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Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods

Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods
Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods
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. Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of radio observations. Statistical sampling approaches to perform Bayesian inference, likeMarkov chainMonte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, traditional high-dimensional samplingmethods are generally limited to smooth (e.g. Gaussian) priors and cannot be used with sparsity-promoting priors. Sparse priors, motivated by the theory of compressive sensing, have been shown to be highly effective for radio interferometric imaging. In this article proximal MCMC methods are developed for radio interferometric imaging, leveraging proximal calculus to support non-differential priors, such as sparse priors, in a Bayesian framework. Furthermore, three strategies to quantify uncertainties using the recovered posterior distribution are developed: (i) local (pixel-wise) credible intervals to provide error bars for each individual pixel; (ii) highest posterior density credible regions; 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.
Methods: data analysis -methods: numerical -methods: statistical, Techniques: image processing, Techniques: interferometric
0035-8711
4154-4169
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175

Cai, Xiaohao, Pereyra, Marcelo and McEwen, Jason D. (2018) Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods. Monthly Notices of the Royal Astronomical Society, 480 (3), 4154-4169. (doi:10.1093/MNRAS/STY2004).

Record type: Article

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. Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of radio observations. Statistical sampling approaches to perform Bayesian inference, likeMarkov chainMonte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from which uncertainties can then be quantified. However, traditional high-dimensional samplingmethods are generally limited to smooth (e.g. Gaussian) priors and cannot be used with sparsity-promoting priors. Sparse priors, motivated by the theory of compressive sensing, have been shown to be highly effective for radio interferometric imaging. In this article proximal MCMC methods are developed for radio interferometric imaging, leveraging proximal calculus to support non-differential priors, such as sparse priors, in a Bayesian framework. Furthermore, three strategies to quantify uncertainties using the recovered posterior distribution are developed: (i) local (pixel-wise) credible intervals to provide error bars for each individual pixel; (ii) highest posterior density credible regions; 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.

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More information

Accepted/In Press date: 9 June 2018
e-pub ahead of print date: 27 July 2018
Published date: November 2018
Keywords: Methods: data analysis -methods: numerical -methods: statistical, Techniques: image processing, Techniques: interferometric

Identifiers

Local EPrints ID: 438773
URI: http://eprints.soton.ac.uk/id/eprint/438773
ISSN: 0035-8711
PURE UUID: 93602e98-b78d-44cb-a1d5-3c711d5811a7

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Date deposited: 24 Mar 2020 17:30
Last modified: 06 Oct 2020 19:25

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Contributors

Author: Xiaohao Cai
Author: Marcelo Pereyra
Author: Jason D. McEwen

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