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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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*

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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*

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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*

**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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*

**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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*

**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.

**Introduction**

Imaging Goes Digital

**Mathematical Preliminaries**

Mathematical Models in Imaging

Signal Transformations

Imaging Systems and Integral Transforms

Statistical Models of Signals and Transformations

**Image Digitization**

Principles of Signal Digitization

Signal Discretization

Image Sampling

Alternative Methods of Discretization in Imaging Devices

Single Scalar Quantization

Basics of Image Data Compression

Basics of Statistical Coding

**Discrete Signal Transformations**

Basic Principles of Discrete Representation of Signal Transformations

Discrete Representation of the Convolution Integral

Discrete Representation of Fourier Integral Transform

Discrete Representation of Fresnel Integral Transform

Discrete Representation of Kirchhoff Integral

Hadamard, Walsh, and Wavelet Transforms

Discrete Sliding Window Transforms and “Time-Frequency” Signal Representation

**Digital Image Formation and Computational Imaging**

Image Recovery from Sparse or Nonuniformly Sampled Data

Digital Image Formation by Means of Numerical Reconstruction of Holograms

Computer-Generated Display Holography

Computational Imaging Using Optics-Less Lambertian Sensors

**Image Resampling and Building Continuous Image Models**

Perfect Resampling Filter

Fast Algorithms for Discrete Sinc Interpolation and Their Applications

Discrete Sinc Interpolation versus Other Interpolation Methods: Performance Comparison

Numerical Differentiation and Integration

Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc Interpolation Algorithms

Image Data Resampling for Image Reconstruction from Projections

**Image Parameter Estimation****: Case Study—Localization of Objects in Images**

Localization of Target Objects in the Presence of Additive Gaussian Noise

Target Localization in Cluttered Images

**Image Perfecting**

Image Perfecting as a Processing Task

Possible Approaches to Restoration of Images Distorted by Blur and Contaminated by Noise

MMSE-Optimal Linear Filters for Image Restoration

Sliding Window Transform Domain Adaptive Image Restoration

Multicomponent Image Restoration and Data Fusion

Filtering Impulse Noise

Correcting Image Grayscale Nonlinear Distortions

Nonlinear Filters for Image Perfecting

**Index**

*Exercises and References appear at the end of each chapter.*