Book description
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control.
Contents:
Part I
Secondorder decomposition model for image processing: numerical experimentation
Optimizing spatial and tonal data for PDEbased inpainting
Image registration using phase・amplitude separation
Rotation invariance in exemplarbased image inpainting
Convective regularization for optical flow
A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
On optical flow models for variational motion estimation
Bilevel approaches for learning of variational imaging models
Part II
Nondegenerate forms of the generalized Euler・Lagrange condition for stateconstrained optimal control problems
The Purcell threelink swimmer: some geometric and numerical aspects related to periodic optimal controls
Controllability of Keplerian motion with lowthrust control systems
Higher variational equation techniques for the integrability of homogeneous potentials
Introduction to KAM theory with a view to celestial mechanics
Invariants of contact subpseudoRiemannian structures and Einstein・Weyl geometry
Timeoptimal control for a perturbed Brockett integrator
Twist maps and Arnold diffusion for diffeomorphisms
A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I
Index
Table of contents
 Cover
 Title Page
 Copyright
 Contents

Part I
 Secondorder decomposition model for image processing: numerical experimentation
 Optimizing spatial and tonal data for PDEbased inpainting
 Image registration using phase–amplitude separation
 Rotation invariance in exemplarbased image inpainting
 Convective regularization for optical flow
 A variational method for quantitative photoacoustic tomography with piecewise constant coefficients
 A Special functions of bounded variation and the SBVcompactness theorem
 On optical flow models for variational motion estimation
 Bilevel approaches for learning of variational imaging models

Part II
 Nondegenerate forms of the generalized Euler–Lagrange condition for stateconstrained optimal control problems
 The Purcell threelink swimmer: some geometric and numerical aspects related to periodic optimal controls
 Controllability of Keplerian motion with lowthrust control systems
 Higher variational equation techniques for the integrability of homogeneous potentials

Introduction to KAM theory with a view to celestial mechanics
 13.1 Twisted conjugacy normal form
 13.2 One step of the Newton algorithm
 13.3 Inverse function theorem
 13.4 Local uniqueness and regularity of the normal form
 13.5 Conditional conjugacy
 13.6 Invariant torus with prescribed frequency
 13.7 Invariant tori with unprescribed frequencies
 13.8 Symmetries
 13.9 Lower dimensional tori
 13.10 Example in the spatial threebody problem
 A Isotropy of invariant tori
 B Two basic estimates
 C Interpolation of spaces of analytic functions
 Invariants of contact subpseudoRiemannian structures and Einstein–Weyl geometry
 Timeoptimal control for a perturbed Brockett integrator
 Twist maps and Arnold diffusion for diffeomorphisms
 A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I
 Index
Product information
 Title: Variational Methods
 Author(s):
 Release date: January 2017
 Publisher(s): De Gruyter
 ISBN: 9783110430493
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