Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods

摘要

Uncertainty quantification is a critical missing component in radiointerferometric imaging that will only become increasingly important as thebig-data era of radio interferometry emerges. Since radio interferometricimaging requires solving a high-dimensional, ill-posed inverse problem,uncertainty quantification is difficult but also critical to the accuratescientific interpretation of radio observations. Statistical samplingapproaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC)sampling, can in principle recover the full posterior distribution of theimage, from which uncertainties can then be quantified. However, traditionalhigh-dimensional sampling methods are generally limited to smooth (e.g.Gaussian) priors and cannot be used with sparsity-promoting priors. Sparsepriors, motivated by the theory of compressive sensing, have been shown to behighly effective for radio interferometric imaging. In this article proximalMCMC methods are developed for radio interferometric imaging, leveragingproximal calculus to support non-differential priors, such as sparse priors, ina Bayesian framework. Furthermore, three strategies to quantify uncertaintiesusing the recovered posterior distribution are developed: (i) local(pixel-wise) credible intervals to provide error bars for each individualpixel; (ii) highest posterior density credible regions; and (iii) hypothesistesting of image structure. These forms of uncertainty quantification providerich information for analysing radio interferometric observations in astatistically robust manner.