Jin, B;
Arridge, S;
Zhang, C;
(2019)
Expectation propagation for Poisson data.
Inverse Problems
, 35
(8)
, Article 085006. 10.1088/1361-6420/ab15a3.
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Abstract
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation for approximating the posterior distribution formed from the Poisson likelihood function and a Laplace type prior distribution, e.g. the anisotropic total variation prior. The approach iteratively yields a Gaussian approximation, and at each iteration, it updates the Gaussian approximation to one factor of the posterior distribution by moment matching. We derive explicit update formulas in terms of one-dimensional integrals, and also discuss stable and efficient quadrature rules for evaluating these integrals. The method is showcased on two-dimensional PET images.
| Type: | Article |
|---|---|
| Title: | Expectation propagation for Poisson data |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6420/ab15a3 |
| Publisher version: | https://doi.org/10.1088/1361-6420/ab15a3 |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence (http://creativecommons.org/licenses/by/3.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| Keywords: | Poisson distribution, Laplace prior, expectation propagation, approximate Bayesian inference |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10071145 |
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