
69
BIBLIOGRAPHY
-
69
4
TRANSMISSION
AND
EMISSION
TOMOGRAPHY
-
71
4.1
X-RAY
COMPUTED
TOMOGRAPHY
-
71
4.2
POSITRON
EMISSION
TOMOGRAPHY
AND
SINGLE-PHOTON
EMISSION
COMPUTED
TOMOGRAPHY
-
75
4.3
NOISE
PROPAGATION
IN
RECONSTRUCTION
-
78
4.3.1
NOISE
VARIANCE
OF
EMISSION
DATA
-
78
4.3.2
NOISE
VARIANCE
OF
TRANSMISSION
DATA
-
79
4.3.3
NOISE
PROPAGATION
IN
AN
FBP
ALGORITHM
-
79
4.4
ATTENUATION
CORRECTION
FOR
EMISSION
TOMOGRAPHY
-
80
4.4.1
PET
------
80
4.4.2
SPECT:
TRETIAK-METZ
FBP
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
81
4.4.3
SPECT:
INOUYE
'
S
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
83
4.5
MATHEMATICAL
EXPRESSIONS
-
85
4.5.1
EXPRESSION
FOR
TRETIAK-METZ
FBP
ALGORITHM
-
85
4.5.2
DERIVATION
FOR
INOUYE
'
S
ALGORITHM
-
85
4.5.3
RULLGARD
'
S
DERIVATIVE-THEN-BACKPROJECTION
ALGORITHM
FOR
UNIFORM
ATTENUATION
-
87
4.5.4
NOVIKOV-NATTERER
FBP
ALGORITHM
FOR
NONUNIFORM
ATTENUATION
SPECT
------88
4.6
WORKED
EXAMPLES
-
89
CONTENTS
-
XI
4.7
SUMMARY
-
91
PROBLEMS
-
91
BIBLIOGRAPHY
-
92
5
THREE-DIMENSIONAL
IMAGE
RECONSTRUCTION
-
94
5.1
PARALLEL
LINE-INTEGRAL
DATA
-
94
5.1.1
BACKPROJECTION-THEN-FILTERING
-
96
5.1.2
FILTERED
BACKPROJECTION
-
98
5.2
PARALLEL
PLANE-INTEGRAL
DATA
-
98
5.3
CONE-BEAM
DATA
-
100
5.3.1
FELDKAMP
'
S
ALGORITHM
-
101
5.3.2
GRANGEAT
'
S
ALGORITHM
-
102
5.3.3
KATSEVICH
'
S
ALGORITHM
-
104
5.4
MATHEMATICAL
EXPRESSIONS
-
108
5.4.1
BACKPROJECTION-THEN-FILTERING
FOR
PARALLEL
LINE-INTEGRAL
DATA
-
108
5.4.2
FBP
ALGORITHM
FOR
PARALLEL
LINE-INTEGRAL
DATA
-
109
5.4.3
THREE-DIMENSIONAL
RADON
INVERSION
FORMULA
(FBP
ALGORITHM)
-
112
5.4.4
THREE-DIMENSIONAL
BACKPROJECTION-THEN-FILTERING
ALGORITHM
FOR
RADON
DATA
-
113
5.4.5
FELDKAMP
'
S
ALGORITHM
-
113
5.4.6
TUY'S
RELATIONSHIP
-
114
5.4.7
GRANGEAT
'
S
RELATIONSHIP
-
117
5.4.8
KATSEVICH
'
S
ALGORITHM
-
119
5.5
RADON
TRANSFORM
AND
RAY
TRANSFORM
IN
N
DIMENSIONS
-
125
5.6
WORKED
EXAMPLES
-
126
5.7
SUMMARY
-
129
PROBLEMS
-
130
BIBLIOGRAPHY
-
130
6
ITERATIVE
RECONSTRUCTION
-
133
6.1
SOLVING
A
SYSTEM
OF
LINEAR
EQUATIONS
-
133
6.2
ALGEBRAIC
RECONSTRUCTION
TECHNIQUE
-
138
6.3
GRADIENT
DESCENT
ALGORITHMS
-
139
6.3.1
THE
GRADIENT
DESCENT
ALGORITHM
-
139
6.3.2
THE
LANDWEBER
ALGORITHM
-
141
6.3.3
THE
CONJUGATE
GRADIENT
ALGORITHM
-
142
6.4
ML-EM
ALGORITHMS
-
143
6.5
OS-EM
ALGORITHM
--------
144
6.6
NOISE
HANDLING
--------
144
6.6.1
ANALYTICAL
METHODS:
WINDOWING
-
145
6.6.2
ITERATIVE
METHODS:
STOPPING
EARLY
-
145
6.6.3
ITERATIVE
METHODS:
CHOOSING
PIXELS
-
146
XII
-
CONTENTS
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
ITERATIVE
METHODS:
ACCURATE
MODELING
-
148
NOISE
MODELING
AS
A
LIKELIHOOD
FUNCTION
-
149
INCLUDING
PRIOR
KNOWLEDGE
(BAYESIAN)
-
152
MATHEMATICAL
EXPRESSIONS
-
153
ART
----
153
THE
LANDWEBER
ALGORITHM
-
154
CG
ALGORITHM
----
155
ML-EM
----
157
OS-EM
----
159
MAP
(GREEN
'
S
ONE-STEP-LATE
ALGORITHM)
-
160
MATCHED
AND
UNMATCHED
PROJECTOR/BACKPROJECTOR
PAIRS
-
162
RECONSTRUCTION
USING
HIGHLY
UNDERSAMPLED
DATA
-
164
WORKED
EXAMPLES
-
167
SUMMARY
-
179
PROBLEMS
-
180
BIBLIOGRAPHY
-
182
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
MRI
RECONSTRUCTION
-
185
THE
"
M
"
----
185
THE
"
R
"
---
187
THE
"
I
"
-----190
TO
OBTAIN
Z-INFORMATION:
SLICE
SELECTION
-
190
TO
OBTAIN
X-INFORMATION:
FREQUENCY
ENCODING
-
191
TO
OBTAIN
Y-INFORMATION:
PHASE
ENCODING
-
192
MATHEMATICAL
EXPRESSIONS
-
195
IMAGE
RECONSTRUCTION
FOR
MRI
-
198
FOURIER
RECONSTRUCTION
-
198
ITERATIVE
RECONSTRUCTION
-
199
WORKED
EXAMPLES
-
200
SUMMARY
-
201
PROBLEMS
-----202
BIBLIOGRAPHY
----
202
8
8.1
USING
FBP
TO
PERFORM
ITERATIVE
RECONSTRUCTION
-
204
THE
LANDWEBER
ALGORITHM:
FROM
RECURSIVE
FORM
TO
NONRECURSIVE
FORM
----
204
8.2
THE
LANDWEBER
ALGORITHM:
FROM
NONRECURSIVE
FORM
TO
CLOSED
FORM
-
205
8.3
THE
LANDWEBER
ALGORITHM:
FROM
CLOSED
FORM
TO
BACKPROJECTION-THEN
FILTERING
ALGORITHM
-
206
8.3.1
IMPLEMENTATION
OF
(ATA)1
IN
THE
FOURIER
DOMAIN
-
206
CONTENTS
-
XIII
8.3.2
8.3.3
8.3.4
8.4
8.4.1
8.4.2
8.4.3
8.5
8.5.1
8.5.2
8.6
8.7
8.8
8.9
IMPLEMENTATION
OF
I
(I
AA
T
A}
K
IN
THE
FOURIER
DOMAIN
-
207
LANDWEBER
ALGORITHM:
BACKPROJECTION-THEN-FILTERING
ALGORITHM
-
207
NUMERICAL
EXAMPLES
OF
THE
WINDOW
FUNCTION
-
207
THE
LANDWEBER
ALGORITHM:
THE
WEIGHTED
FBP
ALGORITHM
-
209
LANDWEBER
ALGORITHM:
FBP
WITHOUT
NOISE
WEIGHTING
-
209
LANDWEBER
ALGORITHM:
FBP
WITH
VIEW-BASED
NOISE
WEIGHTING
-
210
LANDWEBER
ALGORITHM:
FBP
WITH
RAY-BASED
NOISE
WEIGHTING
-
211
FBP
ALGORITHM
WITH
QUADRATIC
CONSTRAINTS
----
213
EXAMPLE
OF
MINIMUM-NORM
CONSTRAINED
FBP
-
214
EXAMPLE
OF
REFERENCE-IMAGE
CONSTRAINED
FBP
-
216
CONVOLUTION
BACKPROJECTION
-
217
NONQUADRATIC
CONSTRAINTS
-
220
A
VIEWPOINT
FROM
CALCULUS
OF
VARIATIONS
-
223
NOISE-WEIGHTED
FBP
ALGORITHM
FOR
UNIFORMLY
ATTENUATED
SPECT
PROJECTIONS
----
226
8.10
8.10.1
8.10.2
OTHER
APPLICATIONS
OF
THE
LANDWEVER-FBP
ALGORITHM
-
227
THE
LANDWEBER-FBP
VERSION
OF
THE
ITERATIVE
FBP
ALGORITHM
-
227
ESTIMATION
OF
THE
INITIAL
IMAGE
'
S
CONTRIBUTIONS
TO
THE
ITERATIVE
LANDWEBER
RECONSTRUCTION
-
228
8.10.3
FBP
IMPLEMENTATION
OF
THE
IMMEDIATELY
AFTER-BACKPROJECTION
FILTERING
-
229
8.10.4
8.11
REAL-TIME
SELECTION
OF
ITERATION
NUMBER
-
230
SUMMARY
-
230
PROBLEMS
----
231
BIBLIOGRAPHY
----
231
9
9.1
MACHINE
LEARNING
-
233
ANALYTIC
ALGORITHMS
VERSUS
ITERATIVE
ALGORITHMS
VERSUS
MACHINE
LEARNING
ALGORITHMS
-
233
9.2
9.2.1
9.2.2
9.2.3
9.2.4
9.2.5
9.3
9.4
BASIC
PRINCIPLES
OF
MACHINE
LEARNING
-
234
ADAPTIVE
LINEAR
NEURON
(ADALINE)
----
235
UNIVERSAL
APPROXIMATION
-
236
A
DEEP
MODEL
FOR
A
CONTINUOUS
UNIVARIATE
FUNCTION
-
242
WHEN
THE
INPUT
IS
AN
N-TUPLE
-
245
AN
N-TUPLE
TO
M-TUPLE
MAPPING
----
246
IMAGE
RECONSTRUCTION
AS
AN
N-TUPLE
TO
M-TUPLE
MAPPING
-
249
CONVOLUTIONAL
NEURAL
NETWORK
(CNN)
AS
A
MATCHED
FILTER
FOR
IDENTIFICATION
-
250
9.5
9.6
9.7
CONVOLUTIONAL
NEURAL
NETWORK
(CNN)
AS
A
NONLINEAR
DENOISE
FILTER
-
255
SUPER-RESOLUTION
-
258
TRAINING
----
260
XIV
-
CONTENTS
9.8
ATTENTION
----
261
9.9
9.10
PERSPECTIVES
-
262
SUMMARY
-
265
PROBLEM
----
266
BIBLIOGRAPHY
-
267
INDEX
-
269 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Zeng, Gengsheng Lawrence |
| author_GND | (DE-588)140930612 |
| author_facet | Zeng, Gengsheng Lawrence |
| author_role | aut |
| author_sort | Zeng, Gengsheng Lawrence |
| author_variant | g l z gl glz |
| building | Verbundindex |
| bvnumber | BV049050029 |
| classification_rvk | ST 640 YR 2200 |
| ctrlnum | (OCoLC)1367862457 (DE-599)DNB1279107227 |
| discipline | Informatik Medizin |
| discipline_str_mv | Informatik Medizin |
| edition | 2nd edition |
| format | Book |
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| id | DE-604.BV049050029 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:21:15Z |
| indexdate | 2024-07-10T09:53:49Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783111055039 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034312400 |
| oclc_num | 1367862457 |
| open_access_boolean | |
| owner | DE-29T DE-1102 DE-739 |
| owner_facet | DE-29T DE-1102 DE-739 |
| physical | XIV, 273 Seiten Illustrationen, Diagramme 24 cm x 17 cm |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spelling | Zeng, Gengsheng Lawrence Verfasser (DE-588)140930612 aut Medical image reconstruction from analytical and iterative methods to machine learning Gengsheng Lawrence Zeng 2nd edition Berlin De Gruyter [2023] © 2023 XIV, 273 Seiten Illustrationen, Diagramme 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Bildrekonstruktion (DE-588)4145435-2 gnd rswk-swf Tomografie (DE-588)4078351-0 gnd rswk-swf 2-dimensional Image Reconstruction 2-dimensionale Bildrekonstruktion 3-dimensional Image Reconstruction 3-dimensionale Bildrekonstruktion Einzelphotonen-Emissions-Computertomographie Magnetic Resonance Imaging Magnetresonanztomographie Single Photon Emission Computed Tomography Tomografie (DE-588)4078351-0 s Bildrekonstruktion (DE-588)4145435-2 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-105540-4 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-105570-1 Vorangegangen ist Medical image reconstruction : a conceptual tutorial 978-3-642-05367-2 (DE-604)BV036117275 X:MVB https://www.degruyter.com/isbn/9783111055039 Beschreibung für Marketing DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034312400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20230125 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Zeng, Gengsheng Lawrence Medical image reconstruction from analytical and iterative methods to machine learning Bildrekonstruktion (DE-588)4145435-2 gnd Tomografie (DE-588)4078351-0 gnd |
| subject_GND | (DE-588)4145435-2 (DE-588)4078351-0 |
| title | Medical image reconstruction from analytical and iterative methods to machine learning |
| title_auth | Medical image reconstruction from analytical and iterative methods to machine learning |
| title_exact_search | Medical image reconstruction from analytical and iterative methods to machine learning |
| title_exact_search_txtP | Medical image reconstruction from analytical and iterative methods to machine learning |
| title_full | Medical image reconstruction from analytical and iterative methods to machine learning Gengsheng Lawrence Zeng |
| title_fullStr | Medical image reconstruction from analytical and iterative methods to machine learning Gengsheng Lawrence Zeng |
| title_full_unstemmed | Medical image reconstruction from analytical and iterative methods to machine learning Gengsheng Lawrence Zeng |
| title_old | Medical image reconstruction : a conceptual tutorial |
| title_short | Medical image reconstruction |
| title_sort | medical image reconstruction from analytical and iterative methods to machine learning |
| title_sub | from analytical and iterative methods to machine learning |
| topic | Bildrekonstruktion (DE-588)4145435-2 gnd Tomografie (DE-588)4078351-0 gnd |
| topic_facet | Bildrekonstruktion Tomografie |
| url | https://www.degruyter.com/isbn/9783111055039 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034312400&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zenggengshenglawrence medicalimagereconstructionfromanalyticalanditerativemethodstomachinelearning AT walterdegruytergmbhcokg medicalimagereconstructionfromanalyticalanditerativemethodstomachinelearning |