Wavelet Analysis with Applications to Image Processing
Wavelet analysis is among the newest additions to the arsenals of mathematicians, scientists, and engineers, and offers common solutions to diverse problems. However, students and professionals in some areas of engineering and science, intimidated by the mathematical background necessary to explore this subject, have been unable to use this powerful tool.
The first book on the topic for readers with minimal mathematical backgrounds, Wavelet Analysis with Applications to Image Processing provides a thorough introduction to wavelets with applications in image processing. Unlike most other works on this subject, which are often collections of papers or research advances, this book offers students and researchers without an extensive math background a step-by-step introduction to the power of wavelet transforms and applications to image processing.
The first four chapters introduce the basic topics of analysis that are vital to understanding the mathematics of wavelet transforms. Subsequent chapters build on the information presented earlier to cover the major themes of wavelet analysis and its applications to image processing. This is an ideal introduction to the subject for students, and a valuable reference guide for professionals working in image processing.
Why Read This Book
You should read this book if you want a practical, gentle introduction to wavelets that emphasizes image processing applications rather than abstract functional analysis. You will get step-by-step explanations and examples that let you move quickly from concept to implementation on real image tasks.
Who Will Benefit
Practitioners and students in image and signal processing who want an applied, low-math-intensity introduction to wavelet methods for tasks such as denoising, compression, and feature extraction.
Level: Beginner — Prerequisites: Basic calculus and linear algebra, a familiarity with signals and systems or digital filtering, and comfort reading algorithmic pseudocode (MATLAB familiarity helpful but not required).
Key Takeaways
- Implement discrete and continuous wavelet transforms for 1D and 2D signals
- Apply multiresolution analysis to image denoising, enhancement, and compression
- Design and use filter-bank realizations of wavelet transforms for practical implementations
- Select and compare wavelet bases (orthogonal and biorthogonal) for image tasks
- Extract features and detect edges using wavelet-domain representations
Topics Covered
- 1. Introduction to Wavelets and Motivation
- 2. Mathematical Background (Basics of functions, orthogonality, and transforms)
- 3. Continuous Wavelet Transform (CWT) — intuition and applications
- 4. Discrete Wavelet Transform (DWT) and Multiresolution Analysis
- 5. Filter Bank Implementations and Fast Algorithms
- 6. Biorthogonal and Compactly Supported Wavelets
- 7. Two-Dimensional Wavelets and Separable Constructions
- 8. Image Denoising and Restoration Using Wavelets
- 9. Image Compression with Wavelets (principles and examples)
- 10. Feature Extraction and Edge Detection in the Wavelet Domain
- 11. Wavelet Packets and Adaptive Decompositions
- 12. Implementation Notes, Examples and Case Studies
- Appendices: Tables of wavelet filters and brief mathematical reminders
Languages, Platforms & Tools
How It Compares
More applied and accessible than Mallat's 'A Wavelet Tour of Signal Processing' and less mathematically rigorous than Daubechies' 'Ten Lectures on Wavelets', making Prasad better for practitioners seeking hands-on image applications.
