Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
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DOI：
10.1093/mnras/sty2015
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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.
不确定性量化是无线电干涉成像中一个关键的缺失部分，随着无线电干涉测量的大数据时代的到来，它只会变得越来越重要。执行贝叶斯推断的统计采样方法，如马尔可夫链蒙特卡罗（MCMC）采样，原则上可以恢复图像的完整后验分布，然后可以量化不确定性。然而，对于大规模的数据大小，如平方公里阵列所预期的数据大小，由于其固有的计算成本，即使不是不可能应用任何MCMC技术，也将是困难的。我们制定贝叶斯推理问题与稀疏促进先验（动机压缩感知），我们恢复最大后验（MAP）点估计的无线电干涉图像的凸优化。利用概率集中理论的最新发展，我们通过后处理恢复MAP估计来量化不确定性。提出了三种量化不确定性的策略：（i）最高后验密度可信区域，（ii）局部可信区间（cf.误差条），以及（iii）图像结构的假设检验。这些形式的不确定性量化提供了丰富的信息，用于分析无线电干涉观测在统计上稳健的方式。我们基于MAP的方法在计算上比最先进的MCMC方法快大约10（5）倍，此外，还支持高度分布式和并行化的算法结构。我们基于MAP的技术首次为无线电干涉成像提供了一种量化不确定性的方法，以实现现实的数据量和实际用途，并可扩展到射电天文学的新兴大数据时代。
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, 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 optimization. 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 10(5) times faster computationally than state-of-theart MCMC methods and, in addition, support highly distributed and parallelized 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.