Inverse Imaging with Poisson Data. From cells to galaxies

The application of Poisson data inversions is important in both specific and very different domains of applied sciences, such as microscopy, medical imaging and astronomy. The purpose of the book is to provide a comprehensive account of theoretical results, methods and algorithms related to the problem of image reconstruction from Poisson data in the framework of the maximum likelihood approach introduced by Shepp and Vardi. This is achieved by first discussing the application domains where this approach is important and their mathematical modelling, including the statistical properties of the data. The authors introduce the maximum likelihood approach which naturally arises from this modelling. Finally, a suitable variational formulation of this approach opens the door to all subsequent advancements and results. The description of the methods proposed in the literature is organized into a few large classes, discussing first the methods for differentiable regularization and subsequently those, more complex, for non-differentiable regularization.