Inverse problems with Poisson data (C09)

• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2011 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 28586557

This project is devoted to regularization theory and algorithms for inverse problems with Poisson distributed data. As typical for photonic imaging applications, data are described by a vector of independent Poisson distributed random variables, or in the continuous case by a Poisson point process. We aim to prove optimal rates of convergence as the expected number of detected photons tends to infinity in some relevant open cases. Moreover, we study new Newton-type regularization methods tailored Kullback-Leibler data fidelity terms. The inversion methods developed in this project will be used for the joint reconstruction of object and phase in isoSTED microscopy and phase retrieval problems in x-ray microscopy.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 755: Nanoscale Photonic Imaging
• Applicant Institution: Georg-August-Universität Göttingen
• Project Head: Professor Dr. Thorsten Hohage