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

Abstract

Uncertainty quantification is a critical missing component in radio\ninterferometric imaging that will only become increasingly important as the\nbig-data era of radio interferometry emerges. Since radio interferometric\nimaging requires solving a high-dimensional, ill-posed inverse problem,\nuncertainty quantification is difficult but also critical to the accurate\nscientific interpretation of radio observations. Statistical sampling\napproaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC)\nsampling, can in principle recover the full posterior distribution of the\nimage, from which uncertainties can then be quantified. However, traditional\nhigh-dimensional sampling methods are generally limited to smooth (e.g.\nGaussian) priors and cannot be used with sparsity-promoting priors. Sparse\npriors, motivated by the theory of compressive sensing, have been shown to be\nhighly effective for radio interferometric imaging. In this article proximal\nMCMC methods are developed for radio interferometric imaging, leveraging\nproximal calculus to support non-differential priors, such as sparse priors, in\na Bayesian framework. Furthermore, three strategies to quantify uncertainties\nusing the recovered posterior distribution are developed: (i) local\n(pixel-wise) credible intervals to provide error bars for each individual\npixel; (ii) highest posterior density credible regions; and (iii) hypothesis\ntesting of image structure. These forms of uncertainty quantification provide\nrich information for analysing radio interferometric observations in a\nstatistically robust manner.\n