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.

翻译：下一代射电干涉仪（如平方公里阵列）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新纪元。充分释放其潜力的关键在于处理海量且复杂的观测数据。这一挑战要求构建能够应对大规模数据、提供高质量图像重建并具备不确定性量化能力的射电干涉成像方法。本研究提出了一种名为QuantifAI的方法，旨在解决高维场景下采用数据驱动（学习型）先验的射电干涉成像中的不确定性量化问题。我们的模型植根于贝叶斯框架，对似然函数采用物理驱动的建模方式。该模型利用一种数据驱动的凸先验，能够编码从仿真数据中隐式学习的复杂信息，并保证后验分布的对数凹性。我们借助高维对数凹后验分布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。通过凸优化方法计算最大后验估计，其计算速度更快且维度扩展性优于MCMC采样策略。该方法能够计算局部可信区间（即贝叶斯误差带），并对重建图像中的结构进行假设检验。此外，我们提出了一种创新的极速算法，用于计算不同尺度下的像素级不确定性。通过在仿真场景中重建射电干涉图像并执行快速可扩展的不确定性量化（经MCMC采样验证），我们展示了该方法的有效性。与基于稀疏性先验的基准方法相比，我们的方法展现出更优的图像质量和更具意义的不确定性量化结果。QuantifAI源代码地址：https://github.com/astro-informatics/QuantifAI。