Cai, X;
Pereyra, M;
McEwen, JD;
(2018)
Uncertainty quantification for radio interferometric imaging: II. MAP estimation.
Monthly Notices of the Royal Astronomical Society
, 480
(3)
pp. 4170-4182.
10.1093/mnras/sty2015.
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Abstract
Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, for massive data sizes, like those anticipated from the Square Kilometre Array, it will be difficult if not impossible to apply any MCMC technique due to its inherent computational cost. We formulate Bayesian inference problems with sparsity-promoting priors (motivated by compressive sensing), for which we recover maximuma posteriori (MAP) point estimators of radio interferometric images by convex optimization. Exploiting recent developments in the theory of probability concentration, we quantify uncertainties by post-processing the recovered MAP estimate. Three strategies to quantify uncertainties are developed: (i) highest posterior density credible regions, (ii) local credible intervals (cf. error bars) for individual pixels and superpixels, and (iii) hypothesis testing of image structure. These forms of uncertainty quantification provide rich information for analysing radio interferometric observations in a statistically robust manner. Our MAP-based methods are approximately 105 times faster computationally than state-of-the-art MCMC methods and, in addition, support highly distributed and parallelized algorithmic structures. For the first time, our MAP-based techniques provide a means of quantifying uncertainties for radio interferometric imaging for realistic data volumes and practical use, and scale to the emerging big data era of radio astronomy.
| Type: | Article |
|---|---|
| Title: | Uncertainty quantification for radio interferometric imaging: II. MAP estimation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/mnras/sty2015 |
| Publisher version: | http://dx.doi.org/10.1093/mnras/sty2015 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | methods: data analysis, methods: numerical, methods: statistical, techniques: image processing, techniques: interferometric |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10077778 |
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