Blind image deconvolution : theory and applications

Title:

Publication Information:

Boca Raton, FL : CRC Press, 2007

ISBN:

9780849373671

Subject Term:

Image processing -- Digital techniques -- Mathematics

Spectrum analysis -- Deconvolution -- Mathematics

Added Author:

Campisi, Patrizio, 1968-

Egiazarian, K. (Karen), 1959-

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010133161	TA1632 B54 2007	Open Access Book	Book	Searching... Unknown

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.

Tom E. Bishop and S. Derin Babacan and Bruno Amizic and Aggelos K. Katsaggelos and Tony Chan and Rafael MolinaPatrizio Campisi and Alessandro Neri and Stefania Colonnese and Gianpiero Panci and Gaetano ScaranoVladimir Katkovnik and Karen Egiazarian and Jaakko AstolaAristidis Likas and Nikolas P. GalatsanosOleg V. Michailovich and Dan R. AdamAndré Jalobeanu and Josiane Zerubia and Laure Blanc-FéraudEric Pantin and Jean-Luc Starck and Fionn MurtaghFilip èroubek and Jan Fusser and Gabriel CristóbalDimitrios Hatzinakos and Alexia Giannoula and Jianxin HanMichael K. Ng and Robert J. Plemmons

1 Blind Image Deconvolution: Problem Formulation and Existing Approaches	p. 1
1.1 Introduction	p. 1
1.2 Mathematical Problem Formulation	p. 4
1.3 Classification of Blind Image Deconvolution Methodologies	p. 5
1.4 Bayesian Framework for Blind Image Deconvolution	p. 6
1.5 Bayesian Modeling of Blind Image Deconvolution	p. 7
1.5.1 Observation Model	p. 7
1.5.2 Parametric Prior Blur Models	p. 8
1.5.3 Prior Image and Blur Models	p. 9
1.5.4 Hyperprior Models	p. 15
1.6 Bayesian Inference Methods in Blind Image Deconvolution	p. 16
1.6.1 Maximum a Posteriori and Maximum Likelihood	p. 16
1.6.2 Minimum Mean Squared Error	p. 18
1.6.3 Marginalizing Hidden Variables	p. 19
1.6.4 Variational Bayesian Approach	p. 21
1.6.5 Sampling Methods	p. 22
1.7 Non-Bayesian Blind Image Deconvolution Models	p. 24
1.7.1 Spectral and Cepstral Zero Methods	p. 25
1.7.2 Zero Sheet Separation Algorithms	p. 26
1.7.3 ARMA Parameter Estimation Algorithms	p. 26
1.7.4 Nonparametric Deterministic Constraints Algorithms	p. 27
1.7.5 Nonparametric Algorithms Based on Higher-Order Statistics	p. 29
1.7.6 Total Least Squares (TLS)	p. 29
1.7.7 Learning-Based Algorithms	p. 30
1.7.8 Methods for Spatially Varying Degradation	p. 30
1.7.9 Multichannel Methods	p. 31
1.8 Conclusions	p. 32
References	p. 32
2 Blind Image Deconvolution Using Bussgang Techniques: Applications to Image Deblurring and Texture Synthesis	p. 43
Abstract	p. 43
2.1 Introduction	p. 44
2.2 Bussgang Processes	p. 46
2.3 Single-Channel Bussgang Deconvolution	p. 48
2.3.1 Convergency Issue	p. 51
2.3.2 Application to Texture Synthesis	p. 55
2.4 Multichannel Bussgang Deconvolution	p. 61
2.4.1 The Observation Model	p. 62
2.4.2 Multichannel Wiener Filter	p. 63
2.4.3 Multichannel Bussgang Algorithm	p. 64
2.4.4 Application to Image Deblurring: Binary Text and Spiky Images	p. 67
2.4.5 Application to Image Deblurring: Natural Images	p. 73
2.5 Conclusions	p. 85
References	p. 88
3 Blind Multiframe Image Deconvolution Using Anisotropic Spatially Adaptive Filtering for Denoising and Regularization	p. 95
Abstract	p. 95
3.1 Introduction	p. 96
3.1.1 Blind and Nonblind Inverse	p. 96
3.1.2 Inverse Regularization	p. 98
3.2 Observation Model and Preliminaries	p. 100
3.3 Frequency Domain Equations	p. 102
3.4 Projection Gradient Optimization	p. 104
3.5 Anisotropic LPA-ICI Spatially Adaptive Filtering	p. 108
3.5.1 Motivation	p. 109
3.5.2 Sectorial Neighborhoods	p. 110
3.5.3 Adaptive Window Size	p. 110
3.5.4 LPA-ICI Filtering	p. 111
3.6 Blind Deconvolution Algorithm	p. 112
3.6.1 Main Procedure	p. 112
3.6.2 Image Alignment	p. 114
3.7 Identifiability and Convergence	p. 114
3.7.1 Perfect Reconstruction	p. 114
3.7.2 Hessian and Identifiability	p. 115
3.7.3 Conditioning and Convergence Rate	p. 117
3.8 Simulations	p. 120
3.8.1 Criteria and Algorithm Parameters	p. 120
3.8.2 Illustrative Results	p. 122
3.8.3 Perfect Reconstruction	p. 128
3.8.4 Numerical Results	p. 128
3.8.5 Image Alignment	p. 130
3.8.6 Reconstruction of Color Images	p. 132
3.9 Conclusions	p. 134
Acknowledgments	p. 136
References	p. 136
4 Bayesian Methods Based on Variational Approximations for Blind Image Deconvolution	p. 141
Abstract	p. 141
4.1 Introduction	p. 142
4.2 Background on Variational Methods	p. 145
4.3 Variational Blind Deconvolution	p. 146
4.3.1 Variational Functional F(q, ?)	p. 146
4.3.2 Maximization of the Variational Bound F(q, ?)	p. 149
4.4 Numerical Experiments	p. 152
4.4.1 Partially Known Case	p. 153
4.4.2 Unknown Case	p. 153
4.5 Conclusions and Future Work	p. 154
Appendix A Computation of the Variational Bound F(q, ?)	p. 155
Appendix B Maximization of F{{q, ?)	p. 157
References	p. 165
5 Deconvolution of Medical Images from Microscopic to Whole Body Images	p. 169
Abstract	p. 169
5.1 Introduction	p. 170
5.1.1 Medical Imaging: Tendencies and Goals	p. 170
5.1.2 Linear Modeling of Image Formation	p. 171
5.1.3 Blind Deconvolution in Medical Ultrasound Imaging	p. 172
5.1.4 Blind Deconvolution in Single Photon Emission Computed Tomography	p. 175
5.1.5 Blind Deconvolution in Confocal Microscopy	p. 176
5.1.6 Organization of the Chapter	p. 178
5.2 Nonblind Deconvolution	p. 179
5.2.1 Regularization via Maximum a Posteriori Estimation	p. 179
5.2.2 Numerical Optimization via Newton Method	p. 182
5.2.3 Blind Deconvolution with Shift-Variant Blurs	p. 183
5.3 Blind Deconvolution in Ultrasound Imaging	p. 184
5.3.1 Blind Deconvolution via Statistical Modeling	p. 185
5.3.2 Blind Deconvolution via Higher-Order Spectra Analysis	p. 190
5.3.3 Horaomorphic Deconvolution: 1-D Case	p. 192
5.3.4 Homomorphic Deconvolution: 2-D Case	p. 199
5.3.5 Generalized Homomorphic Deconvolution	p. 205
5.3.6 Blind Deconvolution via Inverse Filtering	p. 211
5.4 Blind Deconvolution in Spect	p. 215
5.4.1 Origins of the Blurring Artifact in Spect	p. 215
5.4.2 Blind Deconvolution via Alternative Minimization	p. 217
5.4.3 Blind Deconvolution via Nonnegativity and Support Constrains Recursive Inverse Filtering	p. 222
5.5 Blind Deconvolution in Confocal Microscopy	p. 223
5.5.1 Maximum Likelihood Deconvolution in Fluorescence Microscopy	p. 223
5.5.2 Refinements of the EM Algorithms	p. 227
5.5.3 Blind Deconvolution in 3-D Transmitted Light Brightfield Microscopy	p. 227
5.6 Summary	p. 228
References	p. 230
6 Bayesian Estimation of Blur and Noise in Remote Sensing Imaging	p. 239
Abstract	p. 239
6.1 Introduction	p. 240
6.1.1 Blind Deconvolution: State of the Art	p. 241
6.1.2 Constraining a Difficult Problem	p. 243
6.1.3 The Bayesian Viewpoint	p. 244
6.2 The Forward Model	p. 245
6.2.1 Modeling the Natural Scene Using Fractals	p. 245
6.2.2 Understanding the Image Formation	p. 246
6.3 Bayesian Estimation: Invert the Forward Model	p. 249
6.3.1 Marginalization and Related Approximations	p. 250
6.3.2 A Natural Parameter Estimation Algorithm (BLINDE)	p. 251
6.3.3 Why Use a Simplified Model?	p. 253
6.3.4 A Simplified, Optimized Algorithm	p. 255
6.4 Possible Improvements and Further Development	p. 256
6.4.1 Computing Uncertainties	p. 256
6.4.2 Model Assessment and Checking	p. 257
6.4.3 Robustness-Related Improvements	p. 258
6.5 Results	p. 259
6.5.1 First Method: Blinde	p. 259
6.5.2 Second method	p. 259
6.6 Conclusions	p. 271
Acknowledgments	p. 271
References	p. 271
7 Deconvolution and Blind Deconvolution in Astronomy	p. 277
Abstract	p. 277
7.1 Introduction	p. 278
7.2 The Deconvolution Problem	p. 280
7.3 Linear Regularized Methods	p. 282
7.3.1 Least Squares Solution	p. 282
7.3.2 Tikhonov Regularization	p. 282
7.4 Clean	p. 283
7.5 Bayesian Methodology	p. 283
7.5.1 Definition	p. 284
7.5.2 Maximum Likelihood with Gaussian Noise	p. 284
7.5.3 Gaussian Bayes Model	p. 285
7.5.4 Maximum Likelihood with Poisson Noise	p. 285
7.5.5 Maximum a Posteriori with Poisson Noise	p. 286
7.5.6 Maximum Entropy Method	p. 286
7.5.7 Other Regularization Models	p. 287
7.6 Iterative Regularized Methods	p. 288
7.6.1 Constraints	p. 288
7.6.2 Jansson-Van Cittert Method	p. 289
7.6.3 Other Iterative Methods	p. 289
7.7 Wavelet-Based Deconvolution	p. 290
7.7.1 Introduction	p. 290
7.7.2 Regularization from the Multiresolution Support	p. 292
7.7.3 Multiresolution Clean	p. 295
7.7.4 The Wavelet Constraint	p. 295
7.8 Deconvolution and Resolution	p. 300
7.9 Myopic and Blind Deconvolution	p. 301
7.9.1 Myopic Deconvolution	p. 303
7.9.2 Blind Deconvolution	p. 305
7.10 Conclusions and Chapter Summary	p. 308
Acknowledgments	p. 309
References	p. 309
8 Multiframe Blind Deconvolution Coupled with FrameRegistration and Resolution Enhancement	p. 317
Abstract p. 317
8.1 Introduction	p. 318
8.2 Mathematical Model	p. 321
8.3 Polyphase Formulation	p. 323
8.3.1 Integer Downsampling Factor	p. 324
8.3.2 Rational Downsampling Factor	p. 325
8.4 Reconstruction of Volatile Blurs	p. 326
8.4.1 The MBD Case	p. 327
8.4.2 The RSR Case	p. 327
8.5 Blind Superresolution	p. 330
8.6 Experiments	p. 333
8.6.1 Simulated Data	p. 333
8.6.2 Real Data	p. 335
8.6.3 Performance Experiments	p. 338
8.7 Conclusions	p. 345
Acknowledgment	p. 345
References	p. 346
9 Blind Reconstruction of Multiframe Imagery Based on Fusion and Classification	p. 349
Abstract p. 349
9.1 Introduction	p. 350
9.2 System Overview	p. 351
9.3 Recursive Inverse Filtering with Finite Normal-Density Mixtures (RIF-FNM)	p. 352
9.3.1 Image Modeling Using Finite Mixture Distributions	p. 352
9.3.2 Pixel Classification	p. 356
9.3.3 ML-Based Image Fusion	p. 357
9.4 Optimal Filter Adaptation	p. 358
9.5 Effects of Noise	p. 360
9.6 The Fusion and Classification Recursive Inverse Filtering Algorithm (FAC-RIF)	p. 361
9.6.1 The Iterative Algorithm	p. 362
9.6.2 Prefiltering and Postfiltering Processing	p. 363
9.6.3 Classification	p. 363
9.6.4 Fusion-Based Classification	p. 364
9.6.5 Fusion of Reconstructed Images	p. 364
9.7 Experimental Results	p. 365
9.8 Final Remarks	p. 371
References	p. 371
10 Blind Deconvolution and Structured Matrix Computations with Applications to Array Imaging	p. 377
Abstract	p. 377
10.1 Introduction	p. 378
10.2 One-Dimensional Deconvolution Formulation	p. 379
10.3 Regularized and Constrained TLS Formulation	p. 382
10.3.1 Symmetric Point Spread Functions	p. 386
10.4 Numerical Algorithms	p. 388
10.4.1 The Preconditioned Conjugate Gradient Method	p. 390
10.4.2 Cosine Transform-Based Preconditioners	p. 394
10.5 Two-Dimensional Deconvolution Problems	p. 396
10.6 Numerical Examples	p. 398
10.7 Application: High-Resolution Image Reconstruction	p. 400
10.7.1 Mathematical Model	p. 403
10.7.2 Image Reconstruction Formulation	p. 406
10.7.3 Simulation Results	p. 411
10.8 Concluding Remarks and Current Work	p. 416
Acknowledgments	p. 418
References	p. 418
Index	p. 423

Available:*

On Order

Summary

Summary

Table of Contents