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Handbook of Mathematical Methods in Imaging

  • Living reference work
  • © 2020

Overview

Editors:
  1. Otmar Scherzer

    1. Computational Science Center, University of Vienna, Vienna, Austria

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  • Comprehensive and rigorous treatment of mathematical methods in imaging Addresses theoretical and practical aspects
  • Entries in hyperlinked PDF and html format

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About this book

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 (27 entries)

  1. Compressive Sensing

    • Massimo Fornasier, Holger Rauhut

  2. Differential Methods for Multidimensional Visual Data Analysis

    • Werner Benger, René Heinzl, Dietmar Hildenbrand, Tino Weinkauf, Holger Theisel, David Tschumperlé

  3. Distance Measures and Applications to Multimodal Variational Imaging

    • Christiane Pöschl​, Otmar Scherzer

  4. Duality and Convex Programming

    • Jonathan M. Borwein, D. Russell Luke

  5. Electrical Impedance Tomography

    • Andy Adler, Romina Gaburro, William Lionheart

  6. EM Algorithms from a Non-stochastic Perspective

    • Charles Byrne

  7. Energy Minimization Methods

    • Mila Nikolova

  8. Imaging in Random Media

    • Liliana Borcea

  9. Iterative Solution Methods

    • Martin Burger, Barbara Kaltenbacher, Andreas Neubauer

  10. Large-Scale Inverse Problems in Imaging

    • Julianne Chung, Sarah Knepper, James G. Nagy

  11. Local Smoothing Neighborhood Filters

    • Jean-x Morel, Antoni Buades, Tomeu Coll

  12. Mathematical Methods in PET and SPECT Imaging

    • Athanasios S.Fokas, George A.Kastis

  13. Mathematical Modeling of Optical Coherence Tomography

    • Peter Elbau, Leonidas Mindrinos, Otmar Scherzer

  14. Microlocal Analysis in Tomography

    • Venkateswaran P. Krishnan, Eric Todd Quinto

  15. Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration

    • Leah Bar, Tony F. Chan, Ginmo Chung, Miyoun Jung, Nahum Kiryati, Nir Sochen et al.

  16. Neighborhood Filters and the Recovery of 3D Information

    • Julie Digne, Mariella Dimiccoli, Neus Sabater, Philippe Salembier

  17. Nonlinear Image Registration

    • Lars Ruthotto, Jan Modersitzki

  18. Numerical Methods and Applications in Total Variation Image Restoration

    • Raymond Chan, Tony F. Chan, Andy Yip

  19. Optical Flow

    • Florian Becker, Stefania Petrab, Christoph Schnörr

  20. Regularization Methods for Ill-Posed Problems

    • Jin Cheng, Bernd Hofmann
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Editors and Affiliations

  • Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

About the editor

Otmar Scherzer is a professor at the University of Austria.

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