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Researcher: Matthias Ehrhardt

This project is concerned with the efficient reconstruction of positron emission tomography by means of stochastic optimisation. In the last decade, many mathematical tools have been developed that have the ability to enhance clinical imaging in various ways. On the forefront of this wave are non-smooth priors that allow the reconstruction of a smooth image but do not prohibit jumps across meaningful areas like organs in medical imaging. Beside this these new tools also allow the incorporation of a-prior structual knowledge about the solution at hand. However, most of this progress has not been translated into clinical practice as most modern algorithms are too demanding for the huge data sizes encountered. In the past, algorithms have been made "applicable" to clinical practices by only considering a subset if the data at a time. While for some models this leads to satisfactory results, in general this ad-hoc strategy may yield to spurious artefacts. Motivated by the success of similar techniques in machine learning, in this project we extend modern algorithms for imaging that can handle non-smooth priors in a rigorous way to the subset setting by means of "randomisation". While the algorithm and thus its iterates are random, the variances of these are low and converge quickly to the desired deterministic solution.


This project is part of one of our collaborative projects: PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation.

Related Publications 

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications
A Chambolle, MJ Ehrhardt, P Richtarik, CB Schonlieb – SIAM Journal on Optimization (2018) 28, 2783
Faster PET reconstruction with a stochastic primal-dual hybrid gradient method
MJ Ehrhardt, P Markiewicz, A Chambolle, P Richtárik, J Schott, CB Schönlieb – Proceedings of SPIE - The International Society for Optical Engineering (2017) 10394, 103941o
NiftyPET: a High-throughput Software Platform for High Quantitative Accuracy and Precision PET Imaging and Analysis.
PJ Markiewicz, MJ Ehrhardt, K Erlandsson, PJ Noonan, A Barnes, JM Schott, D Atkinson, SR Arridge, BF Hutton, S Ourselin – Neuroinformatics (2017) 16, 95
Faster PET reconstruction with non-smooth priors by randomization and preconditioning.
MJ Ehrhardt, P Markiewicz, C-B Schönlieb – Physics in Medicine and Biology (2019) 64, 225019