Sparse Image and Signal Processing: Wavelets and Related Geometric Multiscale Analysis, Second Edition
This thoroughly updated new edition presents state of the art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB® and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.
Why Read This Book
You will get a modern, application-driven treatment of sparse and multiscale image and signal processing that links solid mathematical foundations with practical algorithms for real data. You will learn how geometric multiscale transforms (wavelets, ridgelets, curvelets), sparse decompositions, and contemporary inverse‑problem methods (in‑painting, compressed sensing, dictionary learning) are used in imaging, remote sensing, and astronomy.
Who Will Benefit
Graduate students, research engineers, and practitioners in signal and image processing who need a unified, up‑to‑date reference on multiscale geometric transforms and sparse methods for inverse problems and applications.
Level: Advanced — Prerequisites: Comfort with linear algebra, Fourier analysis, basic probability/statistics, and introductory signal processing; familiarity with numerical optimization and MATLAB or Python will help.
Key Takeaways
- Understand the theory and construction of linear multiscale geometric transforms (wavelets, ridgelets, curvelets) and nonlinear multiscale operators.
- Apply sparse signal decomposition and regularization techniques to inverse problems such as denoising, deconvolution, and in‑painting.
- Design and implement compressed sensing recovery and practical dictionary learning/nonnegative matrix factorization for imaging data.
- Use multiscale transforms for specialized data types, including 3D data cubes and data on the sphere (geo‑located datasets).
- Evaluate and choose computational strategies and software for large‑scale multiscale/sparse processing (FFT, fast transform implementations, and optimizers).
Topics Covered
- 1. Introduction to Sparse and Multiscale Signal Processing
- 2. Fundamentals of Wavelets and Multiresolution Analysis
- 3. Ridgelets, Curvelets, and Geometric Multiscale Transforms
- 4. Nonlinear Multiscale Operators: Median and Mathematical Morphology
- 5. Fast Algorithms and Computational Considerations
- 6. Sparse Decompositions, Thresholding, and Regularization
- 7. Inverse Problems: Denoising, Deconvolution, and In‑painting
- 8. Compressed Sensing and Sparse Recovery Techniques
- 9. Dictionary Learning and Sparse Coding; Nonnegative Matrix Factorization
- 10. Blind Source Separation and Multiscale Component Analysis
- 11. Multiscale Analysis for 3D Data and Data Cubes
- 12. Multiscale Transforms on the Sphere and Geo‑located Data
- 13. Applications: Astronomy, Remote Sensing, Medical Imaging, and Audio
- 14. Software, Implementation Notes, and Practical Examples
Languages, Platforms & Tools
How It Compares
Compared with Mallat's 'A Wavelet Tour of Signal Processing', this book places more emphasis on sparse geometric transforms and contemporary inverse‑problem applications (compressed sensing, dictionary learning) and adds extensive coverage of 3D and spherical data; for sparse representation foundations it complements Elad's 'Sparse and Redundant Representations'.
