Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Potsdam, Univ., Diss., 1998 |
| Beschreibung: | V, 121 S. Ill., graph. Darst. |
Internformat
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| 100 | 1 | |a Dicken, Volker |d 1967- |e Verfasser |0 (DE-588)12037790X |4 aut | |
| 245 | 1 | 0 | |a Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem |c von Volker Dicken |
| 264 | 1 | |c 1997 | |
| 300 | |a V, 121 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Potsdam, Univ., Diss., 1998 | ||
| 650 | 0 | 7 | |a Tichonov-Regularisierung |0 (DE-588)4124313-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineares inverses Problem |0 (DE-588)4453043-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Radon-Transformation |0 (DE-588)4479199-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a SPECT |0 (DE-588)4239915-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 0 | |a SPECT |0 (DE-588)4239915-4 |D s |
| 689 | 0 | 1 | |a Nichtlineares inverses Problem |0 (DE-588)4453043-2 |D s |
| 689 | 0 | 2 | |a Inkorrekt gestelltes Problem |0 (DE-588)4186951-5 |D s |
| 689 | 0 | 3 | |a Tichonov-Regularisierung |0 (DE-588)4124313-4 |D s |
| 689 | 0 | 4 | |a Radon-Transformation |0 (DE-588)4479199-9 |D s |
| 689 | 0 | |5 DE-604 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008224473 | |
Datensatz im Suchindex
| _version_ | 1807594092251578368 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
MOTIVATION
.
1
1.1.1
THE
MEASUREMENT
PROCESS
.
2
1.1.2
BACKGROUND
INFORMATION
.
4
1.2
DERIVATION
OF
THE
MATHEMATICAL
MODEL
.
5
1.2.1
AN
INTEGRAL
TRANSFORMATION
MODEL
.
5
1.2.2
A
TRANSPORT
DIFFERENTIAL
EQUATION
MODEL
.
5
1.2.3
ON
THE
COLLIMATOR
POINT
SPREAD
FUNCTION
.
6
1.2.4
A
DISCRETE
MODEL
.
8
1.2.5
SOME
HELPFUL
FACTS
.
9
1.3
DATA
CONTAMINATION
.
9
1.4
ATTENUATION
CORRECTION
TECHNIQUES
NOW
IN
USE
.
11
1.5
KNOWN
RESULTS
FOR
INVERTING
THE
NONLINEAR
ATRT
.
13
2
NONLINEAR
ILL-POSED
PROBLEMS
15
2.1
BASIC
DEFINITIONS
AND
NOTATION
.
15
2.2
TIKHONOV
REGULARIZATION
.
17
2.3
MINIMIZATION
OF
THE
TIKHONOV
FUNCTIONAL
.
22
2.3.1
EFFECTIVE
TIKHONOV
MINIMIZATION
.
25
2.3.2
SOLVING
LARGE
LINEAR
SYSTEMS
.
27
2.3.3
CONJUGATE
GRADIENT
METHODS
.
27
2.3.4
MINIMIZATION
OF
A
DISCREPANCY
TIKHONOV
FUNCTIONAL
.
29
2.3.5
MINIMIZATION
OF
A
BANACH-SPACE
TIKHONOV
FUNCTIONAL
.
30
,
2.4
OTHER
REGULARIZATION
TECHNIQUES
.
31
2.4,1
ON
THE
REGULARIZED
GAUSS-NEWTON
METHOD
.
33
3
THE
ATTENUATED
RADON
TRANSFORM
(ATRT)
35
3.1
FACTORIZATION
AND
REDEFINITION
OF
THE
ATRT
.
35
3.2
ON
MAPPING
PROPERTIES
OF
SOME
OPERATORS
.
38
3.3
FOURIER
TRANSFORM
OF
CERTAIN
LINEAR
OPERATORS
.
42
3.4
RANGE
CHARACTERIZATIONS
.
45
3.5
DERIVATIVES
OF
THE
NONLINEAR
OPERATORS
.
48
3.6
SCALING
PROPERTIES
.
49
3.7
ADJOINT
AND
DUAL
OPERATORS
.
50
4
THE
ATRT
AS
INVERSE
PROBLEM
55
4.1
THE
ATRT
IN
HILBERT
SPACE
.
55
4.2
SEMI-DISCRETE
ATRT
OPERATORS
.
64
4.3
ON
THE
DEGREE
OF
NONLINEARITY
OF
THE
ATRT
.
69
5
NUMERICAL
REALIZATION
73
5.1
THE
NUMERICAL
TASK
.
73
5.2
ITERATIVE
RECONSTRUCTION
.
74
5.3
ON
APPROXIMATING
LINE
AND
SPHERE
INTEGRALS
.
75
5.3.1
ON
QUANTIZED
INTERPOLATION
.
75
5.3.2
ON
LINE
INTEGRALS
.
76
5.3.3
ON
RECURSIVE
EVALUATION
OF
THE
EXPONENTIAL
FUNCTION
.
77
5.3.4
ON
APPROXIMATION
OF
ATRT
DERIVATIVES
AND
FAN
BEAM
DATA
.
77
5.3.5
ON
SPHERE
INTEGRALS
ARISING
IN
BACKPROJECTION
OPERATIONS
.
78
5.4
A
REMARK
ON
COMPUTING
TIME
AND
STORAGE
REQUIREMENTS
.
79
5.5
INITIALIZATION
ROUTINES
.
80
5.6
THE
FILTERED
BACKPROJECTION
ALGORITHM
.
80
5.7
THE
ATTENUATION
CORRECTED
FILTERED
BACKPROJECTION
.
81
5.8
NUMERICS
AND
SOBOLEV
SPACES
OF
FRACTIONAL
ORDER
.
81
5.9
CALCULATION
OF
WEIGHT
FUNCTIONS
.
.
.
82
5.10
TEST
FUNCTIONS
.
82
6
RECONSTRUCTION
RESULTS
85
6.1
PHANTOM
DATA
.
85
6.2
ON
THE
RECONSTRUCTION
QUALITY
MEASURE
.
85
6.3
FILTERED
BACKPROJECTION
.
86
6.4
ACTIVITY
RECONSTRUCTION
WITH
ESTIMATED
ATTENUATION
.
87
6.5
ATTENUATION
RECONSTRUCTION
WITH
ESTIMATED
ACTIVITY
.
87
6.6
SIMULTANEOUS
ACTIVITY
AND
ATTENUATION
RECONSTRUCTION
.
87
6.7
RECONSTRUCTIONS
FROM
CLINICAL
DATA
.
88
6.8
ILLUSTRATION
OF
THE
ALGORITHM
.
89
A
TOOLS
FROM
FUNCTIONAL
ANALYSIS
99
A.L
P-SPACES
AND
ESTIMATES
.
99
A.
2
THE
FOURIER
TRANSFORM
AND
SOBOLEV
SPACES
.
102
A.3
SOME
NONLINEAR
FUNCTIONAL
ANALYSIS
.
106
A.3.1
ON
COMPACT
AND
WEAKLY
SEQUENTIALLY
CLOSED
OPERATORS
.
106
A.3.
2
DIFFERENTIATION
IN
BANACH
SPACES
.
107
A.3.3
SOME
REMARKS
ON
COMPOSITION
OPERATORS
.
109
B
DOCUMENTATION
OF
THE
C++
IMPLEMENTATION
115
B.L
STRUCTURE
OF
THE
PROGRAM
.
115
B.2
PARAMETERS
OF
THE
REGULARIZATION
ALGORITHM
.
116
B.3
HELP
AND
ESCAPE
SEQUENCES
.
117 |
| any_adam_object | 1 |
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| author_GND | (DE-588)12037790X |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV012142848 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T00:54:19Z |
| institution | BVB |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008224473 |
| oclc_num | 245887096 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-11 |
| physical | V, 121 S. Ill., graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| record_format | marc |
| spelling | Dicken, Volker 1967- Verfasser (DE-588)12037790X aut Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem von Volker Dicken 1997 V, 121 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Potsdam, Univ., Diss., 1998 Tichonov-Regularisierung (DE-588)4124313-4 gnd rswk-swf Nichtlineares inverses Problem (DE-588)4453043-2 gnd rswk-swf Radon-Transformation (DE-588)4479199-9 gnd rswk-swf Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd rswk-swf SPECT (DE-588)4239915-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content SPECT (DE-588)4239915-4 s Nichtlineares inverses Problem (DE-588)4453043-2 s Inkorrekt gestelltes Problem (DE-588)4186951-5 s Tichonov-Regularisierung (DE-588)4124313-4 s Radon-Transformation (DE-588)4479199-9 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008224473&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dicken, Volker 1967- Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem Tichonov-Regularisierung (DE-588)4124313-4 gnd Nichtlineares inverses Problem (DE-588)4453043-2 gnd Radon-Transformation (DE-588)4479199-9 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd SPECT (DE-588)4239915-4 gnd |
| subject_GND | (DE-588)4124313-4 (DE-588)4453043-2 (DE-588)4479199-9 (DE-588)4186951-5 (DE-588)4239915-4 (DE-588)4113937-9 |
| title | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem |
| title_auth | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem |
| title_exact_search | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem |
| title_full | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem von Volker Dicken |
| title_fullStr | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem von Volker Dicken |
| title_full_unstemmed | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem von Volker Dicken |
| title_short | Simultaneous activity and attenuation reconstruction in single photon emission computed tomography, a nonlinear Ill-posed-problem |
| title_sort | simultaneous activity and attenuation reconstruction in single photon emission computed tomography a nonlinear ill posed problem |
| topic | Tichonov-Regularisierung (DE-588)4124313-4 gnd Nichtlineares inverses Problem (DE-588)4453043-2 gnd Radon-Transformation (DE-588)4479199-9 gnd Inkorrekt gestelltes Problem (DE-588)4186951-5 gnd SPECT (DE-588)4239915-4 gnd |
| topic_facet | Tichonov-Regularisierung Nichtlineares inverses Problem Radon-Transformation Inkorrekt gestelltes Problem SPECT Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008224473&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT dickenvolker simultaneousactivityandattenuationreconstructioninsinglephotonemissioncomputedtomographyanonlinearillposedproblem |