Presents comprehensive and rigorous treatment of mathematical methods in imaging
The material is grouped around the central themes of Inverse Problems (Algorithmic Reconstruction), and Signal and Image Processing
The entries are cross-referenced for easy navigation through connected topics
Entries in the online edition include hyperlinked PDF and html format
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.
Introduction.- Linear and Inverse Problems.- (Nonlinear) Ill-Posed Problems.- Statistical Inverse Problems.- Thermacoustic Tomography.- Sampling Methods.- Expansion Methods.- EM Algorithms.- Large Scale Inverse Problems.- Special Topics in CT, Including Spiral.- Inverse Scattering.- Wave Phenomena.- Radar.- Ultrasound, Elasticity.- Imaging in Random Media.- Learning, Classification, Data Mining.- Partial Differential Equations: Images and Movies.- Filtering of M-Channel Data.- Numerical Methods for Variational Approach in Image Analysis.- Segmentation with Priors.- Image Registration.- Duality and Convex Minimization.- Total Variation in Imaging.- Statistical Data Analysis with Applications.- Manifold Intrinsic Similarity.- Neighborhood Filters.- Mumford-Shah, Phase Field Models.- Photoacoustic and Thermoacoustic.- Mathematical Tools for Visualization.-Regularization Methods for Ill-Posed Problems.- Iterative Solution Methods.- EIT.- Astronomy.- Multi-Modal Image Processing.- Compressed Sensing.- Shape Spaces.- Subject Index.