Phase retrieval and zero crossings: mathematical methods in image reconstruction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1989
|
| Series: | Mathematics and its applications
52 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 304 S. Ill. |
| ISBN: | 0792302109 |
Staff View
MARC
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| 100 | 1 | |a Hurt, Norman E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Phase retrieval and zero crossings |b mathematical methods in image reconstruction |c by Norman E. Hurt |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1989 | |
| 300 | |a XV, 304 S. |b Ill. | ||
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Record in the Search Index
| _version_ | 1804116913417093120 |
|---|---|
| adam_text | Contents
Preface ix
1 Introduction 1
1.1 Signal Recovery 1
1.2 Band limited Extrapolation and Phase Retrieval 1
1.3 Spectrum Shaping and Kinoforms 3
1.4 Radar Signal Synthesis 4
1.5 Beam Shaping and Antenna Design 4
1.6 Optical and Microwave Beam Shaping 5
1.7 Wavefront Sensing 5
1.8 Spectroscopy 5
1.9 X Ray Crystallography 5
1.10 Radio Astronomy 6
1.11 Tomography 6
1.12 Signal Reconstruction from Zero Crossings 6
1.13 Reconstruction and Resolution Limits 8
1.14 111 Posed Problems and Regularization 9
2 Polynomials: A Review 11
2.1 Introduction 11
2.2 Polynomials and Trigonometric Polynomials 15
3 Entire Functions and Signal Recovery 17
3.1 Introduction 17
3.2 Band Limited Functions 20
3.3 Zeros of EFETs 21
3.4 Encoding of Information by Zeros 25
3.5 Far Field Distributions for Point Sources 25
3.6 Radar Waveform Construction a la Huffman 27
3.7 Hayes Fundamental Theorem 28
3.8 Brightness Distribution (Bruck Sodin) 29
3.9 Specified Autocorrelation Functions 30
3.10 Autocorrelation Function of Pulses 32
3.11 Autocorrelation Functions 33
xii CONTENTS
3.12 Monochromatic Radiation 33
3.13 Coherence Theory 34
3.14 Blackbody Radiation 36
3.15 Holography and Zeros 36
3.16 Akutowicz Representation Theorem 37
3.17 Walther s Theorem and Zero Flipping 40
3.18 Summary of Phase Retrieval in One Dimension 45
4 Homometric Distributions 47
4.1 Introduction 47
5 Analytic Signals and Signal Recovery from Zero Crossings 55
5.1 Introduction 55
5.2 Amplitude Modulation 55
5.3 Single Sideband Modulation 56
5.4 Exponential Single Sideband Modulation 56
5.5 Distortionless Demodulation 57
5.6 Modulation Reconstruction from Zeros 59
5.7 Recovery from Zero Crossings 60
5.8 A Zero Crossing Spectrum Analyzer 64
6 Signal Representation by Fourier Phase and Magnitude in
One Dimension 67
6.1 Introduction 67
6.2 Arrival Time Determination 69
6.3 Fourier Representation by Fourier Magnitude 70
6.4 Representation by Fourier Signed Magnitude 71
6.5 Representation by One Bit of Fourier Phase 72
7 Recovery of Distorted Band Limited Signals 73
7.1 Introduction 73
7.2 Landau s Convolution Equation 75
7.3 Time Limited and Band Limited Functions 77
7.4 Prolate Spheroidal Functions 79
7.5 Extrapolation by PSWFs 80
7.6 Riemann Zeta Function 82
7.7 Recovery of Stochastic Processes 83
8 Compact Operators, Singular Value Analysis and Repro¬
ducing Kernel Hilbert Spaces 87
8.1 Introduction 87
8.2 Singular Value Analysis 91
8.3 The Effect of Noise on Inversion 94
8.4 Laplace Transform Inversion 95
CONTENTS xiii
8.5 Resolution with Incoherent Illumination 98
8.6 Reproducing Kernel Hilbert Spaces 98
9 Kaczmarz Method, Landweber Iteration, Gerchberg Papoulis
and Regularization 103
9.1 Introduction 103
9.2 The Cimmino Method 104
9.3 Cimmino for Fredholm 105
9.4 Filtering and Landweber s Iteration 108
9.5 Image Restoration by the Projections 109
9.6 Van Cittert Deconvolution 109
9.7 Gerchberg Papoulis Algorithm Ill
9.8 Extrapolation by Gori s Algorithm 112
9.9 Gerchberg s Method of Extrapolation 113
9.10 Gerchberg Papoulis Again 114
9.11 Landweber s Iteration 116
9.12 Discrete Continuous Iterative Extrapolation 118
9.13 Discrete Discrete Extrapolation 118
9.14 The Xu Chamzas Algorithm 120
9.15 The Discrete Xu Chamzas Algorithm 122
9.16 Adaptive Extrapolation 123
9.17 Karhunen Loeve Expansion 126
9.18 Stopping Algorithms 126
9.19 Regularization 127
9.20 Tikhonov Regularization 128
9.21 Landweber Regularization 128
9.22 Regularization in Optics 129
9.23 Moment Discretization 130
9.24 Biraud s Algorithm 131
10 Two Dimensional Signal Recovery Problems 135
10.1 Introduction 135
10.2 Phase Retrieval from Magnitude 137
10.3 Entire Functions in Two Dimensions 139
10.4 Radial Geometry 143
10.5 Factorization and Exponential Type 146
10.6 Eisenstein Criterion for Irreducibility 148
10.7 The Result of Sanz Huang 149
11 Reconstruction Algorithms in Two Dimensions 151
11.1 Canterakis Algorithm 151
11.2 Berenyi Deighton Fiddy Algorithm 154
11.3 Logarithmic Hilbert Transforms 155
11.4 Algorithm of Nakajima and Asakura 157
xiv CONTENTS
11.5 Zero Crossings in 2 D 158
11.6 The Israelevitz Lim Algorithm 162
11.7 The Rotem Zeevi Algorithm 164
12 Nonexpansive Maps and Signal Recovery 165
12.1 Introduction 165
12.2 Time and Frequency Mappings 172
12.3 Time Limited Extrapolation 173
12.4 Phase Only Reconstruction 174
12.5 Minimal Phase Signals 175
12.6 Min and Max Constraints 176
12.7 Masks for Microlithography 176
12.8 Energy Reduction Algorithms 178
13 Projections on Convex Sets in Signal Recovery 179
13.1 Introduction 179
13.2 Alternating Projections 185
13.3 Reconstruction by Projections 187
13.4 Regularization 188
13.5 Convex Projection in Noise 189
13.6 Inconsistent Constraints 190
13.7 Algebraic Reconstruction Techniques 191
13.8 Nonnegative Spatial Constraints 193
13.9 Reconstruction from Zero Crossings 194
13.10A Phase Retrieval Example 195
13.11Lent Tuy Algorithm 196
13.12Example of Lent Tuy 196
13.13Divergence Free Vector Fields 197
14 Method of Generalized Projections and Steepest Descent 199
14.1 Introduction 199
14.2 Phase Retrieval 200
14.3 Deconvolution by POCS 200
14.4 Fuzzy Sets 202
14.5 Method of Steepest Descent 203
14.6 Least Squares Solutions 203
14.7 Design of FIR Filters 207
14.8 Projection onto Nonconvex Sets 209
15 Closed Form Reconstruction of the Support and the Object211
15.1 Introduction 211
CONTENTS xv
10 Fiemip s Input Output Algorithms and Variations on this
Theme 215
1G.1 Introduction 215
17 Topics and Applications of Signal Recovery 221
17.1 Maximum Entropy Estimation 221
17.2 Stellar Speckle Interferometry 222
17.3 Radio Astronomy 223
17.4 The CLEAN Method 223
17.5 The Knox Method 225
17.6 Filter Design 226
17.7 Microwave Holographic Metrology 227
17.8 Misell Algorithm 230
17.9 Radio Holography 234
17.lOPinhole Projections 235
17.11Tomography 235
17.12The Spin Glass Model 237
17.13Simulated Annealing 238
17.14Robbins Monro 238
17.15Minimum Variance Algorithm 240
17.16Newton Direction Algorithms 241
17.17Sandberg s Algorithm 242
17.18FM Demodulation 243
17.19Toeplitz Equations 244
17.20Moses Prosser Algorithm 245
17.21The Baghlay Algorithm 246
17.22Gonsalves Algorithm 247
17.23Neural Nets and POCS 247
17.24Synthetic Aperture Radar 249
17.25NMR Tomography 250
17.26Multiple Threshold Crossings 251
17.27Block Iterative Methods 252
A The Geometry of Projections on Convex Sets 257
B Reference Summary 263
C References 267
Index 300
|
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| isbn | 0792302109 |
| language | English |
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| series2 | Mathematics and its applications |
| spelling | Hurt, Norman E. Verfasser aut Phase retrieval and zero crossings mathematical methods in image reconstruction by Norman E. Hurt Dordrecht u.a. Kluwer 1989 XV, 304 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 52 Signal, Théorie du (Télécommunications) - Mathématiques) ram Mathematik Image reconstruction Signal theory (Telecommunication) Mathematics Bildrekonstruktion (DE-588)4145435-2 gnd rswk-swf Signalregenerierung (DE-588)4181274-8 gnd rswk-swf Signalregenerierung (DE-588)4181274-8 s DE-604 Bildrekonstruktion (DE-588)4145435-2 s Mathematics and its applications 52 (DE-604)BV008163334 52 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001615156&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hurt, Norman E. Phase retrieval and zero crossings mathematical methods in image reconstruction Mathematics and its applications Signal, Théorie du (Télécommunications) - Mathématiques) ram Mathematik Image reconstruction Signal theory (Telecommunication) Mathematics Bildrekonstruktion (DE-588)4145435-2 gnd Signalregenerierung (DE-588)4181274-8 gnd |
| subject_GND | (DE-588)4145435-2 (DE-588)4181274-8 |
| title | Phase retrieval and zero crossings mathematical methods in image reconstruction |
| title_auth | Phase retrieval and zero crossings mathematical methods in image reconstruction |
| title_exact_search | Phase retrieval and zero crossings mathematical methods in image reconstruction |
| title_full | Phase retrieval and zero crossings mathematical methods in image reconstruction by Norman E. Hurt |
| title_fullStr | Phase retrieval and zero crossings mathematical methods in image reconstruction by Norman E. Hurt |
| title_full_unstemmed | Phase retrieval and zero crossings mathematical methods in image reconstruction by Norman E. Hurt |
| title_short | Phase retrieval and zero crossings |
| title_sort | phase retrieval and zero crossings mathematical methods in image reconstruction |
| title_sub | mathematical methods in image reconstruction |
| topic | Signal, Théorie du (Télécommunications) - Mathématiques) ram Mathematik Image reconstruction Signal theory (Telecommunication) Mathematics Bildrekonstruktion (DE-588)4145435-2 gnd Signalregenerierung (DE-588)4181274-8 gnd |
| topic_facet | Signal, Théorie du (Télécommunications) - Mathématiques) Mathematik Image reconstruction Signal theory (Telecommunication) Mathematics Bildrekonstruktion Signalregenerierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001615156&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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