Theoretical Foundations of Digital Imaging Using Matlab(r)

Name: Theoretical Foundations of Digital Imaging Using Matlab(r)
Brand: CRC PR INC
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By: Leonid P. Yaroslavsky

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Hardcover | 26 November 2012 | Edition Number 1

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Hardcover
493 Pages

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23.62 x 16.26 x 3.05

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With the ubiquitous use of digital imaging, a new profession has emerged: imaging engineering. Designed for newcomers to imaging science and engineering, Theoretical Foundations of Digital Imaging Using MATLAB^® treats the theory of digital imaging as a specific branch of science. It covers the subject in its entirety, from image formation to image perfecting.

Based on the author's 50 years of working and teaching in the field, the text first addresses the problem of converting images into digital signals that can be stored, transmitted, and processed on digital computers. It then explains how to adequately represent image transformations on computers. After presenting several examples of computational imaging, including numerical reconstruction of holograms and virtual image formation through computer-generated display holograms, the author introduces methods for image perfect resampling and building continuous image models. He also examines the fundamental problem of the optimal estimation of image parameters, such as how to localize targets in images. The book concludes with a comprehensive discussion of linear and nonlinear filtering methods for image perfecting and enhancement.

Helping you master digital imaging, this book presents a unified theoretical basis for understanding and designing methods of imaging and image processing. To facilitate a deeper understanding of the major results, it offers a number of exercises supported by MATLAB programs, with the code available at www.crcpress.com.

Industry Reviews

"This seminal and highly influential monograph focuses on concrete phenomena for understanding and designing methods of imaging and image processing. ... The reader will find a careful discussion of computational imaging, standard material about image reconstruction from sparse sampled data, description of statistically optimal estimation of image numerical parameters, and a presentation of various exercises supported by MATLAB programs."
-Christian Brosseau, Optics & Photonics News

"this is an excellent in-depth review of the fundamentals of digital imaging, best read for its general foundational content" -Contemporary Physics (Aug 2016)

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Preface	p. xv
Author	p. xvii
Introduction	p. 1
Imaging Goes Digital	p. 1
Briefly about the Book Structure	p. 7
References	p. 8
Mathematical Preliminaries	p. 9
Mathematical Models in Imaging	p. 9
Primary Definitions	p. 9
Linear Signal Space, Basis Functions, and Signal Representation as Expansion over a Set of Basis Functions	p. 12
Signal Transformations	p. 17
Imaging Systems and Integral Transforms	p. 20
Direct Imaging and Convolution Integral	p. 20
Multiresolution Imaging: Wavelet Transforms	p. 22
Imaging in Transform Domain and Diffraction Integrals	p. 23
Properties of the Integral Fourier Transform	p. 29
Invertibility	p. 29
Separability	p. 31
Symmetry Properties	p. 33
Transforms in Sliding Window (Windowed Transforms) and Signal Sub-Band Decomposition	p. 34
Imaging from Projections and Radon Transform	p. 37
Statistical Models of Signals and Transformations	p. 40
Principles of Statistical Treatment of Signals and Signal Transformations and Basic Definitions	p. 40
Models of Signal Random Interferences	p. 45
Additive Signal-Independent Noise Model	p. 45
Multiplicative Noise Model	p. 47
Poisson Model	p. 47
Impulse Noise Model	p. 48
Speckle Noise Model	p. 48
Quantifying Signal-Processing Quality	p. 52
Basics of Optimal Statistical Parameter Estimation	p. 53
Appendix	p. 57
Derivation of Equation 2.32	p. 57
Derivation of Equation 2.65	p. 57
Derivations of Equations 2.84 through 2.87	p. 58
Reference	p. 58
Image Digitization	p. 59
Principles of Signal Digitization	p. 59
Signal Discretization	p. 60
Signal Discretization as Expansion over a Set of Basis Functions	p. 60
Typical Basis Functions and Classification	p. 61
Shift (Convolutional) Basis Functions	p. 61
Scale (Multiplicative) Basis Functions	p. 66
Wavelets	p. 70
Optimality of Bases: Karhunen-Loeve and Related Transform	p. 73
Image Sampling	p. 78
The Sampling Theorem and Signal Sampling	p. 78
1D Sampling Theorem	p. 80
Sampling Two-Dimensional and Multidimensional Signals	p. 86
Sampling Artifacts: Quantitative Analysis	p. 91
Sampling Artifacts: Qualitative Analysis	p. 94
Alternative Methods of Discretization in Imaging Devices	p. 96
Signal Scalar Quantization	p. 100
Optimal Quantization: Principles	p. 100
Design of Optimal Quantizers	p. 102
Quantization in Digital Holography	p. 111
Basics of Image Data Compression	p. 113
What Is Image Data Compression and Why Do We Need It?	p. 113
Signal Rate Distortion Function, Entropy, and Statistical Encoding	p. 115
Outline of Image Compression Methods	p. 117
Appendix	p. 120
Derivation of Equation 3.31	p. 120
Derivation of Equation 3.44	p. 121
Derivation of Equation 3.45	p. 122
Derivation of Equation 3.78	p. 122
Derivation of Equation 3.98	p. 123
Derivation of Equation 3.105	p. 124
Derivation of Equation 3.136	p. 127
Basics of Statistical Coding	p. 128
Exercises	p. 130
References	p. 130
Discrete Signal Transformations	p. 133
Basic Principles of Discrete Representation of Signal Transformations	p. 133
Discrete Representation of the Convolution Integral	p. 137
Digital Convolution	p. 137
Treatment of Signal Borders in Digital Convolution	p. 141
Discrete Representation of Fourier Integral Transform	p. 142
Discrete Fourier Transforms	p. 142
2D Discrete Fourier Transforms	p. 147
Properties of Discrete Fourier Transforms	p. 148
Invertibility and sincd-Function	p. 149
Energy Preservation Property	p. 150
Cyclicity	p. 151
Symmetry Properties	p. 153
SDFT Spectra of Sinusoidal Signals	p. 154
Mutual Correspondence between Signal Frequencies and Indices of Its SDFTs Spectral Coefficients	p. 155
DFT Spectra of Sparse Signals and Spectrum Zero Padding	p. 156
Discrete Cosine and Sine Transforms	p. 161
Signal Convolution in the DCT Domain	p. 166
DFTs and Discrete Frequency Response of Digital Filter	p. 169
Discrete Representation of Fresnel Integral Transform	p. 171
Canonical Discrete Fresnel Transform and Its Versions	p. 171
Invertibility of Discrete Fresnel Transforms and frincd-Function	p. 175
Convolutional Discrete Fresnel and Angular Spectrum Propagation Transforms	p. 178
Two-Dimensional Discrete Fresnel Transforms	p. 182
Discrete Representation of Kirchhoff Integral	p. 184
Hadamard, Walsh, and Wavelet Transforms	p. 184
Binary Transforms	p. 185
Hadamard and Walsh Transforms	p. 185
Haar Transform	p. 186
Discrete Wavelet Transforms and Multiresolution Analysis	p. 187
Discrete Sliding Window Transforms and "Time-Frequency" Signal Representation	p. 192
Appendix	p. 197
Derivation of Equation 4.24	p. 197
Derivation of Equation 4.30	p. 197
Reasonings Regarding Equation 4.31	p. 198
Derivation of Equations 4.37 and 4.38	p. 198
Principle of Fast Fourier Transform Algorithm	p. 199
Representation of Scaled DFT as Convolution	p. 200
Derivation of Equation 4.53	p. 201
Derivation of Equations 4.58 and 4.60	p. 202
Derivation of Equation 4.63	p. 203
Derivation of Equation 4.65	p. 204
Derivation of Equation 4.68	p. 205
Derivation of Equation 4.70	p. 207
Derivation of Equations 4.72 and 4.74	p. 208
Derivation of Equation 4.75	p. 209
Derivation of Equation 4.76	p. 209
Derivation of Equation 4.85	p. 211
Rotated and Scaled DFTs as Digital Convolution	p. 212
Derivation of Equation 4.93	p. 213
Derivation of Equation 4.98	p. 214
Derivation of Equation 4.104	p. 214
Derivation of Equation 4.118	p. 215
Derivation of Equation 4.124	p. 215
Derivation of Equation 4.149	p. 216
Derivation of Equation 4.183	p. 217
Exercises	p. 217
Reference	p. 217
Digital Image Formation and Computational Imaging	p. 219
Image Recovery from Sparse or Nonuniformly Sampled Data	p. 219
Formulation of the Task	p. 219
Discrete Sampling Theorem	p. 220
Algorithms for Signal Recovery from Sparse Sampled Data	p. 223
Analysis of Transforms	p. 224
Discrete Fourier Transform	p. 224
Discrete Cosine Transform	p. 226
Wavelets and Other Bases	p. 231
Selection of Transform for Image Band-Limited Approximation	p. 235
Application Examples	p. 236
Image Superresolution from Multiple Differently Sampled Video Frames	p. 236
Image Reconstruction from Sparse Projections in Computed Tomography	p. 238
Discrete Sampling Theorem and "Compressive Sensing"	p. 238
Digital Image Formation by Means of Numerical Reconstruction of Holograms	p. 241
Introduction	p. 241
Principles of Hologram Electronic Recording	p. 241
Numerical Algorithms for Hologram Reconstruction	p. 246
Hologram Pre- and Postprocessing	p. 249
Point Spread Functions of Numerical Reconstruction of Holograms General Formulation	p. 250
Point Spread Function of Numerical Reconstruction of Holograms Recorded in Far Diffraction Zone (Fourier Holograms)	p. 254
Point Spread Function of Numerical Reconstruction of Holograms Recorded in Near Diffraction Zone (Fresnel Holograms)	p. 258
Fourier Reconstruction Algorithm	p. 259
Convolution Reconstruction Algorithm	p. 261
Computer-Generated Display Holography	p. 264
3D Imaging and Computer-Generated Holography	p. 264
Recording Computer-Generated Holograms on Optical Media	p. 266
Optical Reconstruction of Computer-Generated Holograms	p. 269
Computational Imaging Using Optics-Less Lambertian Sensors	p. 272
Optics-Less Passive Sensors: Motivation	p. 272
Imaging as a Parameter Estimation Task	p. 273
Optics-Less Passive Imaging Sensors: Possible Designs, Expected Performance, Advantages, and Disadvantages	p. 278
Appendix	p. 284
Derivation of Equation 5.47	p. 284
Derivation of Equation 5.63	p. 285
Derivation of Equation 5.69	p. 286
Derivation of Equation 5.81	p. 286
Derivation of Equation 5.88	p. 289
Derivation of Equation 5.89	p. 290
Exercises	p. 290
References	p. 290
Image Resampling and Building Continuous Image Models	p. 293
Perfect Resampling Filter	p. 294
Fast Algorithms for Discrete Sine Interpolation and Their Applications	p. 298
Signal Subsampling (Zooming-In) by Means of DFT or DCT Spectra Zero Padding	p. 298
DFT- and DCT-Based Signal Fractional Shift Algorithms and Their Basic Applications	p. 301
Fast Image Rotation Using the Fractional Shift Algorithms	p. 306
Image Zooming and Rotation Using "Scaled" and Rotated DFTs	p. 308
Discrete Sine Interpolation versus Other Interpolation Methods: Performance Comparison	p. 310
Numerical Differentiation and Integration	p. 313
Perfect Digital Differentiation and Integration	p. 313
Traditional Numerical Differentiation and Integration Algorithms versus DFT/DCT-Based Ones: Performance Comparison	p. 317
Local ("Elastic") Image Resampling: Sliding Window Discrete Sine Interpolation Algorithms	p. 322
Image Data Resampling for Image Reconstruction from Projections	p. 325
Discrete Radon Transform: An Algorithmic Definition and Filtered Back Projection Method for Image Reconstruction	p. 325
Direct Fourier Method of Image Reconstruction	p. 327
Image Reconstruction from Fan-Beam Projections	p. 328
Appendix	p. 330
Derivation of Equations 6.6 and 6.7	p. 330
PSF of Signal Zooming by Means of Zero Padding of Its DCT Spectrum	p. 334
Derivation of Equation 6.18	p. 338
Derivation of Equation 6.28	p. 339
Derivation of Equation 6.29	p. 340
Exercises	p. 342
References	p. 342
Image Parameter Estimation: Case Study-Localization of Objects in Images	p. 343
Localization of Target Objects in the Presence of Additive Gaussian Noise	p. 343
Optimal Localization Device for Target Localization in Noncorrelated Gaussian Noise	p. 343
Performance of ML-Optimal Estimators: Normal and Anomalous Localization Errors	p. 345
Target Object Localization in the Presence of Nonwhite (Correlated) Additive Gaussian Noise	p. 351
Localization Accuracy for the SNR-Optimal Filter	p. 354
Optimal Localization in Color and Multicomponent Images	p. 355
Object Localization in the Presence of Multiple Nonoverlapping Nontarget Objects	p. 357
Target Localization in Cluttered Images,	p. 359
Formulation of the Approach	p. 359
SCR-Optimal Adaptive Correlator	p. 360
Local Adaptive SCR-Optimal Correlators	p. 366
Object Localization in Blurred Images	p. 370
Object Localization and Edge Detection: Selection of Reference Objects for Target Tracking	p. 372
Appendix	p. 378
Distribution Density and Variances of Normal Localization Errors	p. 378
Evaluation of the Probability of Anomalous Localization Errors	p. 386
Derivation of Equations 7.49, 7.50, and 7.51	p. 389
Exercises	p. 394
References	p. 394
Image Perfecting	p. 395
Image Perfecting as a Processing Task	p. 395
Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise	p. 397
MMSE-Optimal Linear Filters for Image Restoration	p. 401
Transform Domain MSE-Optimal Scalar Filters	p. 401
Empirical Wiener Filters for Image Denoising	p. 403
Empirical Wiener Filters for Image Deblurring	p. 411
Sliding Window Transform Domain Adaptive Image Restoration	p. 420
Local Adaptive Filtering	p. 420
Sliding Window DCT Transform Domain Filtering	p. 422
Hybrid DCT/Wavelet Filtering	p. 427
Multicomponent Image Restoration and Data Fusion	p. 429
Filtering Impulse Noise	p. 435
Correcting Image Grayscale Nonlinear Distortions	p. 440
Nonlinear Filters for Image Perfecting	p. 443
Nonlinear Filter Classification Principles	p. 443
Filter Classification Tables and Particular Examples	p. 451
Nonlinear Filters for Multicomponent Images	p. 458
Display Options for Image Enhancement	p. 460
Appendix	p. 463
Derivation of Equation 8.16	p. 463
Empirical Estimation of Variance of Additive Signal-Independent Broad Band Noise in Images	p. 464
Derivation of Equation 8.45	p. 466
Derivation of Equation 8.51	p. 468
Verification of Equation 8.66	p. 473
Exercises	p. 475
References	p. 475
Index	p. 477
Table of Contents provided by Ingram. All Rights Reserved.

Theoretical Foundations of Digital Imaging Using Matlab(r)

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