M9. Inverse Problems Under Poisson Noise

Poisson noise is a very common noise statistic in inverse problems, specifically when data is obtained by photon counting. Poisson noise arises in a wide range of applications, such as phase retrieval, computed tomography (CT), fluorescence microscopy, and astronomical imaging. Inverse problems with Poisson noise, such as the recovery of an image from a blurred and noisy version, requires a regularization to model the underlying image as well as a data fidelity term taking into account the Poisson noise statistics. Some popular regularizations for imaging applications include total variation (TV), fractional order TV (FOTV), wavelet thresholding, and low-rank models.

The data fidelity term for Poisson noise is well known to be the Kullback-Leibler divergence, which suffers from a nonlinearity, making it more complicated than the least-squares term for Gaussian noise. It can be avoided by applying a variance stabilizing transform that converts the Poissonian data into (approximately) Gaussian data, or by approximating the Poisson fidelity term by a weighted least-squares model. Otherwise, the nonlinearity causes difficulties in designing efficient algorithms and analyzing the convergence properties. Some optimization techniques used for Poisson noises include trust region algorithms, augmented Lagrangian methods, primal-dual majorization-minimization, and iteratively reweighted algorithms. In addition, recent advances in deep learning can be borrowed to deal with Poisson noise including neural networks, self-supervised denoising models, and dictionary learning.

In this minisymposium, we aim to bring together a wide range of experts in this field to share ideas and findings in theoretical, numerical, and practical aspects. Topics include real-data applications, algorithmic approaches, the usage of neural networks for image restoration, Bayesian approaches, as well as semi-blind and blind problems. Of interest will also be mixed noise models, which occur in many practical applications. The objective is to have a thorough understanding of the behaviours and properties of Poisson noises and to brainstorm in-depth discussions on the numerical methods to effectively remove Poisson noise.

Organizers:
Federico Benvenuto, University of Genoa, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Paolo Massa, University of Applied Sciences and Arts Northwestern Switzerland, Switzerland, This email address is being protected from spambots. You need JavaScript enabled to view it.

Invited Speakers:
Alessia Guidetti, Università di Genova, Italy, This email address is being protected from spambots. You need JavaScript enabled to view it.
Adaptive group-sparse regularization for Poisson linear inverse problems

Martin Klakow, University of Würzburg, Germany, This email address is being protected from spambots. You need JavaScript enabled to view it.
Regularized hypothesis testing for inverse problems with Poisson data

Daniele Pedemonte, Università di Genova, Italy. This email address is being protected from spambots. You need JavaScript enabled to view it.
Poisson-based risk estimation for hyperparameter optimization in regularized binary regression on DHEAL-COM datasets

Patricia Römer, Fraunhofer IMTE, GERMANY, This email address is being protected from spambots. You need JavaScript enabled to view it.
Recovery strategies for low-count Poisson phase retrieval