How to Optimally Sample and Resample Images: Theory and Methods Using MATLAB

Table of Contents

Chapter 1 Introduction
1.1. What is Meant by Optimal Image Sampling and Resampling?
1.2. Overview of the Book

Chapter 2 Summary of the Classic Sampling Theory
2.1. Sampling Band-Limited Signals
2.1.1. Sampling 1D Band-Limited Signals: The Classic Sampling Theorem
2.1.2. Sampling 1D Band-Pass Signals
2.1.3. Separable Sampling 2D Band-Limited Signals
2.2. Optimization of Sampling Lattices for Image Sampling
2.3. Image Sampling Through Their Sub-Band Decomposition And

• Evaluating the Image Minimal Sampling Rate

2.4. Signal Distortions Caused by Signal Sampling with Sub-Nyquist

• Sampling Rates

2.5. Exercises

Chapter 3 Sampling Real Not Band-Limited Signals
3.1. Mathematical Models of Image Sampling and Reconstruction

• Devices

3.2. a Realistic Re-Formulation of the Sampling Theorem
3.3. Sampling Distortions of Real, Not Bandlimited Signals:

• Illustrations

3.4. Exercises

Chapter 4 The General Sampling Theorem
4.1. the Discrete Sampling Theorem
4.2. Discrete Sampling Theorem Formulations for Specific

• Transforms …….…………………………………………………………………………

4.2.1. Discrete Fourier Transform and Discrete Cosine Transforms
4.2.2. Wavelets and Other Transforms
4.3. the General Sampling Theorem

Chapter 5 Compressed Sensing: a Method of Reconstruction of Signals

• Sampled with Aliasing

5.1. the Ubiquitous Redundancy of Images Sampled Over Regular

• Rectangular Sampling Lattices

5.2. Compressed Sensing and Reconstruction of Signals Sampled With

• The Aliasing

5.3. is the Compressed Sensing a Solution to the Problem Of

• Minimization of the Image Sampling Rate?

5.4. Exercises

Chapter 6 How One Can Sample Images with Sampling Rates Close to The

• Theoretical Minimum

6.1. a Method of Image Sampling and Reconstruction with Sampling

• Rates Close to the Theoretical Minimum

6.2. Experimental Verification of the Workability of the Method
6.3. Some Practical Issues
6.4. Other Possible Applications of the Asbsr Method of Image

• Sampling and Reconstruction

6.4.1. Demosaicing Color Images
6.4.2. Image Super-Resolution from Multiple Chaotically Sampled Video Frames
6.4.3. Image Reconstruction from Their Sparsely Sampled or Decimated Projections
6.4.4. Image Reconstruction from Their Sparsely Sampled Fourier Spectra
6.4.5. Image Reconstruction from the Modulus of Its Fourier Spectrum
6.5. Exercise

• Part Ii Image Resampling

Chapter 7 Image Resampling: Preliminaries and Problem Formulation
7.1. Image Resampling as a Digital Filtering Problem
7.2. Point Spread Functions and Frequency Responses of Digital And

• Their Equivalent Analog Filters

7.3. the Perfect Fractional Shift Filter-Interpolator

Chapter 8. Image Resampling: Fast Computational Algorithms
8.1. Fast Fractional Shift Algorithms and Building Analog Image

• Models

8.1.1. Fft Based Algorithm
8.1.2. Fast Dct Based Algorithm
8.2. Discrete Sinc Interpolated Sub-Sampling Signals by Zero-Padding

• Their Dft and Dct Spectra

8.2.1. Zero Padding Dft Spectra of Signals
8.2.2. Zero Padding Signal Dct Spectra
8.3. Exercises

Chapter 9 Examples of Applications of Signal and Image Resampling Using

• Discrete Sinc Interpolation

9.1. Quasi-Continuous Spectral and Correlation Analysis
9.2. Image Rotation
9.2.1. Fast Image Rotation Using the Fractional Shift Algorithms
9.2.2. Image Rotation: Discrete Sinc Interpolation Vs. Other Interpolation Methods
9.3. Image Data Resampling for Image Reconstruction From

• Projections

9.3.1. Discrete Radon Transform and the Filtered Back-Projection Algorithm for Image

• Reconstruction from Parallel Beam Projections

9.3.2. the Direct Fourier Method of Image Reconstruction
9.3.3. Image Reconstruction from Fan-Beam Projections
9.4. Precise Numerical Differentiation and Integration of Sampled

• Signals

9.4.1. the Perfect Digital Differentiator and Integrator
9.4.2. Conventional Numerical Differentiation and Integration Algorithms Versus Perfect

• Dft/Dct Based Ones: Performance Comparison

9.5. Local (“Elastic”) Image Resampling: Sliding Window Discrete Sinc

• Interpolation Algorithms

9.6. Exercises

• References
• Subject Index

Author

• Leonid Yaroslavsky