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Uncertainty quantification for radio interferometric imaging: II. MAP estimation

Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
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 maximum a 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. OurMAP-based methods are approximately 105 times faster computationally than state-of-theart 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.
Methods: data analysis, Methods: numerical, Methods: statistical, Techniques: image processing, Techniques: interferometric
0035-8711
4170-4182
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: II. MAP estimation. Monthly Notices of the Royal Astronomical Society, 480 (3), 4170-4182. (doi:10.1093/MNRAS/STY2015).

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. 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 maximum a 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. OurMAP-based methods are approximately 105 times faster computationally than state-of-theart 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.

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More information

Accepted/In Press date: 20 July 2018
e-pub ahead of print date: 2 August 2018
Published date: November 2018
Keywords: Methods: data analysis, Methods: numerical, Methods: statistical, Techniques: image processing, Techniques: interferometric

Identifiers

Local EPrints ID: 438774
URI: http://eprints.soton.ac.uk/id/eprint/438774
ISSN: 0035-8711
PURE UUID: 9e867fde-acca-4da0-be67-95c5ca3ae43e

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Date deposited: 24 Mar 2020 17:30
Last modified: 06 Oct 2020 22:08

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Contributors

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

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