The maximum entropy method:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin, [u.a.]
Springer
[1997]
|
| Series: | Springer series in information sciences
32 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 317 - 321 |
| Physical Description: | XII, 327 Seiten Illustrationen |
| ISBN: | 3540619658 9783642644849 |
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| 100 | 1 | |a Wu, Nailong |d 1946- |0 (DE-588)173108474 |4 aut | |
| 245 | 1 | 0 | |a The maximum entropy method |c Nailong Wu |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c [1997] | |
| 264 | 4 | |c © 1997 | |
| 300 | |a XII, 327 Seiten |b Illustrationen | ||
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| 490 | 1 | |a Springer series in information sciences |v 32 | |
| 500 | |a Literaturverzeichnis Seite 317 - 321 | ||
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| 650 | 7 | |a Numerieke methoden |2 gtt | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Maximum entropy method | |
| 650 | 4 | |a Signal processing | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
| 650 | 0 | 7 | |a Maximum-Entropie-Methode |0 (DE-588)4277537-1 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-007535869 | |
Record in the Search Index
| _version_ | 1825834743793451008 |
|---|---|
| adam_text |
NAILONG WU
THE
MAXIMUM ENTROPY
METHOD
WITH 53 FIGURES
SPRINGER
TABL
E OF CONTENT
S
1
. INTRODUCTIO
N
1
1.1 WHA
T IS TH
E MAXIMU
M ENTROP
Y METHO
D 1
1.2 DEFINITION OF ENTROP
Y 4
1.3 RATIONAL
E OF TH
E MAXIMU
M ENTROP
Y METHO
D 6
1.4 PRESEN
T AN
D FUTUR
E RESEARCH 9
2
. MAXIMU
M ENTROP
Y METHO
D MEM
L
AN
D IT
S APPLICATIO
N I
N SPECTRA
L ANALYSI
S
15
2.1 DEFINITION AN
D EXPRESSION
S OF ENTROP
Y
HI
15
2.1.1 APPROAC
H 1 16
2.1.2 APPROAC
H 2 20
2.1.3 DISCUSSION 23
2.2 FORMULATIO
N AN
D SOLUTION 25
2.2.1 FORMULATIO
N 25
2.2.2 SOLUTION 25
2.2.3 DISCUSSION 32
2.3 EQUIVALENT
S AN
D SIGNAL MODEL 34
2.3.1 AC
F EXTENSIO
N SUBJEC
T
T
O TH
E NONNEGATIVIT
Y CONSTRAIN
T 34
2.3.2 PRINCIPL
E OF MC
E 38
2.3.3 A
R PROCES
S (SIGNAL MODEL) 44
2.3.4 BAYESIAN METHO
D 48
2.3.5 WIENER FILTE
R AN
D APPROXIMATIO
N THEORETI
C APPROAC
H 50
2.4 ALGORITHM
S AN
D NUMERICA
L EXAMPL
E (GIVEN ACF
) 51
2.4.1 LEVINSON'
S RECURSION FOR 1-D NOISELESS DAT
A 53
2.4.2 LIM-MALIK ALGORITH
M FOR 2-D NOISELESS DAT
A 57
2.4.3 WERNECKE-D'ADDARI
O ALGORITH
M
FOR 2-D NOISY DAT
A 62
2.4.4 NUMERICA
L EXAMPL
E 67
2.5 ALGORITHM
S AN
D NUMERICA
L EXAMPL
E (GIVEN TIM
E SERIES) .
. 67
2.5.1 BUR
G ALGORITH
M 68
2.5.2 MARPL
E ALGORITH
M 72
2.5.3 OTHE
R FAS
T ALGORITHM
S 89
2.5.4 NUMERICA
L EXAMPL
E 91
X TABLE OF CONTENTS
2.6 ORDER SELECTION 92
2.6.1 FP
E CRITERION 92
2.6.2 AIC CRITERION 99
2.6.3 OTHER CRITERIA 105
2.6.4 SUMMARY 108
3. MAXIMU
M ENTROPY METHO
D MEM
2
AND IT
S APPLICATIO
N IN IMAGE RESTORATIO
N
109
3.1 DEFINITION AND EXPRESSIONS OF ENTROPY
HI
110
3.1.1 MLM 110
3.1.2 DIRECT DEFINITION METHOD 112
3.1.3 DISCUSSION 113
3.2 FORMULATION AND IMPLICIT SOLUTION 115
3.2.1 FORMULATION 115
3.2.2 IMPLICIT SOLUTION 115
3.2.3 ITERATIVE ALGORITHM 120
3.2.4 DISCUSSION 122
3.3 EXPLICIT SOLUTION 124
3.3.1 EXPLICIT SOLUTION 124
3.3.2 DISCUSSION 126
3.3.3 EXAMPLES 130
3.4 EQUIVALENTS AND SIGNAL MODEL 133
3.4.1 ACF EXTENSION SUBJECT
T
O THE NONNEGATIVITY CONSTRAINT 133
3.4.2 PRINCIPLE OF MCE 138
3.4.3 EXPONENTIAL PROCESS (SIGNAL MODEL) 139
3.4.4 BAYESIAN METHOD 140
3.4.5 MLM 141
3.5
R-X
PROCEDURE 142
3.5.1 STATEMENTS OF THE MEM2 PROBLEM 142
3.5.2
R-X
PROCEDURE 143
3.5.3 EXAMPLE 147
3.6 ALGORITHMS AND NUMERICAL EXAMPLES (I) 149
3.6.1 FRIEDEN ALGORITHM 150
3.6.2 GULL-DANIELL ALGORITHM 152
3.6.3 REVISED GD ALGORITHM 154
3.6.4 SIMPLIFIED NEWTON-RAPHSON ALGORITHM 157
3.6.5 NUMERICAL EXAMPLE 161
3.7 ALGORITHMS AND NUMERICAL EXAMPLES (II) 162
3.7.1 SKILLING-BRYAN ALGORITHM 162
3.7.2 DIFFERENTIAL EQUATION APPROACH 169
3.8 ALGORITHMS AND NUMERICAL EXAMPLES (III) 176
3.8.1 MEM/MEMSYS5 PACKAGE 177
3.8.2 MEM TASK IN IRAF 181
3.8.3 RESTORATION WITH VARIABLE RESOLUTION 184
TABLE OF CONTENTS XI
3.8.4 NUMERICAL EXAMPLES 187
3.8.5 OTHER ALGORITHMS 189
4
. ANALYSI
S AND COMPARISON
OF TH
E MAXIMU
M ENTROPY METHO
D
191
4.1 GENERALIZED MEM 191
4.1.1 FORMULATION OF GMEM 192
4.1.2 "ENTROPY" EXPRESSIONS IN GMEM 194
4.1.3 PROPERTIES OF GMEM 196
4.2 EXPRESSIONS OF ENTROPY 198
4.3 SOLUTION'S PROPERTIES 198
4.3.1 EXISTENCE 198
4.3.2 UNIQUENESS 201
4.3.3 CONSISTENCY 204
4.3.4 STATISTICAL PROPERTIES 209
4.4 RESOLUTION ENHANCEMENT AND DATA EXTENSION
(EXPERIMENTAL RESULTS) 210
4.4.1 EXAMPLES 212
4.4.2 RESOLVABILITY IN 1-D SPECTRAL ESTIMATION 216
4.4.3 RESOLVABILITY IN 2-D SPECTRAL ESTIMATION 219
4.4.4 SUPERRESOLUTION AND SPECTRAL LINE SPLITTING 220
4.5 RESOLUTION ENHANCEMENT AND DATA EXTENSION
(THEORETICAL ANALYSIS) 224
4.5.1 DATA EXTENSION IN MEM1 AND MEM2 224
4.5.2 RESOLUTION ENHANCEMENT OF MEM1 AND MEM2 226
4.5.3 MEM1 AND MEM2 SPECTRA AT LOW SNR 227
4.5.4 LINE SPLITTING OF MEM1 229
4.6 PEAK LOCATION AND RELATIVE POWER ESTIMATION
(EXPERIMENTAL RESULTS) 231
4.6.1 PEAK LOCATION (GIVEN ACF) 231
4.6.2 PEAK LOCATION (GIVEN TIME SERIES) 233
4.6.3 RELATIVE POWER ESTIMATION (GIVEN ACF) 235
4.6.4 SUMMARY AND COMMENTS 237
4.7 PEAK LOCATION AND RELATIVE POWER ESTIMATION
(THEORETICAL ANALYSIS) 238
4.7.1 INTERFERENCE BETWEEN PEAKS CAUSES PEAK SHIFTING 239
4.7.2 EXPLANATION OF THE PEAK SHIFTING IN MEM1 SPECTRA .
. 239
4.7.3 RELATIVE POWER ESTIMATION FOR MEM1 243
4.7.4 SUMMARY FOR SECTS. 4.4-4.7 247
4.8 COMMENTS ON THE THREE SCHOOLS OF THOUGHT ON MEM 247
5. APPLICATION
S OF TH
E MAXIMU
M ENTROPY METHO
D
I
N MATHEMATIC
S AND PHYSIC
S
251
5.1 SOLUTION OF MOMENT PROBLEMS 252
5.1.1 GENERAL THEORY 252
XII TABLE OF CONTENTS
5.1.2 NUMERICAL METHODS 255
5.1.3 NOISY MOMENT PROBLEMS 256
5.1.4 NUMERICAL EXAMPLES 258
5.2 SOLUTION OF INTEGRAL EQUATIONS 263
5.2.1 CONVERSION OF INTEGRAL EQUATIONS
T
O MOMENT PROBLEMS 263
5.2.2 SOLUTION OF MOMENT PROBLEMS BY MEM 264
5.2.3 NUMERICAL EXAMPLES 267
5.2.4 DISCUSSION 273
5.3 SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 273
5.3.1 THEORY 273
5.3.2 NUMERICAL EXAMPLE 275
5.3.3 DISCUSSION 280
5.4 PREDICTIVE STATISTICAL MECHANICS 282
5.4.1 FORMULATION AND SOLUTION 282
5.4.2 USEFUL FORMULAE 285
5.5 DISTRIBUTIONS OF PARTICLES AMONG ENERGY LEVELS 287
5.5.1 BOLTZMANN DISTRIBUTION 287
5.5.2 FERMI-DIRAC AND BOSE-EINSTEIN DISTRIBUTIONS 290
5.6 CLASSICAL STATISTICAL ENSEMBLES 293
5.6.1 MICRO CANONICAL ENSEMBLE 295
5.6.2 CANONICAL ENSEMBLE 296
5.6.3 GRAND CANONICAL ENSEMBLE 297
5.7 QUANTUM STATISTICAL ENSEMBLES 299
5.7.1 MICROCANONICAL ENSEMBLE 301
5.7.2 CANONICAL ENSEMBLE 302
5.7.3 GRAND CANONICAL ENSEMBLE 303
APPENDICE
S
305
A. CEPSTRAL ANALYSIS 305
A.I CEPSTRAL ANALYSIS SYSTEM 305
A.2 I/
O RELATIONSHIP 306
A.3 PROPERTIES OF THE COMPLEX CEPSTRUM 307
A.4 I/
O RELATIONSHIP FOR MINIMUM-PHASE INPUT 309
B. IMAGE RESTORATION 311
B.
I IMAGE FORMATION 311
B.2 IMAGE RESTORATION 313
B.3 RELATIONSHIP BETWEEN IMAGE RESTORATION
AND SPECTRAL ESTIMATION 314
REFERENCES
317
INDEX
323 |
| any_adam_object | 1 |
| author | Wu, Nailong 1946- |
| author_GND | (DE-588)173108474 |
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| discipline | Physik Informatik Mathematik |
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| id | DE-604.BV011230133 |
| illustrated | Illustrated |
| indexdate | 2025-03-06T09:01:40Z |
| institution | BVB |
| isbn | 3540619658 9783642644849 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007535869 |
| oclc_num | 36178608 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-29 DE-29T DE-824 DE-355 DE-BY-UBR DE-20 DE-526 DE-83 DE-188 |
| owner_facet | DE-703 DE-384 DE-29 DE-29T DE-824 DE-355 DE-BY-UBR DE-20 DE-526 DE-83 DE-188 |
| physical | XII, 327 Seiten Illustrationen |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in information sciences |
| series2 | Springer series in information sciences |
| spelling | Wu, Nailong 1946- (DE-588)173108474 aut The maximum entropy method Nailong Wu Berlin, [u.a.] Springer [1997] © 1997 XII, 327 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer series in information sciences 32 Literaturverzeichnis Seite 317 - 321 Entropie (informatietheorie) gtt Numerieke methoden gtt Mathematische Physik Mathematical physics Maximum entropy method Signal processing Spectral theory (Mathematics) Maximum-Entropie-Methode (DE-588)4277537-1 gnd rswk-swf Maximum-Entropie-Methode (DE-588)4277537-1 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-60629-8 Springer series in information sciences 32 (DE-604)BV000008063 32 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007535869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wu, Nailong 1946- The maximum entropy method Springer series in information sciences Entropie (informatietheorie) gtt Numerieke methoden gtt Mathematische Physik Mathematical physics Maximum entropy method Signal processing Spectral theory (Mathematics) Maximum-Entropie-Methode (DE-588)4277537-1 gnd |
| subject_GND | (DE-588)4277537-1 |
| title | The maximum entropy method |
| title_auth | The maximum entropy method |
| title_exact_search | The maximum entropy method |
| title_full | The maximum entropy method Nailong Wu |
| title_fullStr | The maximum entropy method Nailong Wu |
| title_full_unstemmed | The maximum entropy method Nailong Wu |
| title_short | The maximum entropy method |
| title_sort | the maximum entropy method |
| topic | Entropie (informatietheorie) gtt Numerieke methoden gtt Mathematische Physik Mathematical physics Maximum entropy method Signal processing Spectral theory (Mathematics) Maximum-Entropie-Methode (DE-588)4277537-1 gnd |
| topic_facet | Entropie (informatietheorie) Numerieke methoden Mathematische Physik Mathematical physics Maximum entropy method Signal processing Spectral theory (Mathematics) Maximum-Entropie-Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007535869&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008063 |
| work_keys_str_mv | AT wunailong themaximumentropymethod |