Quantitative Coherent Imaging: Theory, Methods and Some Applications discusses the principles of interpreting the structure and material properties of objects by the way in which they scatter electromagnetic and acoustic radiation. It presents an account of the fundamental physical principles which are common to nearly all imaging systems. The book is divided into three parts. Part One deals with the mathematical and computational background to the subject. Part Two discusses the theory of quantitative coherent imaging, presenting the theoretical foundations used in a variety of applications. It looks at both acoustic and electromagnetic imaging systems. Part Three examines some of the data-processing techniques which are common to most types of imagery. It cites methods of deconvolution, image enhancement, and noise reduction. This book caters to the reader interested in different fields of research in imaging science. It explains the principles of coherent imaging and provides a text that covers the theoretical foundations of imaging science in an integrated form.

Preface
Acknowledgments

Part One Mathematical and Computational Background

1 Introduction

1.1 Signals and Images

1.2 Quantitative Coherent Imaging

1.3 Basic Equations and Problems

1.4 Resolution, Distortion, Fuzziness and Noise

1.5 About This Book

2 Fourier Transforms

2.1 The Dirac Delta Function

2.2 The Fourier Transform in 1D

2.3 Convolution and Correlation

2.4 Modulation and Demodulation

2.5 The Hilbert Transform and Quadrature Detection

2.6 The Analytic Signal

2.7 Filters

2.8 The Fourier Transform in 2D

2.9 The Sampling Theorem and Sinc Interpolation

2.10 The Discrete Fourier Transform

2.11 The Fast Fourier Transform (FFT)

2.12 Some Important Applications of the FFT

3 Scattering Theory

3.1 Green's Functions

3.2 Fields Generated by Sources

3.3 Fields Generated by Born Scatterers

3.4 Examples of Born Scattering

3.5 Field Equations and Wave Equations

Part Two Coherent Imaging Techniques

4 Quantitative Imaging of Layered Media

4.1 Pulse-Echo Experiments

4.2 Quantitative Electromagnetic Imaging of a Layered Dielectric

4.3 Quantitative Acoustic Imaging of a Layered Medium

4.4 Some Applications

5 Projection Tomography

5.1 Basic Principles

5.2 The Radon Transform

5.3 The Point Spread Function

5.4 The Projection Slice Theorem

6 Diffraction Tomography

6.1 Diffraction Tomography Using CW Fields

6.2 Diffraction Tomography Using Pulsed Fields

6.3 The Diffraction Slice Theorem

6.4 Quantitative Diffraction Tomography

7 Synthetic Aperture Imaging

7.1 Synthetic Aperture Radar (SAR)

7.2 Principles of SAR

7.3 Electromagnetic Scattering Theory for SAR

7.4 Polarization Effects

7.5 Quantitative Imaging with SAR

7.6 Synthetic Aperture Sonar

Part Three Data Processing

8 Deconvolution I: Linear Restoration

8.1 The Least Squares Method and The Orthogonality Principle

8.2 The Inverse Filter

8.3 The Weiner Filter

8.4 The Power Spectrum Equalization Filter

8.5 The Matched Filter

8.6 Constrained Deconvolution

8.7 A Linear Deconvolution Program: 2D Weiner Filter

9 Deconvolution II: Nonlinear Restoration

9.1 Bayes Rule and Bayesian Estimation

9.2 Maximum Likelihood Filter

9.3 Maximum a Posteriori Filter

9.4 Maximum Entropy Filter

9.5 Homomorphic Filtering

9.6 Blind Deconvolution

10 Deconvolution III: Super Resolution

10.1 Bandlimited Functions and Spectral Extrapolation

10.2 Linear Least Squares Method

10.3 Bayesian Estimation

10.4 Nonlinear Models and Methods

11 Image Enhancement

11.1 Simple Transforms

11.2 Histogram Equalization

11.3 Homomorphic Filtering

11.4 High Emphasis Filtering

11.5 AM, FM and Phase Imaging

12 Noise Reduction

12.1 The Lowpass Filter

12.2 The Neighborhood Averaging Filter

12.3 The Median Filter

Index