@book {IOPORT.06086522, author = {Werner, Frank}, title = {Inverse problems with Poisson data: Tikhonov-type regularization and iteratively regularized Newton methods.}, year = {2012}, pages = {127~p.}, publisher = {Uelvesb\"ull: Der Andere Verlag; G\"ottingen: Univ. G\"ottingen, Mathematisch-Naturwissenschaftliche Fakult\"aten (Diss.)}, abstract = {Summary: The pivotal challenge in photonic imaging consists in reconstructing an unknown object of interest from photon counts of a related photon density. Usually this leads to an inverse problem with Poisson data. This thesis deals with methods for the solution of such problems. We present an adequate framework for inverse problems with Poisson data, prove convergence rates in expectation under general classes of abstract smoothness assumptions on the unknown solution as the observation time tends to infinity and discuss three applications from photonic imaging. The performance of the proposed method is illustrated numerically and compared with standard methods.}, identifier = {06086522}, }