Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods
Uncertainty quantification for radio interferometric imaging - I. Proximal MCMC methods
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DOI：
10.1093/mnras/sty2004
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发表时间：
2018-11-01
影响因子：
4.8
通讯作者：
McEwen, Jason D.
中科院分区：
文献类型：
--
作者：
Cai, Xiaohao;Pereyra, Marcelo;McEwen, Jason D.
不确定度量化是射电干涉成像中一个关键的缺失部分，随着射电干涉大数据时代的到来，不确定度量化将变得越来越重要。由于射电干涉成像需要解决高维、不适定逆问题，因此不确定性量化是困难的，但对于射电观测的准确科学解释也是至关重要的。执行贝叶斯推理的统计抽样方法，如马尔可夫链蒙特卡罗（MCMC）抽样，原则上可以恢复图像的完整后验分布，然后可以从中量化不确定性。然而，传统的高维采样方法通常局限于光滑（如高斯）先验，不能与稀疏性提升先验一起使用。稀疏先验，由压缩感知理论激发，已被证明是非常有效的无线电干涉成像。在本文中，近端MCMC方法被开发用于无线电干涉成像，利用近端演算在贝叶斯框架中支持非微分先验，如稀疏先验。此外，提出了三种使用恢复后验分布来量化不确定性的策略：(i)局部（逐像素）可信区间为每个单个像素提供误差条；（ii）最高后验密度可信区域；（三）图像结构的假设检验。这些形式的不确定度量化以统计稳健的方式为分析无线电干涉观测提供了丰富的信息。
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. Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of radio observations. 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, traditional high-dimensional sampling methods are generally limited to smooth (e.g. Gaussian) priors and cannot be used with sparsity-promoting priors. Sparse priors, motivated by the theory of compressive sensing, have been shown to be highly effective for radio interferometric imaging. In this article proximal MCMC methods are developed for radio interferometric imaging, leveraging proximal calculus to support non-differential priors, such as sparse priors, in a Bayesian framework. Furthermore, three strategies to quantify uncertainties using the recovered posterior distribution are developed: (i) local (pixel-wise) credible intervals to provide error bars for each individual pixel; (ii) highest posterior density credible regions; 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.