Scalable Bayesian uncertainty quantification with data-driven priors for
  radio interferometric imaging
Tobías I. Liaudat Matthijs Mars Matthew A. Price Marcelo Pereyra Marta M. Betcke Jason D. McEwen
Next-generation radio interferometers like the Square Kilometer Array have
the potential to unlock scientific discoveries thanks to their unprecedented
angular resolution and sensitivity. One key to unlocking their potential
resides in handling the deluge and complexity of incoming data. This challenge
requires building radio interferometric imaging methods that can cope with the
massive data sizes and provide high-quality image reconstructions with
uncertainty quantification (UQ). This work proposes a method coined QuantifAI
to address UQ in radio-interferometric imaging with data-driven (learned)
priors for high-dimensional settings. Our model, rooted in the Bayesian
framework, uses a physically motivated model for the likelihood. The model
exploits a data-driven convex prior, which can encode complex information
learned implicitly from simulations and guarantee the log-concavity of the
posterior. We leverage probability concentration phenomena of high-dimensional
log-concave posteriors that let us obtain information about the posterior,
avoiding MCMC sampling techniques. We rely on convex optimisation methods to
compute the MAP estimation, which is known to be faster and better scale with
dimension than MCMC sampling strategies. Our method allows us to compute local
credible intervals, i.e., Bayesian error bars, and perform hypothesis testing
of structure on the reconstructed image. In addition, we propose a novel
blazing-fast method to compute pixel-wise uncertainties at different scales. We
demonstrate our method by reconstructing radio-interferometric images in a
simulated setting and carrying out fast and scalable UQ, which we validate with
MCMC sampling. Our method shows an improved image quality and more meaningful
uncertainties than the benchmark method based on a sparsity-promoting prior.
QuantifAI's source code: https://github.com/astro-informatics/QuantifAI.