C 9 - Inverse problems with Poisson data

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.


members of this project:

Prof. Thorsten Hohage
Benjamin Sprung

Associated members of this project:


Publications

Sprung, B. and Hohage, T. (2019)
Higher order convergence rates for Bregman iterated variational regularization of inverse problems Numer. Math., 4(1): 215-251, DOI:10.1007/s00211-018-0987-x

Hohage, T. and Frederic, W. (2017)
Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods
SIAM J. Numer. Anal., 2: 598-620, DOI:10.1137/16M1067445

Werner, F. (2015)
On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition
J. Inverse Ill-Posed Probl., DOI:10.1515/jiip-2013-0074

Hohage, T. and Werner, F. (2013)
Convergence Rates for Inverse Problems with Impulsive Noise
SIAM Journal on Numerical Analysisopen access,, 52(3): 1203-1221, DOI:10.1137/130932661

Hohage, T. and Werner, F. (2012)
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
Numer. Math.open access,, 123(4): 745-779, DOI:10.1007/s00211-012-0499-z

Werner, F. and Hohage, T. (2012)
Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data
Inverse Probl., 28(10): 104004, DOI:10.1088/0266-5611/28/10/104004