Inverse problems with Poisson data: statistical regularization theory, applications and algorithms (Q2832965)

Inverse problems involving Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. There has been a substantial amount of work on the design and analysis of regularization methods for such problems. In this nice topical review, the authors present a comprehensive overview of statistical regularization theory for such problems, important applications and prominent algorithms. The focus is on variational regularization methods, i.e., penalized maximum likelihood estimators. The authors also discuss consistency results, and estimators based on wavelet-vaguelette decomposition of the forward operator. The applications covered in the paper include positron emission tomography, fluorescent microscopy, and phase retrieval. Several algorithms are also described and discussed.