Handbook of Mathematical Methods in Imaging / edited by Otmar Scherzer.

Format:

Book

Contributor:

Scherzer, Otmar., Editor.

Language:

English

Subjects (All):

Computer science--Mathematics.

Computer science.

Computer vision.

Signal processing.

Numerical analysis.

Radiology.

Mathematical Applications in Computer Science.

Computer Vision.

Signal, Speech and Image Processing .

Numerical Analysis.

Local Subjects:

Mathematical Applications in Computer Science.

Computer Vision.

Signal, Speech and Image Processing .

Numerical Analysis.

Radiology.

Physical Description:

1 online resource (472 illus., 200 illus. in color. eReference.)

Edition:

2nd ed. 2015.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2015.

Language Note:

English

Summary:

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. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. 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 200 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.

Contents:

Linear Inverse Problems

Large-Scale Inverse Problems in Imaging

Regularization Methods for Ill-Posed Problems

Distance Measures and Applications to Multi-Modal Variational Imaging

Energy Minimization Methods

Compressive Sensing

Duality and Convex Programming

EM Algorithms

Iterative Solution Methods

Level Set Methods for Structural Inversion and Image Reconstructions

Expansion Methods

Sampling Methods

Inverse Scattering

Electrical Impedance Tomography

Synthetic Aperture Radar Imaging

Tomography

Optical Imaging

Photoacoustic and Thermoacoustic Tomography: Image Formation Principles

Mathematics of Photoacoustic and Thermoacoustic Tomography

Wave Phenomena

Statistical Methods in Imaging

Supervised Learning by Support Vector Machines

Total Variation in Imaging

Numerical Methods and Applications in Total Variation Image Restoration

Mumford and Shah Model and its Applications in Total Variation Image Restoration

Local Smoothing Neighbourhood Filters

Neighbourhood Filters and the Recovery of 3D Information

Splines and Multiresolution Analysis

Gabor Analysis for Imaging

Shaper Spaces

Variational Methods in Shape Analysis

Manifold Intrinsic Similarity

Image Segmentation with Shape Priors: Explicit Versus Implicit Representations

Starlet Transform in Astronomical Data Processing

Differential Methods for Multi-Dimensional Visual Data Analysis

Wave fronts in Imaging, Quinto

Ultrasound Tomography, Natterer

Optical Flow, Schnoerr

Morphology, Petros

Maragos

PDEs, Weickert. - Registration, Modersitzki

Discrete Geometry in Imaging, Bobenko, Pottmann

Visualization, Hege

Fast Marching and Level Sets, Osher

Couple Physics Imaging, Arridge

Imaging in Random Media, Borcea

Conformal Methods, Gu

Texture, Peyre

Graph Cuts, Darbon

Imaging in Physics with Fourier Transform (i.e.Phase Retrieval e.g Dark field imaging), J. R. Fienup

Electron Microscopy, Öktem Ozan

Mathematical Imaging OCT (this is also FFT based), Mark E. Brezinski

Spect, PET, Faukas, Louis.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

1-4939-0790-5

OCLC:

912394909