Handbook of Mathematical Methods in Imaging

By Otmar Scherzer. Handbook of Mathematical Methods in Imaging, 2015

421 citations recorded by the source corpus.

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, Oktem Ozan.- Mathematical Imaging OCT (this is also FFT based), Mark E. Brezinski.- Spect, PET, Faukas, Louis.

Subfields: Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6533403dbe4da92a9a16eedfec37ba2d31d75521

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Citations in the corpus

An introduction to continuous optimization for imaging (2016, background): “…smoother than during the first iterations, and some authors have succeeded in exploiting this ‘partial smoothness’ to show better (linear) convergence of the FB descent (Bredies and Lorenz 2008, Grasmair, Haltmeier and Scherzer 2011, Liang, Fadili and Peyré 2014, Tao, Boley and Zhang 2015).”
Using Non-invertible Data Transformations to Build Adversary-Resistant Deep Neural Networks (2016, methodology): “We then test our methods with cross model adversarial samples to show that we achieve our secondary design goal.”
The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing (2012, background): “O C ] 4 N ov 2 01 3 This paper deals with the computational complexity of conditions which guarantee that theNP-hard problem of finding the sparsest solution to an underdetermined linear system can be solved by efficient algorithms.”
Sparse stabilization and optimal control of the Cucker-Smale model (2013, background): “This theory is known in mathematical signal processing under the name of compressed sensing , see the seminal work [6] and [25], see also the review chapter [29].”
Using Non-invertible Data Transformations to Build Adversarial-Robust Neural Networks (2016, methodology): “We then test our methods with cross model adversarial samples to show that we achieve our secondary design goal.”
Model-Based Learning for Accelerated, Limited-View 3-D Photoacoustic Tomography (2017, methodology): “A common way to model the acoustic part of the signal generation is to consider the following initial value problem for the wave equation [8], [12], [35],”