Handbook of Mathematical Methods in Imaging

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Table of Contents

Chapter 1. Linear Inverse Problems
Chapter 2. Large-Scale Inverse Problems in Imaging
Chapter 3. Regularization Methods for Ill-Posed Problems
Chapter 4. Distance Measures and Applications to Multi-Modal Variational Imaging
Chapter 5. Energy Minimization Methods
Chapter 6. Compressive Sensing
Chapter 7. Duality and Convex Programming
Chapter 8. EM Algorithms
Chapter 9. Iterative Solution Methods
Chapter 10. Level Set Methods for Structural Inversion and Image Reconstruction
Chapter 11. Expansion Methods
Chapter 12. Sampling Methods
Chapter 13. Inverse Scattering
Chapter 14. Electrical Impedance Tomography
Chapter 15. Synthetic Aperture Radar Imaging
Chapter 16. Tomography
Chapter 17. Optical Imaging
Chapter 18. Photoacoustic and Thermoacoustic Tomography: Image Formation Principles
Chapter 19. Mathematics of Photoacoustic and Thermoacoustic Tomography
Chapter 20. Wave Phenomena
Chapter 21. Statistical Methods in Imaging
Chapter 22. Supervised Learning by Support Vector Machines
Chapter 23. Total Variation in Imaging
Chapter 24. Numerical Methods and Applications in Total Variation Image Restoration
Chapter 25. Mumford and Shah Model and its Applications to Image Segmentation and Image Restoration
Chapter 26. Local Smoothing Neighborhood Filters
Chapter 27. Neighborhood Filters and the Recovery of 3D Information
Chapter 28. Splines and Multiresolution Analysis
Chapter 29. Gabor Analysis for Imaging
Chapter 30. Shape Spaces
Chapter 31. Variational Methods in Shape Analysis
Chapter 32. Manifold Intrinsic Similarity
Chapter 33. Image Segmentation with Shape Priors: Explicit Versus Implicit Representations
Chapter 34. Starlet Transform in Astronomical Data Processing
Chapter 35. Differential Methods for Multi-Dimensional Visual Data Analysis