使用数据驱动先验为射电干涉成像提供可扩展的贝叶斯不确定性量化
Scalable Bayesian uncertainty quantification with data-driven priors for radio interferometric imaging
AI总结：
提出基于贝叶斯框架和数据驱动凸先验的 QuantifAI 方法，通过凸优化与概率集中现象高效计算射电干涉成像的高质量重建与多尺度不确定性，避免了 MCMC 采样，显著提升了图像质量与不确定性量化的效率。
摘要：
诸如平方公里阵列（Square Kilometer Array）等下一代射电干涉仪，凭借其前所未有的角分辨率和灵敏度，有望开启科学发现的大门。释放其潜力的关键之一在于处理海量且复杂的输入数据。这一挑战要求构建能够应对海量数据规模，并提供高质量图像重建及不确定性量化（UQ）的射电干涉成像方法。本工作提出了一种名为 QuantifAI 的方法，旨在解决高维环境下使用数据驱动（学习）先验的射电干涉成像中的 UQ 问题。我们的模型根植于贝叶斯框架，采用基于物理动机的似然模型。该模型利用数据驱动的凸先验，能够编码从模拟中隐式学习到的复杂信息，并保证后验的对数凹性。我们利用高维对数凹后验的概率集中现象来获取后验信息，从而避免使用 MCMC 采样技术。我们依靠凸优化方法计算 MAP 估计，该方法比 MCMC 采样策略速度更快且在维度上具有更好的扩展性。我们的方法允许计算局部可信区间（即贝叶斯误差条），并对重建图像上的结构进行假设检验。此外，我们提出了一种新颖的极速方法来计算不同尺度上的逐像素不确定性。我们通过在模拟环境中重建射电干涉图像并执行快速且可扩展的 UQ 来演示该方法，并使用 MCMC 采样对其进行了验证。与基于稀疏促进先验的基准方法相比，我们的方法展现出更高的图像质量和更有意义的不确定性。QuantifAI 源代码：https://github.com/astro-informatics/QuantifAI。
英文摘要：
Next-generation radio interferometers like the Square Kilometer Array have the potential to unlock scientific discoveries thanks to their unprecedented angular resolution and sensitivity. One key to unlocking their potential resides in handling the deluge and complexity of incoming data. This challenge requires building radio interferometric imaging methods that can cope with the massive data sizes and provide high-quality image reconstructions with uncertainty quantification (UQ). This work proposes a method coined QuantifAI to address UQ in radio-interferometric imaging with data-driven (learned) priors for high-dimensional settings. Our model, rooted in the Bayesian framework, uses a physically motivated model for the likelihood. The model exploits a data-driven convex prior, which can encode complex information learned implicitly from simulations and guarantee the log-concavity of the posterior. We leverage probability concentration phenomena of high-dimensional log-concave posteriors that let us obtain information about the posterior, avoiding MCMC sampling techniques. We rely on convex optimisation methods to compute the MAP estimation, which is known to be faster and better scale with dimension than MCMC sampling strategies. Our method allows us to compute local credible intervals, i.e., Bayesian error bars, and perform hypothesis testing of structure on the reconstructed image. In addition, we propose a novel blazing-fast method to compute pixel-wise uncertainties at different scales. We demonstrate our method by reconstructing radio-interferometric images in a simulated setting and carrying out fast and scalable UQ, which we validate with MCMC sampling. Our method shows an improved image quality and more meaningful uncertainties than the benchmark method based on a sparsity-promoting prior. QuantifAI's source code: https://github.com/astro-informatics/QuantifAI.
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