Full Description
Inverse problems such as imaging or parameter identification deal with the recovery of unknown quantities from indirect observations, connected via a model describing the underlying context. While traditionally inverse problems are formulated and investigated in a static setting, we observe a significant increase of interest in time-dependence in a growing number of important applications over the last few years. Here, time-dependence affects a) the unknown function to be recovered and / or b) the observed data and / or c) the underlying process. Challenging applications in the field of imaging and parameter identification are techniques such as photoacoustic tomography, elastography, dynamic computerized or emission tomography, dynamic magnetic resonance imaging, super-resolution in image sequences and videos, health monitoring of elastic structures, optical flow problems or magnetic particle imaging to name only a few. Such problems demand for innovation concerning their mathematical description and analysis as well as computational approaches for their solution.
Contents
1. Joint phase reconstruction and magnitude segmentation from velocity-encoded MRI data.- 2. Dynamic Inverse Problems for the Acoustic Wave Equation.- 3. Motion compensation strategies in tomography.- 4. Microlocal properties of dynamic Fourier integral operators.- 5. The tangential cone condition for some coefficient identification model problems in parabolic PDEs.- 6. Sequential subspace optimization for recovering stored energy functions in hyperelastic materials from time-dependent data.- 7. Joint Motion Estimation and Source Identification using Convective Regularisation with an Application to the Analysis of Laser Nanoablations.- 8. Quantitative OCT reconstructions for dispersive media.- 9. Review of Image Similarity Measures for Joint Image Reconstruction from Multiple Measurements.- 10. Holmgren-John Unique Continuation Theorem for Viscoelastic Systems.- 11. Tomographic Reconstruction for Single Conjugate Adaptive Optics.- 12. Inverse Problems of Single Molecule Localization Microscopy.- 13. Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging.- 14. An inverse source problem related to acoustic nonlinearity parameter imaging.
