1
Introduction

2 Examples of
applications

3
Mathematical modeling

4 Statistical
approaches in a discrete setting

5 Simple
reconstruction methods

6
Optimization methods

7 Numerics

8 Specific
topics in image deblurring

9 Towards a
regularization theory

A Appendix

Inverse Imaging with Poisson Data is an invaluable resource for graduate students, postdocs and researchers interested in the application of inverse problems to the domains of applied sciences, such as microscopy, medical imaging and astronomy. The purpose of the book is to provide a comprehensive account of the theoretical results, methods and algorithms related to the problem of image reconstruction from Poisson data within the framework of the maximum likelihood approach introduced by Shepp and Vardi. This is achieved by 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 that naturally arises from this modelling. Finally, a suitable variational formulation of this approach opens the door to all subsequent advancements and results.

Patrizia Boccacci received her advanced degree in physics from the University of Genova in Italy in 1980. She is currently an associate professor in the Department of Informatics, Bioengineering, Robotics and System Engineering at the University of Genova.

Valeria Ruggiero received her advanced degree in mathematics from the University of Ferrara in Italy in 1978. She is a professor in numerical analysis at the University of Ferrara and is the director of the National Group for Scientific Computation of the Istituto Nazionale di Alta Matematica (INdAM).