# Uncertainty quantification for radio interferometric imaging: II. MAP estimation

arXiv: https://arxiv.org/abs/1711.04819 · HTML: https://mlsanity.com/paper/1711.04819/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution](https://mlsanity.com/paper/2206.13894/) (2022)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling](https://mlsanity.com/paper/2308.09460/) (2023)
- [Learned Interferometric Imaging for the SPIDER Instrument](https://mlsanity.com/paper/2301.10260/) (2023)
- [Hypothesis Testing in Imaging Inverse Problems](https://mlsanity.com/paper/2505.22481/) (2025)

## Abstract (arXiv)

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 (SKA), 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 optimisation. 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. Our MAP-based methods are approximately 105 times faster computationally than state-of-the-art MCMC methods and, in addition, support highly distributed and parallelised 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.