Time-dependent Problems in Imaging and Parameter Identification
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Beschreibung
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.
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.
Time-dependent inverse problems: This is a current hot topic. A monograph or collection in this area is missing Challenging and important real-word applications: The book will comprise applications that cannot be addressed in the usual (classical) static inverse problems setting Mixture of theoretical and numerical aspects: The book will contain contributions on numerical methods for dynamic inverse problems as well as on theoretical aspects such as uniqueness theorems, tangential cone conditions or microlocal analysis
Autor*in
Barbara Kaltenbacher
Themen in »Time-dependent Problems in Imaging and Parameter Identification«
Dynamic inverse problem imaging parameter identification regularization methods dynamic tomography dynamic magnetic resonance evolution equations elasticity viscoelasticity magnetic particle imaging emission tomography motion compensation wave equation velocity estimation movement manipulation