Variational Methods

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

Second-order decomposition model for image processing: numerical experimentation

Optimizing spatial and tonal data for PDE-based inpainting

Image registration using phase·amplitude separation

Rotation invariance in exemplar-based 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

Non-degenerate forms of the generalized Euler·Lagrange condition for state-constrained optimal control problems

The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls

Controllability of Keplerian motion with low-thrust 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 sub-pseudo-Riemannian structures and Einstein·Weyl geometry

Time-optimal 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