Blind image deconvolution is constantly receiving increasing attention from the academic as well the industrial world due to both its theoretical and practical implications. The field of blind image deconvolution has several applications in different areas such as image restoration, microscopy, medical imaging, biological imaging, remote sensing, astronomy, nondestructive testing, geophysical prospecting, and many others. Blind Image Deconvolution: Theory and Applications surveys the current state of research and practice as presented by the most recognized experts in the field, thus filling a gap in the available literature on blind image deconvolution. Explore the gamut of blind image deconvolution approaches and algorithms that currently exist and follow the current research trends into the future. This comprehensive treatise discusses Bayesian techniques, single- and multi-channel methods, adaptive and multi-frame techniques, and a host of applications to multimedia processing, astronomy, remote sensing imagery, and medical and biological imaging at the whole-body, small-part, and cellular levels. Everything you need to step into this dynamic field is at your fingertips in this unique, self-contained masterwork. For image enhancement and restoration without a priori information, turn to Blind Image Deconvolution: Theory and Applications for the knowledge and techniques you need to tackle real-world problems.
Author(s): Patrizio Campisi, Karen Egiazarian
Edition: 1
Publisher: CRC Press
Year: 2007
Language: English
Pages: 436
Tags: Приборостроение;Обработка сигналов;
BLIND IMAGE DECONVOLUTION: Theory and Applications......Page 1
Contents......Page 5
Preface......Page 12
Editors......Page 14
Contributors......Page 15
1.1 Introduction......Page 18
1.2 Mathematical Problem Formulation......Page 21
1.3 Classification of Blind Image Deconvolution Methodologies......Page 22
1.4 Bayesian Framework for Blind Image Deconvolution......Page 23
1.5.1 Observation Model......Page 24
1.5.2.2 Atmospheric Turbulence Blur......Page 25
1.5.3 Prior Image and Blur Models......Page 26
1.5.3.1 Stationary Gaussian Models......Page 27
1.5.3.2 Autoregressive Models......Page 28
1.5.3.3 Markov Random Field Models......Page 29
1.5.3.4 Anisotropic Diffusion and Total Variation Type Models......Page 30
1.5.4 Hyperprior Models......Page 32
1.6.1 Maximum a Posteriori and Maximum Likelihood......Page 33
1.6.2 Minimum Mean Squared Error......Page 35
1.6.3 Marginalizing Hidden Variables......Page 36
1.6.4 Variational Bayesian Approach......Page 38
1.6.5 Sampling Methods......Page 39
1.7 Non–Bayesian Blind Image Deconvolution Models......Page 41
1.7.1 Spectral and Cepstral Zero Methods......Page 42
1.7.3 ARMA Parameter Estimation Algorithms......Page 43
1.7.4.1 The Iterative Blind Deconvolution Algorithms......Page 44
1.7.4.2 The NAS-RIF Algorithms......Page 45
1.7.6 Total Least Squares (TLS)......Page 46
1.7.8 Methods for Spatially Varying Degradation......Page 47
1.7.9 Multichannel Methods......Page 48
References......Page 49
Abstract......Page 59
2.1 Introduction......Page 60
2.2 Bussgang Processes......Page 62
2.3 Single-Channel Bussgang Deconvolution......Page 64
2.3.1 Convergency Issue......Page 67
2.3.2 Application to Texture Synthesis......Page 71
2.3.2.1 Texture Model......Page 72
2.3.2.2 Texture Parameters Identification Procedure......Page 73
2.3.2.3 Texture Synthesis and Experimental Results......Page 75
2.4 Multichannel Bussgang Deconvolution......Page 77
2.4.1 The Observation Model......Page 78
2.4.2 Multichannel Wiener Filter......Page 79
2.4.3 Multichannel Bussgang Algorithm......Page 80
2.4.4 Application to Image Deblurring: Binary Text and Spiky Images......Page 83
2.4.4.1 Binary Text Images......Page 84
2.4.4.2 Spiky Images......Page 88
2.4.5 Application to Image Deblurring: Natural Images......Page 89
2.4.5.1 Local Radon Transform of the Edge Image: Original Image and Blur Characterization......Page 93
Strong Edges......Page 95
Weak Edges and Textured Regions......Page 96
2.5 Conclusions......Page 101
References......Page 104
Abstract......Page 110
3.1.1 Blind and Nonblind Inverse......Page 111
3.1.2 Inverse Regularization......Page 113
3.2 Observation Model and Preliminaries......Page 115
3.3 Frequency Domain Equations......Page 117
3.4 Projection Gradient Optimization......Page 119
3.5 Anisotropic LPA–ICI SpatiallyA daptive Filtering......Page 123
3.5.1 Motivation......Page 124
3.5.3 Adaptive Window Size......Page 125
3.5.4 LPA-ICI Filtering......Page 126
3.6.1 Main Procedure......Page 127
3.7.1 Perfect Reconstruction......Page 129
3.7.2.1 Estimation of X......Page 130
3.7.2.2 Estimation of Hj......Page 131
3.7.3 Conditioning and Convergence Rate......Page 132
3.8.1.1 Criteria......Page 135
3.8.1.3 Parameters of the LPA–ICI Filtering......Page 136
3.8.2 Illustrative Results......Page 137
3.8.4 Numerical Results......Page 143
3.8.5 Image Alignment......Page 145
3.8.6 Reconstruction of Color Images......Page 147
3.9 Conclusions......Page 149
References......Page 151
Abstract......Page 159
4.1 Introduction......Page 160
4.2 Background on Variational Methods......Page 163
4.3.1 Variational Functional…......Page 164
4.3.2 Maximization of the Variational Bound…......Page 167
4.4 Numerical Experiments......Page 170
4.4.2 Unknown Case......Page 171
4.5 Conclusions and Future Work......Page 172
APPENDIX A: Computation of the Variational Bound…......Page 173
APPENDIX B: Maximization of…......Page 175
References......Page 183
Abstract......Page 186
5.1.1 Medical Imaging: Tendencies and Goals......Page 187
5.1.2 Linear Modeling of Image Formation......Page 188
5.1.3 Blind Deconvolution in Medical Ultrasound Imaging......Page 189
5.1.4 Blind Deconvolution in Single Photon Emission Computed Tomography......Page 192
5.1.5 Blind Deconvolution in Confocal Microscopy......Page 193
5.1.6 Organization of the Chapter......Page 195
5.2.1 Regularization via Maximum a Posteriori Estimation......Page 196
5.2.2 Numerical Optimization via Newton Method......Page 199
5.2.3 Blind Deconvolution with Shift-Variant Blurs......Page 200
5.3 Blind Deconvolution in Ultrasound Imaging......Page 201
5.3.1.1 Modeling by ARMA Process......Page 202
5.3.1.2 Estimation of the ARMA Parameters......Page 204
5.3.2 Blind Deconvolution via Higher-Order Spectra Analysis......Page 207
5.3.3 Homomorphic Deconvolution: 1-D Case......Page 209
5.3.3.1 Smoothness Properties of Fourier Phases......Page 210
5.3.3.2 Cepstrum-Based Estimation of the PSF......Page 212
5.3.3.4 Computation of Complex Cepstra......Page 214
5.3.4 Homomorphic Deconvolution: 2-D Case......Page 216
5.3.4.1 Phase Unwrapping in 2-D......Page 217
5.3.4.2 Phase Unwrapping via Smoothing Integration......Page 218
5.3.5.1 Estimation of the Fourier Magnitude of the PSF......Page 222
5.3.5.2 Outlier Resistant Denoising......Page 223
5.3.5.3 Estimation of the Fourier Phase of the PSF......Page 225
5.3.5.4 Generalized Homomorphic Estimation vs. Standard Homomorphic Estimation......Page 226
5.3.6 Blind Deconvolution via Inverse Filtering......Page 228
5.3.6.1 Moment-Based Estimation of the Inverse Filter......Page 229
5.3.6.3 “Hybrid” Deconvolution......Page 230
5.4.1 Origins of the Blurring Artifact in SPECT......Page 232
5.4.2 Blind Deconvolution via Alternative Minimization......Page 234
5.4.3 Blind Deconvolution via Nonnegativity and Support Constrains Recursive Inverse Filtering......Page 239
5.5.1 Maximum Likelihood Deconvolution in Fluorescence Microscopy......Page 240
5.5.3 Blind Deconvolution in 3-D Transmitted Light Brightfield Microscopy......Page 244
5.6 Summary......Page 245
References......Page 247
Abstract......Page 255
6.1 Introduction......Page 256
6.1.1.1 Independent Blur Identification and Deblurring......Page 257
6.1.1.2 Joint Blur Estimation and Deblurring......Page 258
6.1.2 Constraining a Difficult Problem......Page 259
6.1.3 The Bayesian Viewpoint......Page 260
6.2.1 Modeling the Natural Scene Using Fractals......Page 261
6.2.2.1 Atmospheric, Optical, and Sensor MTF Modeling......Page 262
6.2.2.2 Sampling and Sensor Noise......Page 264
6.3 Bayesian Estimation: Invert the Forward Model......Page 265
6.3.1 Marginalization and Related Approximations......Page 266
6.3.2.1 Noise Variance Marginalization......Page 267
6.3.2.3 The Algorithm......Page 268
6.3.3 Why Use a Simplified Model?......Page 269
6.3.4 A Simplified, Optimized Algorithm......Page 271
6.4.1 Computing Uncertainties......Page 272
6.4.2 Model Assessment and Checking......Page 273
6.4.3 Robustness-Related Improvements......Page 274
6.5.2 Second method......Page 275
References......Page 287
Abstract......Page 292
7.1 Introduction......Page 293
7.2 The Deconvolution Problem......Page 295
7.3.2 Tikhonov Regularization......Page 297
7.5 Bayesian Methodology......Page 298
7.5.2 Maximum Likelihood with Gaussian Noise......Page 299
7.5.4 Maximum Likelihood with Poisson Noise......Page 300
7.5.6 Maximum Entropy Method......Page 301
7.5.7 Other Regularization Models......Page 302
7.6.1 Constraints......Page 303
7.6.3 Other Iterative Methods......Page 304
Towards Multiresolution......Page 305
7.7.2.2 Regularization of Van Cittert’s Algorithm......Page 307
7.7.2.6 Examples......Page 308
7.7.4 The Wavelet Constraint......Page 310
7.7.4.1 Multiscale Entropy......Page 311
7.7.4.2 Total Variation and Undecimated Haar Transform......Page 312
7.7.4.4 Constraints in the Object or Image Domains......Page 313
7.7.4.5 The Combined Deconvolution Method......Page 314
7.8 Deconvolution and Resolution......Page 315
7.9 Myopic and Blind Deconvolution......Page 316
7.9.1 Myopic Deconvolution......Page 318
7.9.2 Blind Deconvolution......Page 320
7.10 Conclusions and Chapter Summary......Page 323
References......Page 324
Abstract......Page 332
8.1 Introduction......Page 333
8.2 Mathematical Model......Page 336
8.3 Polyphase Formulation......Page 338
8.3.1 Integer Downsampling Factor......Page 339
8.3.2 Rational Downsampling Factor......Page 340
8.4 Reconstruction of Volatile Blurs......Page 341
8.4.2 The BSR Case......Page 342
8.5 Blind Superresolution......Page 345
8.6.1 Simulated Data......Page 348
8.6.2 Real Data......Page 350
8.6.3 Performance Experiments......Page 353
Acknowledgment......Page 360
References......Page 361
Abstract......Page 364
9.1 Introduction......Page 365
9.2 System Overview......Page 366
9.3.1 Image Modeling Using Finite Mixture Distributions......Page 367
9.3.2 Pixel Classification......Page 371
9.3.3 ML-Based Image Fusion......Page 372
9.4 Optimal Filter Adaptation......Page 373
9.5 Effects of Noise......Page 375
9.6 The Fusion and Classification Recursive Inverse Filtering Algorithm (FAC-RIF)......Page 376
9.6.1 The Iterative Algorithm......Page 377
9.6.3 Classification......Page 378
9.6.5 Fusion of Reconstructed Images......Page 379
9.7 Experimental Results......Page 380
References......Page 386
Abstract......Page 391
10.1 Introduction......Page 392
10.2 One-Dimensional Deconvolution Formulation......Page 393
10.3 Regularized and Constrained TLS Formulation......Page 396
10.3.1 Symmetric Point Spread Functions......Page 400
10.4 Numerical Algorithms......Page 402
10.4.1 The Preconditioned Conjugate Gradient Method......Page 404
10.4.2 Cosine Transform-Based Preconditioners......Page 408
10.5 Two-Dimensional Deconvolution Problems......Page 410
10.6 Numerical Examples......Page 412
10.7 Application: High-Resolution Image Reconstruction......Page 414
10.7.1 Mathematical Model......Page 417
10.7.2 Image Reconstruction Formulation......Page 420
10.7.3 Simulation Results......Page 425
10.8 Concluding Remarks and Current Work......Page 430
References......Page 432
