book

Image Super-Resolution and Applications

by Fathi Abd El-Samie, Mohiy M. Hadhoud, Said E. El-Khamy

December 2012

Intermediate to advanced

502 pages

9h 30m

English

CRC Press

Read now

Unlock full access

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
Authors
1 Introduction
1.1 Image Interpolation1.2 Image Super-Resolution
2 Polynomial Image Interpolation
2.1 Introduction2.2 Classical Image Interpolation2.3 B-Spline Image Interpolation2.3.1 Polynomial Splines2.3.2 B-Spline Variants2.3.2.1 Nearest Neighbor Interpolation2.3.2.2 Linear Interpolation2.3.2.3 Cubic Spline Interpolation2.3.3 Digital Filter Implementation of B-Spline Interpolation2.4 O-MOMS Interpolation2.5 Keys’ (Bicubic) Interpolation2.6 Artifacts of Polynomial Image Interpolation2.6.1 Ringing2.6.2 Aliasing2.6.3 Blocking2.6.4 Blurring

3 Adaptive Polynomial Image Interpolation
3.1 Introduction3.2 Low-Resolution Image Degradation Model3.3 Linear Space-Invariant Image Interpolation3.4 Warped-Distance Image Interpolation3.5 Weighted Image Interpolation3.6 Iterative Image Interpolation3.7 Simulation Examples
4 Neural Modeling of Polynomial Image Interpolation
4.1 Introduction4.2 Fundamentals of ANNs4.2.1 Cells4.2.2 Layers4.2.3 Arcs4.2.4 Weights4.2.5 Activation Rules4.2.6 Activation Functions4.2.6.1 Identity Function4.2.6.2 Step Function4.2.6.3 Sigmoid Function4.2.6.4 Piecewise-Linear Function4.2.6.5 Arc Tangent Function4.2.6.6 Hyperbolic Tangent Function4.2.7 Outputs4.2.8 Learning Rules4.2.8.1 Supervised Learning4.2.8.2 Unsupervised Learning4.3 Neural Network Structures4.3.1 Multi-Layer Perceptrons4.3.2 Radial Basis Function Networks4.3.3 Wavelet Neural Network4.3.4 Recurrent ANNs4.4 Training Algorithm4.5 Neural Image Interpolation4.6 Simulation Examples
5 Color Image Interpolation
5.1 Introduction5.2 Color Filter Arrays5.2.1 White Balance5.2.2 Bayer Interpolation5.3 Linear Interpolation with Laplacian Second Order Correction5.4 Adaptive Color Image Interpolation
6 Image Interpolation for Pattern Recognition
6.1 Introduction6.2 Cepstral Pattern Recognition6.3 Feature Extraction6.3.1 Extraction of MFCCs6.3.1.1 Framing and Windowing6.3.1.2 Discrete Fourier Transform6.3.1.3 Mel Filter Bank6.3.1.4 Discrete Cosine Transform6.3.2 Polynomial Coe?cients6.4 Feature Extraction from Discrete Transforms6.4.1 Discrete Wavelet Transform6.4.2 Discrete Cosine Transform6.4.3 Discrete Sine Transform6.5 Feature Matching Using ANNs6.6 Simulation Examples
7 Image Interpolation as Inverse Problem
7.1 Introduction7.2 Adaptive Least-Squares Image Interpolation7.3 LMMSE Image Interpolation7.4 Maximum Entropy Image Interpolation7.5 Regularized Image Interpolation7.6 Simulation Examples7.7 Interpolation of Infrared Images.
8 Image Registration
8.1 Introduction8.2 Applications of Image Registration8.2.1 Different Viewpoints (Multi-View Analysis)8.2.2 Different Times (Multi-Temporal Analysis)8.2.3 Different Sensors (Multi-Modal Analysis)8.2.4 Scene-to-Model Registration8.3 Steps of Image Registration8.3.1 Feature Detection Step8.3.2 Feature Matching Step8.3.2.1 Area-Based Methods8.3.2.2 Feature-Based Methods8.3.3 Transform Model Estimation8.3.3.1 Global Mapping Models8.3.3.2 Local Mapping Models8.3.4 Image Resampling and Transformation8.4 Evaluation of Image Registration Accuracy
9 Image Fusion
9.1 Introduction9.2 Objectives of Image Fusion9.3 Implementation of Image Fusion9.4 Pixel Level Image Fusion9.5 Principal Component Analysis Fusion9.6 Wavelet Fusion9.6.1 DWT Fusion9.6.2 DWFT Fusion9.7 Curvelet Fusion9.7.1 Sub-Band Filtering9.7.2 Tiling9.7.3 Ridgelet Transform9.8 IHS Fusion9.9 High-Pass Filter Fusion9.10 Gram–Schmidt Fusion9.11 Fusion of Satellite Images9.12 Fusion of MR and CT Images
10 Super-Resolution with a Priori Information
10.1 Introduction10.2 Multiple Observation LR Degradation Model10.3 Wavelet-Based Image Super-Resolution10.4 Simplified Multi-Channel Degradation Model10.5 Multi-Channel Image Restoration10.5.1 Multi-Channel LMMSE Restoration10.5.2 Multi-Channel Maximum Entropy Restoration10.5.3 Multi-Channel Regularized Restoration10.6 Simulation Examples
11 Blind Super-Resolution Reconstruction of Images
11.1 Introduction11.2 Problem Formulation11.3 Two-Dimensional GCD Algorithm11.4 Blind Super-Resolution Reconstruction Approach11.5 Simulation Examples
Appendix A: Discrete B-Splines
Appendix B: Toeplitz-to-Circulant Approximations
Appendix C: Newton’s Method
Appendix D: MATLAB® Codes
References
Index

Content preview from Image Super-Resolution and Applications

Appendix B: Toeplitz-to-Circulant Approximations

B.1 Toeplitz-to-Circulant Approximation

Let H be an S × S Toeplitz matrix of the following form:

$H = [\begin{matrix} h (0) & \dots & h (- 1) & 0 \\ ⋮ & ⋱ & ⋱ \\ h (k) & ⋱ & h (- 1) \\ ⋱ & ⋱ & ⋮ \\ 0 & h (k) & \dots & h (0) \end{matrix}]$

(B.1)

which is approximated by an S × S circulant matrix H^c defined as [77]:

$H^{c} = [\begin{matrix} h (0) & \dots & \dots & h (- 1) & 0 & \dots & h (k) & \dots & h (1) \\ ⋮ & ⋱ & ⋱ & ⋱ & \dots & ⋱ \\ ⋮ & ⋱ & ⋱ & ⋱ & \dots & h (k) \\ h (k) & ⋱ & ⋱ & \dots \\ 0 & ⋱ & ⋱ & ⋱ & 0 \\ ⋮ & ⋱ & ⋱ & ⋱ & h (- 1) \\ h (- 1) & ⋮ & ⋱ & ⋱ & ⋱ & ⋮ \\ ⋮ & ⋱ & ⋮ & ⋱ & ⋱ & ⋱ & ⋮ \\ h (- 1) & \dots & h (- 1) & ⋮ & 0 & h (k) & \dots & \dots & h (0) \end{matrix}]$

(B.2)

where each row is a circular shift of the row above and the first row is a circular shift of the last row. The primary difference between the matrices H and H^c is in the elements added in the upper right and lower left corners to produce the cyclic structure in the rows. If S is large and the number of non-zero elements on the main diagonals compared to the number of zero elements is small (i.e., ...

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.

Read now

Unlock full access

More than 5,000 organizations count on O’Reilly

O’Reilly covers everything we've got, with content to help us build a world-class technology community, upgrade the capabilities and competencies of our teams, and improve overall team performance as well as their engagement.

Julian F.

Head of Cybersecurity

I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.

Addison B.

Field Engineer

I’ve been on the O’Reilly platform for more than eight years. I use a couple of learning platforms, but I'm on O'Reilly more than anybody else. When you're there, you start learning. I'm never disappointed.

Amir M.

Data Platform Tech Lead

I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.

Mark W.

Embedded Software Engineer

Publisher Resources

ISBN: 9781466557970

Cloud Computing

Data Engineering

Data Science

AI & ML

Programming Languages

Software Architecture

IT/Ops

Security

Design

Business

Soft Skills

Image Super-Resolution and Applications

by Fathi Abd El-Samie, Mohiy M. Hadhoud, Said E. El-Khamy

Appendix B: Toeplitz-to-Circulant Approximations

B.1 Toeplitz-to-Circulant Approximation

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.