【下载】Bayesian Approach to Inverse Problems~Jérôme Idier.Wiley.2008

相似文件 换一批

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

Bayesian Approach to Inverse Problems(解逆问题的贝叶斯方法)

作者:Jérôme Idier

基本信息·出版社：Wiley-ISTE
·页码：392 页
·出版日期：2008年06月
·ISBN：1848210329
·条形码：9781848210325
·装帧：精装
·正文语种：英语
·外文书名：解逆问题的贝叶斯方法


内容简介
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data.
Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems.
The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation.
The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

作者简介
Jérôme Idier was born in France in 1966. He received the diploma degree in electrical engineering from the Ecole Superieure d'Electricité, Gif-sur-Yvette, France, in 1988, the Ph.D. degree in physics from the Universite de Paris-Sud, Orsay, France, in 1991, and the HDR (Habilitation a diriger des recherches) from the same university in 2001. Since 1991, he is a full time researcher at CNRS (Centre National de la Recherche Scientifique). He has been with the Laboratoire des Signaux et Systemes from 1991 to 2002, and with IRCCyN (Institut de Recherches en Cybernetique de Nantes (IRCCyN) since september 2002.
His major scientific interest is in statistical approaches to inverse problems for signal and image processing. More specifically, he studies probabilistic modeling, inference and optimization issues yielded by data processing problems such as denoising, deconvolution, spectral analysis, reconstruction from projections. The investigated applications are mainly non destructive testing, astronomical imaging and biomedical signal processing, and also radar imaging and geophysics. Dr Idier has been involved in joint research programs with several specialized research centers: EDF (Electricite de France), CEA (Commissariat a l'Energie Atomique), CNES (Centre National d'Etudes Spatiales), ONERA (Office National d'Etudes et de Recherches Aerospatiales), Loreal, Thales, Schlumberger.

专业书评
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data.
Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems.
The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation.
The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏1 回帖

关键词：Problems Bayesian Approach problem inverse Bayesian Approach inverse Problems Idier

Table of Contents

Introduction 15

Jérôme IDIER

PART I FUNDAMENTAL PROBLEMS AND TOOLS 23

Chapter 1 Inverse Problems, Ill-posed Problems 25

Guy DEMOMENT, Jérôme IDIER

1.1Introduction 25

1.2.Basic example26

1.3Ill-posedproblem30

1.3.1.Case of discrete data 31

1.3.2Continuous case 32

1.4.Generalizedinversion 34

1.4.1Pseudo-solutions 35

1.4.2.Generalizedsolutions 35

1.4.3.Example 35

1.5.Discretization and conditioning 36

1.6.Conclusion 38

1.7.Bibliography 39

Chapter 2 Main Approaches to the Regularization of Ill-posed Problems 41

Guy DEMOMENT, Jérôme IDIER

2.1.Regularization 41

2.1.1Dimensionality control 42

2.1.1.1Truncated singular value decomposition 42

2.1.1.2.Change ofdiscretization 43

2.1.1.3Iterative methods 43

2.1.2.Minimizationof a composite criterion 44

2.1.2.1.Euclidiandistances 45

2.1.2.2Roughness measures 46

2.1.2.3Non-quadratic penalization 47

2.1.2.4Kullback pseudo-distance 47

2.2Criterion descent methods 48

2.2.1.Criterionminimizationfor inversion 48

2.2.2.The quadraticcase 49

2.2.2.1.Non-iterativetechniques 49

2.2.2.2Iterative techniques 50

2.2.3.The convexcase 51

2.2.4.General case 52

2.3.Choice of regularizationcoefficient 53

2.3.1.Residual error energycontrol 53

2.3.2“L-curve”method 53

2.3.3.Cross-validation 54

2.4.Bibliography 56

Chapter 3 Inversion within the Probabilistic Framework 59

Guy DEMOMENT, Yves GOUSSARD

3.1Inversionand inference 59

3.2.Statistical inference60

3.2.1.Noise lawanddirect distributionfor data 61

3.2.2Maximum likelihood estimation 63

3.3.Bayesian approachto inversion 64

3.4Links with deterministic methods 66

3.5Choice of hyperparameters 67

3.6A priorimodel 68

3.7.Choice of criteria 70

3.8.The linear,Gaussian case 71

3.8.1.Statistical propertiesof the solution 71

3.8.2Calculation of marginal likelihood 73

3.8.3.Wienerfiltering 74

3.9.Bibliography 76

PART II DECONVOLUTION 79

Chapter 4 Inverse Filtering and Other Linear Methods 81

Guy LE BESNERAIS, Jean-François GIOVANNELLI, Guy DEMOMENT

4.1Introduction 81

4.2Continuous-time deconvolution 82

4.2.1Inversefiltering 82

4.2.2.Wienerfiltering 84

4.3.Discretization of the problem 85

4.3.1Choice of a quadrature method 85

4.3.2Structure of observation matrix H 87

4.3.3Usual boundary conditions 89

4.3.4.Problemconditioning 89

4.3.4.1.Case of the circulantmatrix 90

4.3.4.2Case of the Toeplitz matrix 90

4.3.4.3Opposition between resolution and conditioning 91

4.3.5.Generalizedinversion 91

4.4.Batch deconvolution 92

4.4.1.Preliminarychoices 92

4.4.2.Matrix formof the estimate 93

4.4.3Hunt’s method (periodic boundary hypothesis) 94

4.4.4Exact inversion methods in the stationary case 96

4.4.5Case of non-stationary signals 98

4.4.6.Results and discussionon examples 98

4.4.6.1Compromise between bias and variance in 1D deconvolution 98

4.4.6.2.Results for 2Dprocessing 100

4.5.Recursive deconvolution 102

4.5.1.Kalmanfiltering 102

4.5.2Degenerate state model and recursive least squares 104

4.5.3.Autoregressivestatemodel 105

4.5.3.1Initialization 106

4.5.3.2Criterion minimized by Kalman smoother 107

4.5.3.3.Exampleof result 108

4.5.4.FastKalmanfiltering 108

4.5.5Asymptotic techniques in the stationary case 110

4.5.5.1Asymptotic Kalman filtering 110

4.5.5.2.Small kernelWienerfilter 111

4.5.6ARMA model and non-standard Kalman filtering 111

4.5.7Case of non-stationary signals 111

4.5.8.On-lineprocessing: 2Dcase 112

4.6.Conclusion 112

4.7.Bibliography 113

Chapter 5 Deconvolution of Spike Trains 117

Frédéric CHAMPAGNAT, Yves GOUSSARD, Stéphane GAUTIER, Jérôme IDIER

5.1Introduction 117

5.2Penalization of reflectivities, L2LP/L2Hy deconvolutions 119

5.2.1.Quadratic regularization 121

5.2.2.Non-quadraticregularization 122

5.2.3L2LPorL2Hy deconvolution 123

5.3Bernoulli-Gaussian deconvolution 124

5.3.1Compound BG model 124

5.3.2.Various strategies for estimation 124

5.3.3General expression for marginal likelihood 125

5.3.4An iterative method for BG deconvolution 126

5.3.5Other methods 128

5.4Examples of processing and discussion 130

5.4.1.Natureof the solutions 130

5.4.2Setting the parameters 132

5.4.3.Numerical complexity 133

5.5.Extensions 133

5.5.1Generalization of structures of R and H 134

5.5.2Estimation of the impulse response 134

5.6.Conclusion 136

5.7.Bibliography 137

Chapter 6 Deconvolution of Images 141

Jérôme IDIER, Laure BLANC-FÉRAUD

6.1Introduction 141

6.2Regularization in the Tikhonov sense 142

6.2.1.Principle 142

6.2.1.1Case of a monovariate signal 142

6.2.1.2.Multivariate extensions 143

6.2.1.3.Discrete framework 144

6.2.2Connection with image processing by linear PDE 144

6.2.3Limits of Tikhonov’s approach 145

6.3.Detection-estimation 148

6.3.1.Principle 148

6.3.2.Disadvantages 149

6.4.Non-quadraticapproach 150

6.4.1Detection-estimation and non-convex penalization 154

6.4.2.AnisotropicdiffusionbyPDE 155

6.5.Half-quadraticaugmentedcriteria 156

6.5.1Duality between non-quadratic criteria and HQ criteria 157

6.5.2.MinimizationofHQcriteria 158

6.5.2.1.Principle of relaxation 158

6.5.2.2Case of a convex function φ 159

6.5.2.3Case of a non-convex function φ 159

6.6.Applicationin imagedeconvolution 159

6.6.1.Calculationof the solution 159

6.6.2.Example 161

6.7.Conclusion 164

6.8.Bibliography 165

PART III ADVANCED PROBLEMS AND TOOLS 169

Chapter 7 Gibbs-Markov Image Models 171

Jérôme IDIER

7.1Introduction 171

7.2.Bayesian statistical framework 172

7.3.Gibbs-Markovfields 173

7.3.1.Gibbsfields 174

7.3.1.1Definition 174

7.3.1.2.Trivial examples 175

7.3.1.3Pairwise interactions, improper laws 176

7.3.1.4.Markovchains 176

7.3.1.5Minimum cliques, non-uniqueness of potential 177

7.3.2Gibbs-Markovequivalence 177

7.3.2.1Neighborhood relationship 177

7.3.2.2Definition of a Markov field 178

7.3.2.3.AGibbsfield is aMarkovfield 179

7.3.2.4.Hammersley-Cliffordtheorem 179

7.3.3.Posterior lawof aGMRF 180

7.3.4.Gibbs-Markovmodels for images 181

7.3.4.1Pixels with discrete values and label fields for classification 181

7.3.4.2.GaussianGMRF 182

7.3.4.3Edge variables, composite GMRF 183

7.3.4.4Interactive edgevariables 184

7.3.4.5.Non-GaussianGMRFs 185

7.4Statistical tools, stochastic sampling 185

7.4.1.Statistical tools 185

7.4.2.Stochastic sampling 188

7.4.2.1Iterative sampling methods 189

7.4.2.2Monte Carlo method of the MCMC kind 192

7.4.2.3.Simulated annealing 193

7.5.Conclusion 194

7.6.Bibliography 195

Chapter 8 Unsupervised Problems 197

Xavier DESCOMBES, Yves GOUSSARD

8.1Introduction and statement of problem 197

8.2.Directly observedfield 199

8.2.1Likelihood properties 199

8.2.2.Optimization 200

8.2.2.1.Gradientdescent 200

8.2.2.2Importancesampling 200

8.2.3.Approximations 202

8.2.3.1Encoding methods 202

8.2.3.2Pseudo-likelihood 203

8.2.3.3.Meanfield 204

8.3Indirectlyobservedfield 205

8.3.1.Statement of problem 205

8.3.2.EMalgorithm 206

8.3.3Application to estimation of the parameters of a GMRF 207

8.3.4.EMalgorithmandgradient 208

8.3.5Linear GMRF relative to hyperparameters 210

8.3.6Extensions and approximations 212

8.3.6.1Generalized maximum likelihood 212

8.3.6.2.FullBayesian approach 213

8.4.Conclusion 215

8.5.Bibliography 216

PART IV SOME APPLICATIONS 219

Chapter 9 DeconvolutionApplied toUltrasonicNon-destructive Evaluation 221

Stéphane GAUTIER, Frédéric CHAMPAGNAT, Jérôme IDIER

9.1Introduction 221

9.2Example of evaluation and difficulties of interpretation 222

9.2.1.Descriptionof the part to be inspected 222

9.2.2.Evaluationprinciple 222

9.2.3.Evaluationresults andinterpretation 223

9.2.4Help with interpretation by restoration of discontinuities 224

9.3Definition of direct convolution model 225

9.4.Blind deconvolution 226

9.4.1Overview of approaches for blind deconvolution 226

9.4.1.1.Predictivedeconvolution 226

9.4.1.2Minimum entropy deconvolution 228

9.4.1.3Deconvolution by “multipulse” technique 228

9.4.1.4Sequential estimation: estimation of the kernel, then the input 228

9.4.1.5Joint estimation of kernel and input 229

9.4.2.DL2Hy/DBGdeconvolution 230

9.4.2.1Improveddirectmodel 230

9.4.2.2Prior information on double reflectivity 230

9.4.2.3Double Bernoulli-Gaussian (DBG) deconvolution 230

9.4.2.4Double hyperbolic (DL2Hy) deconvolution 231

9.4.2.5Behavior of DL2Hy/DBG deconvolution methods 231

9.4.3.BlindDL2Hy/DBGdeconvolution 232

9.5.Processing real data 232

9.5.1Processing by blind deconvolution 233

9.5.2.Deconvolutionwith ameasuredwave 234

9.5.3Comparison between DL2Hy and DBG 237

9.5.4.Summary 240

9.6.Conclusion 240

9.7.Bibliography 241

Chapter 10 Inversion in Optical Imaging through Atmospheric Turbulence 243

Laurent MUGNIER, Guy LE BESNERAIS, SergeMEIMON

10.1Optical imaging through turbulence 243

10.1.1Introduction 243

10.1.2Image formation 244

10.1.2.1.Diffraction 244

10.1.2.2Principle of optical interferometry 245

10.1.3Effect of turbulence on image formation 246

10.1.3.1.Turbulenceand phase 246

10.1.3.2Long-exposure imaging 247

10.1.3.3Short-exposure imaging 247

10.1.3.4Case of a long-baseline interferometer 248

10.1.4Imagingtechniques 249

10.1.4.1.Speckle techniques 249

10.1.4.2Deconvolution from wavefront sensing (DWFS) 250

10.1.4.3.Adaptiveoptics 251

10.1.4.4.Optical interferometry 251

10.2Inversion approach and regularization criteria used 253

10.3.Measurementof aberrations 254

10.3.1Introduction 254

10.3.2.Hartmann-Shacksensor 255

10.3.3.Phase retrieval and phasediversity 257

10.4Myopic restoration in imaging 258

10.4.1.Motivationand noise statistic 258

10.4.2Data processing in deconvolution from wavefront sensing 259

10.4.2.1Conventional processing of short-exposure images 259

10.4.2.2Myopic deconvolution of short-exposure images 260

10.4.2.3.Simulations 261

10.4.2.4.Experimental results 262

10.4.3Restoration of images corrected by adaptive optics 263

10.4.3.1Myopic deconvolution of images corrected by adaptive optics 263

10.4.3.2.Experimental results 265

10.4.4.Conclusion267

10.5Image reconstruction in optical interferometry (OI) 268

10.5.1.Observationmodel 268

10.5.2.TraditionalBayesian approach 271

10.5.3Myopic modeling 272

10.5.4.Results 274

10.5.4.1Processing of synthetic data 274

10.5.4.2Processing of experimental data 276

10.6.Bibliography 277

Chapter 11 Spectral Characterization in Ultrasonic Doppler Velocimetry 285

Jean-François GIOVANNELLI, Alain HERMENT

11.1Velocity measurement in medical imaging 285

11.1.1Principle of velocity measurement in ultrasound imaging 286

11.1.2Information carried by Doppler signals 286

11.1.3.Some characteristics andlimitations 288

11.1.4.Data andproblems treated 288

11.2.Adaptive spectral analysis 290

11.2.1Least squares and traditional extensions 290

11.2.2Long AR models – spectral smoothness – spatial continuity 291

11.2.2.1.Spatial regularity 291

11.2.2.2.Spectral smoothness 292

11.2.2.3Regularized least squares 292

11.2.2.4.Optimization 293

11.2.3.Kalman smoothing 293

11.2.3.1State and observation equations 293

11.2.3.2Equivalence between parameterizations 294

11.2.4Estimation of hyperparameters 294

11.2.5Processing results and comparisons 296

11.2.5.1.Hyperparameter tuning 296

11.2.5.2Qualitative comparison 296

11.3.Trackingspectralmoments 297

11.3.1Proposed method 298

11.3.1.1Likelihood 298

11.3.1.2Amplitudes: prior distribution and marginalization 298

11.3.1.3Frequencies: prior law and posterior law 300

11.3.1.4.Viterbi algorithm 302

11.3.2Likelihood of the hyperparameters 302

11.3.2.1Forward-Backward algorithm 302

11.3.2.2Likelihood gradient 303

11.3.3Processing results and comparisons 304

11.3.3.1Tuning the hyperparameters 304

11.3.3.2Qualitative comparison 305

11.4.Conclusion 306

11.5.Bibliography 307

Chapter 12 Tomographic Reconstruction from Few Projections 311

Ali MOHAMMAD-DJAFARI, Jean-Marc DINTEN

12.1Introduction 311

12.2.Projectiongenerationmodel 312

12.32D analytical methods 313

12.43D analytical methods 317

12.5Limitations of analytical methods 317

12.6.Discrete approachto reconstruction 319

12.7Choice of criterion and reconstruction methods 321

12.8.Reconstructionalgorithms 323

12.8.1Optimization algorithms for convex criteria 323

12.8.1.1.Gradient algorithms 324

12.8.1.2SIRT (Simultaneous Iterative Relaxation Techniques) 325

12.8.1.3ART (Algebraic Reconstruction Technique) 325

12.8.1.4.ARTby blocks 326

12.8.1.5ICD (Iterative Coordinate Descent) algorithms 326

12.8.1.6Richardson-Lucy algorithm 326

12.8.2Optimization or integration algorithms 327

12.9.Specificmodels forbinaryobjects 328

12.10Illustrations 328

12.10.1.2Dreconstruction 328

12.10.2.3Dreconstruction 329

12.11.Conclusions 331

12.12.Bibliography 332

Chapter 13 Diffraction Tomography 335

Hervé CARFANTAN, AliMOHAMMAD-DJAFARI

13.1Introduction 335

13.2.Modelingthe problem 336

13.2.1Examples of diffraction tomography applications 336

13.2.1.1.Microwave imaging 337

13.2.1.2Non-destructive evaluation of conducting materials using

eddycurrents 337

13.2.1.3Geophysical exploration 338

13.2.2Modeling the direct problem 338

13.2.2.1Equations of propagation in an inhomogeneous medium 338

13.2.2.2Integral modeling of the direct problem 339

13.3.Discretizationof the directproblem340

13.3.1.Choice of algebraic framework 340

13.3.2.Methodofmoments 341

13.3.3Discretization by the method of moments 342

13.4Construction of criteria for solving the inverse problem 343

13.4.1First formulation: estimation of x 344

13.4.2Second formulation: simultaneous estimation of x and φ 345

13.4.3.Properties of the criteria 347

13.5.Solvingthe inverseproblem 347

13.5.1.Successive linearizations 348

13.5.1.1.Approximations 348

13.5.1.2.Regularization 349

13.5.1.3Interpretation 349

13.5.2Jointminimization 350

13.5.3.MinimizingMAPcriterion 351

13.6.Conclusion 353

13.7.Bibliography 354

Chapter 14 Imaging from Low-intensity Data 357

Ken SAUER, Jean-Baptiste THIBAULT

14.1Introduction 357

14.2Statistical properties of common low-intensity image data 359

14.2.1Likelihood functions and limiting behavior 359

14.2.2.PurelyPoissonmeasurements 360

14.2.3Inclusion of background counting noise 362

14.2.4Compound noise models with Poisson information 362

14.3Quantum-limited measurements in inverse problems 363

14.3.1Maximum likelihood properties 363

14.3.2.Bayesian estimation 366

14.4Implementation and calculation of Bayesian estimates 368

14.4.1Implementation for pure Poisson model 368

14.4.2Bayesian implementation for a compound data model 370

14.5.Conclusion 372

14.6.Bibliography 372

List of Authors 375

Index 377

感谢LZ分享！

好东西，谢谢楼主

这本书绝对是经典!