Tomographic inverse problems remain a cornerstone of medical investigations, allowing the visualization of patients' interior features. While the infinite-dimensional operators modeling the measurement process (e.g., the Radon transform) are well understood, in practice one can only observe finitely many measurements and employ finitely many computations in reconstruction. Thus, proper...
In the standard photoacoustic tomography (PAT) measurement setup, the data used consist of time-dependent signals
measured on an observation surface. In contrast, the measurement data of the recently invented full-field detection
technique provides the solution of the wave equation in the spatial domain at a single point in time. While reconstruction
using classical PAT data has been...
Quantitative dynamic positron emission tomography (PET) attempts to reconstruct kinetic tissue parameters based on a time series of images showing the concentration of the PET tracer over time. The underlying problem is a nonlinear parameter identification problem which is based on an estimation of the arterial input function obtained by costly and time-consuming blood sample analysis. Our...
