Exploring maximum likelihood and Bayesian approaches for two-dimensional image restoration: A machine learning perspective

K. Topolnicki, S. Sharma, Yu Volkotrub, M. Das,
Exploring maximum likelihood and Bayesian approaches for two-dimensional image restoration: A machine learning perspective,
Computer Physics Communications,
2025,
109913,
ISSN 0010-4655,
https://doi.org/10.1016/j.cpc.2025.109913.
(https://www.sciencedirect.com/science/article/pii/S001046552500414X)
Abstract: Different approaches to representing a two dimensional statistical distribution for likelihood optimization and Bayesian inference are investigated. The suggested methods can be generalized to more dimensions, opening up the possibility of using these representations for more complex problems. We use the PyTorch Machine Learning library and all calculations related to the investigated methods are easily expressible within this framework. The capabilities provided by modern Machine Learning libraries are utilized in order to be flexible and applicable to a wide range of problems. Our calculations were performed using a simple statistical toy model, similar in some aspects to techniques used in two dimensional medical imaging. We present numerical results for image reconstruction based on sparse data consisting of only 1000 registered data points and on a larger sample of 80000 data points.
Keywords: machine learning; bayesian inference; image restoration; positron emission tomography