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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.
Inhaltsverzeichnis
Introduction.- Part 1: Inverse Problems.- Tomography.- MR DTI.- Hybrid Methods.- Nonlinear Inverse Problems.- EIT.- Scattering.- Sampling Methods.- Expansion Methods.- Regularization Methods for Ill-Posed Problems.- Iterative Solution Methods.- Wave Phenomena.- Seismic.- Radar.- Ultrasound.- Part 2: Signal and Image Processing.- Morphological Image Processing.- Learning, Classification, Data Mining.- Partial Differential Equations.- Variational Methods for Image Analysis.- Level Set Methods Including Fast Marching Methods.- Segmentation.- Registration, Optical Flow.- Duality and Convex Minimization.- Spline, Statistics.- Wavelets.- Fourier Analysis.- Compressed Sensing.- Geometry Processing.- Compression.- Computational Geometry.- Shape Spaces.- PDEs and Variational Methods on Manifold.- References.- Subject Index.
Zusammenfassung
Offering a comprehensive review of mathematical techniques used in imaging science, this handbook centers on two main themes: Inverse Problems and Signal and Image Processing. Coverage includes applications, mathematics, numerical methods and open questions.
Bericht
From the reviews:
"The book is divided into three volumes: methods, case examples and image restoration and analysis. ... The book succeeds in achieving a broad coverage of subjects, but is also very detailed in its coverage of individual topics. The book is also very well referenced. This book would thus form an excellent reference for both individual researchers and research groups working in this field." (Peter R. T. Munro, Contemporary Physics, Vol. 54 (1), 2013)
