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E-raamat: Theoretical Foundations of Digital Imaging Using MATLAB(R)

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(Tel Aviv University, Israel)
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Yaroslavsky (emeritus, engineering, Tel Aviv U.) offers a textbook on the theoretical foundations of digital imaging for students entering the field of imaging engineering. After setting out mathematical preliminaries, he covers image digitization, discrete signal transformations, digital image formation and computational imaging, image resampling and building continuous image models, case study of estimating image parameters, and image perfecting. The MATLAB files can be downloaded from the website. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)

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.

Arvustused

"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)

Preface xv
Author xvii
1 Introduction
1(8)
Imaging Goes Digital
1(6)
Briefly about the Book Structure
7(1)
References
8(1)
2 Mathematical Preliminaries
9(50)
Mathematical Models in Imaging
9(1)
Primary Definitions
9(3)
Linear Signal Space, Basis Functions, and Signal Representation as Expansion over a Set of Basis Functions
12(5)
Signal Transformations
17(3)
Imaging Systems and Integral Transforms
20(1)
Direct Imaging and Convolution Integral
20(2)
Multiresolution Imaging: Wavelet Transforms
22(1)
Imaging in Transform Domain and Diffraction Integrals
23(6)
Properties of the Integral Fourier Transform
29(1)
Invertibility
29(2)
Separability
31(2)
Symmetry Properties
33(1)
Transforms in Sliding Window (Windowed Transforms) and Signal Sub-Band Decomposition
34(3)
Imaging from Projections and Radon Transform
37(3)
Statistical Models of Signals and Transformations
40(1)
Principles of Statistical Treatment of Signals and Signal Transformations and Basic Definitions
40(5)
Models of Signal Random Interferences
45(1)
Additive Signal-Independent Noise Model
45(2)
Multiplicative Noise Model
47(1)
Poisson Model
47(1)
Impulse Noise Model
48(1)
Speckle Noise Model
48(4)
Quantifying Signal-Processing Quality
52(1)
Basics of Optimal Statistical Parameter Estimation
53(4)
Appendix
57(1)
Derivation of Equation 2.32
57(1)
Derivation of Equation 2.65
57(1)
Derivations of Equations 2.84 through 2.87
58(1)
Reference
58(1)
3 Image Digitization
59(74)
Principles of Signal Digitization
59(1)
Signal Discretization
60(1)
Signal Discretization as Expansion over a Set of Basis Functions
60(1)
Typical Basis Functions and Classification
61(1)
Shift (Convolutional) Basis Functions
61(5)
Scale (Multiplicative) Basis Functions
66(4)
Wavelets
70(3)
Optimality of Bases: Karhunen-Loeve and Related Transform
73(5)
Image Sampling
78(1)
The Sampling Theorem and Signal Sampling
78(2)
ID Sampling Theorem
80(6)
Sampling Two-Dimensional and Multidimensional Signals
86(5)
Sampling Artifacts: Quantitative Analysis
91(3)
Sampling Artifacts: Qualitative Analysis
94(2)
Alternative Methods of Discretization in Imaging Devices
96(4)
Signal Scalar Quantization
100(1)
Optimal Quantization: Principles
100(2)
Design of Optimal Quantizers
102(9)
Quantization in Digital Holography
111(2)
Basics of Image Data Compression
113(1)
What Is Image Data Compression and Why Do We Need It?
113(2)
Signal Rate Distortion Function, Entropy, and Statistical Encoding
115(2)
Outline of Image Compression Methods
117(3)
Appendix
120(1)
Derivation of Equation 3.31
120(1)
Derivation of Equation 3.44
121(1)
Derivation of Equation 3.45
122(1)
Derivation of Equation 3.78
122(1)
Derivation of Equation 3.98
123(1)
Derivation of Equation 3.105
124(3)
Derivation of Equation 3.136
127(1)
Basics of Statistical Coding
128(2)
Exercises
130(1)
References
130(3)
4 Discrete Signal Transformations
133(86)
Basic Principles of Discrete Representation of Signal Transformations
133(4)
Discrete Representation of the Convolution Integral
137(1)
Digital Convolution
137(4)
Treatment of Signal Borders in Digital Convolution
141(1)
Discrete Representation of Fourier Integral Transform
142(1)
Discrete Fourier Transforms
142(5)
2D Discrete Fourier Transforms
147(1)
Properties of Discrete Fourier Transforms
148(1)
Invertibility and sined-Function
149(1)
Energy Preservation Property
150(1)
Cyclicity
151(2)
Symmetry Properties
153(1)
SDFT Spectra of Sinusoidal Signals
154(1)
Mutual Correspondence between Signal Frequencies and Indices of Its SDFTs Spectral Coefficients
155(1)
DFT Spectra of Sparse Signals and Spectrum Zero Padding
156(5)
Discrete Cosine and Sine Transforms
161(5)
Signal Convolution in the DCT Domain
166(3)
DFTs and Discrete Frequency Response of Digital Filter
169(2)
Discrete Representation of Fresnel Integral Transform
171(1)
Canonical Discrete Fresnel Transform and Its Versions
171(4)
Invertibility of Discrete Fresnel Transforms and frined-Function
175(3)
Convolutional Discrete Fresnel and Angular Spectrum Propagation Transforms
178(4)
Two-Dimensional Discrete Fresnel Transforms
182(2)
Discrete Representation of Kirchhoff Integral
184(1)
Hadamard, Walsh, and Wavelet Transforms
184(1)
Binary Transforms
185(1)
Hadamard and Walsh Transforms
185(1)
Haar Transform
186(1)
Discrete Wavelet Transforms and Multiresolution Analysis
187(5)
Discrete Sliding Window Transforms and "Time-Frequency"
Signal Representation
192(5)
Appendix
197(1)
Derivation of Equation 4.24
197(1)
Derivation of Equation 4.30
197(1)
Reasonings Regarding Equation 4.31
198(1)
Derivation of Equations 4.37 and 4.38
198(1)
Principle of Fast Fourier Transform Algorithm
199(1)
Representation of Scaled DFT as Convolution
200(1)
Derivation of Equation 4.53
201(1)
Derivation of Equations 4.58 and 4.60
202(1)
Derivation of Equation 4.63
203(1)
Derivation of Equation 4.65
204(1)
Derivation of Equation 4.68
205(2)
Derivation of Equation 4.70
207(1)
Derivation of Equations 4.72 and 4.74
208(1)
Derivation of Equation 4.75
209(1)
Derivation of Equation 4.76
209(2)
Derivation of Equation 4.85
211(1)
Rotated and Scaled DFTs as Digital Convolution
212(1)
Derivation of Equation 4.93
213(1)
Derivation of Equation 4.98
214(1)
Derivation of Equation 4.104
214(1)
Derivation of Equation 4.118
215(1)
Derivation of Equation 4.124
215(1)
Derivation of Equation 4.149
216(1)
Derivation of Equation 4.183
217(1)
Exercises
217(1)
Reference
217(2)
5 Digital Image Formation and Computational Imaging
219(74)
Image Recovery from Sparse or Nonuniformly Sampled Data
219(1)
Formulation of the Task
219(1)
Discrete Sampling Theorem
220(3)
Algorithms for Signal Recovery from Sparse Sampled Data
223(1)
Analysis of Transforms
224(1)
Discrete Fourier Transform
224(2)
Discrete Cosine Transform
226(5)
Wavelets and Other Bases
231(4)
Selection of Transform for Image Band-Limited
Approximation
235(1)
Application Examples
236(1)
Image Superresolution from Multiple Differently Sampled Video Frames
236(2)
Image Reconstruction from Sparse Projections in Computed Tomography
238(1)
Discrete Sampling Theorem and "Compressive Sensing"
238(3)
Digital Image Formation by Means of Numerical Reconstruction of Holograms
241(1)
Introduction
241(1)
Principles of Hologram Electronic Recording
241(5)
Numerical Algorithms for Hologram Reconstruction
246(3)
Hologram Pre- and Postprocessing
249(1)
Point Spread Functions of Numerical Reconstruction of Holograms General Formulation
250(4)
Point Spread Function of Numerical Reconstruction of Holograms Recorded in Far Diffraction Zone (Fourier
Holograms)
254(4)
Point Spread Function of Numerical Reconstruction of Holograms Recorded in Near Diffraction Zone (Fresnel Holograms)
258(1)
Fourier Reconstruction Algorithm
259(2)
Convolution Reconstruction Algorithm
261(3)
Computer-Generated Display Holography
264(1)
3D Imaging and Computer-Generated Holography
264(2)
Recording Computer-Generated Holograms on Optical Media
266(3)
Optical Reconstruction of Computer-Generated Holograms
269(3)
Computational Imaging Using Optics-Less Lambertian Sensors
272(1)
Optics-Less Passive Sensors: Motivation
272(1)
Imaging as a Parameter Estimation Task
273(5)
Optics-Less Passive Imaging Sensors: Possible Designs, Expected Performance, Advantages, and Disadvantages
278(6)
Appendix
284(1)
Derivation of Equation 5.47
284(1)
Derivation of Equation 5.63
285(1)
Derivation of Equation 5.69
286(1)
Derivation of Equation 5.81
286(3)
Derivation of Equation 5.88
289(1)
Derivation of Equation 5.89
290(1)
Exercises
290(1)
References
290(3)
6 Image Resampling and Building Continuous Image Models
293(50)
Perfect Resampling Filter
294(4)
Fast Algorithms for Discrete Sine Interpolation
Their Applications
298(1)
Signal Subsampling (Zooming-In) by Means of DFT or DCT Spectra Zero Padding
298(3)
DFT- and DCT-Based Signal Fractional Shift Algorithms and Their Basic Applications
301(5)
Fast Image Rotation Using the Fractional Shift Algorithms
306(2)
Image Zooming and Rotation Using "Scaled" and Rotated DFTs
308(2)
Discrete Sine Interpolation versus Other Interpolation Methods: Performance Comparison
310(3)
Numerical Differentiation and Integration
313(1)
Perfect Digital Differentiation and Integration
313(4)
Traditional Numerical Differentiation and Integration Algorithms versus DFT/DCT-Based Ones: Performance Comparison
317(5)
Local ("Elastic") Image Resampling: Sliding Window Discrete Sine Interpolation Algorithms
322(3)
Image Data Resampling for Image Reconstruction from Projections
325(1)
Discrete Radon Transform: An Algorithmic Definition and Filtered Back Projection Method for Image Reconstruction
325(2)
Direct Fourier Method of Image Reconstruction
327(1)
Image Reconstruction from Fan-Beam Projections
328(2)
Appendix
330(1)
Derivation of Equations 6.6 and 6.7
330(4)
PSF of Signal Zooming by Means of Zero Padding of Its DCT Spectrum
334(4)
Derivation of Equation 6.18
338(1)
Derivation of Equation 6.28
339(1)
Derivation of Equation 6.29
340(2)
Exercises
342(1)
References
342(1)
7 Image Parameter Estimation: Case Study---Localization of Objects in Images
343(52)
Localization of Target Objects in the Presence of Additive Gaussian Noise
343(1)
Optimal Localization Device for Target Localization in Noncorrelated Gaussian Noise
343(2)
Performance of ML-Optimal Estimators: Normal and Anomalous Localization Errors
345(6)
Target Object Localization in the Presence of Nonwhite (Correlated) Additive Gaussian Noise
351(3)
Localization Accuracy for the SNR-Optimal Filter
354(1)
Optimal Localization in Color and Multicomponent Images
355(2)
Object Localization in the Presence of Multiple Nonoverlapping Nontarget Objects
357(2)
Target Localization in Cluttered Images
359(1)
Formulation of the Approach
359(1)
SCR-Optimal Adaptive Correlator
360(6)
Local Adaptive SCR-Optimal Correlators
366(4)
Object Localization in Blurred Images
370(2)
Object Localization and Edge Detection: Selection of Reference Objects for Target Tracking
372(6)
Appendix
378(1)
Distribution Density and Variances of Normal Localization Errors
378(8)
Evaluation of the Probability of Anomalous Localization Errors
386(3)
Derivation of Equations 7.49, 7.50, and 7.51
389(5)
Exercises
394(1)
References
394(1)
8 Image Perfecting
395(82)
Image Perfecting as a Processing Task
395(2)
Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise
397(4)
MMSE-Optimal Linear Filters for Image Restoration
401(1)
Transform Domain MSE-Optimal Scalar Filters
401(2)
Empirical Wiener Filters for Image Denoising
403(8)
Empirical Wiener Filters for Image Deblurring
411(9)
Sliding Window Transform Domain Adaptive Image Restoration
420(1)
Local Adaptive Filtering
420(2)
Sliding Window DCT Transform Domain Filtering
422(5)
Hybrid DCT/Wavelet Filtering
427(2)
Multicomponent Image Restoration and Data Fusion
429(6)
Filtering Impulse Noise
435(5)
Correcting Image Grayscale Nonlinear Distortions
440(3)
Nonlinear Filters for Image Perfecting
443(1)
Nonlinear Filter Classification Principles
443(8)
Filter Classification Tables and Particular Examples
451(7)
Nonlinear Filters for Multicomponent Images
458(2)
Display Options for Image Enhancement
460(3)
Appendix
463(1)
Derivation of Equation 8.16
463(1)
Empirical Estimation of Variance of Additive Signal-Independent Broad Band Noise in Images
464(2)
Derivation of Equation 8.45
466(2)
Derivation of Equation 8.51
468(5)
Verification of Equation 8.66
473(2)
Exercises
475(1)
References
475(2)
Index 477
Leonid P. Yaroslavsky is a professor emeritus at Tel Aviv University. A fellow of the Optical Society of America, Dr. Yaroslavsky has authored more than 100 papers on digital image processing and digital holography.
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