Extreme-scale precision Imaging in Radio Astronomy (EIRA)

射电天文学中的干涉孔径合成是一项强大的技术，它允许用天线阵列以其他难以达到的角度分辨率和灵敏度观测天空。然而，图像的形成是一个复杂的问题。无线电干涉测量提供了关于天空的不完全线性信息，定义了不适定逆成像问题。需要强大的计算成像算法将先验信息注入到数据中并恢复底层图像。从射电天文观测中设想的未来几十年的转型科学已经引发了新的巨型射电望远镜的发展，例如平方公里阵列（SKA），能够以更高的分辨率成像天空，比目前的仪器具有更高的灵敏度，在更宽的视野范围内。在这种情况下，宽带图像立方体将呈现丰富的结构，并达到1tb到1pb的大小，而相关的数据量将达到EB级。赋予SKA和探路者预期的敏锐视觉，需要能够转换数据并提供目标成像精度（即分辨率和动态范围）的图像形成算法，同时具有鲁棒性（即解决校准和不确定性量化挑战），并可扩展到极端的图像尺寸和数据量。该领域常用的成像算法被称为CLEAN，它的成功归功于它的简单性和计算速度。然而，CLEAN缺乏处理复杂信号模型的通用性，从而限制了形成图像的可实现分辨率和动态范围。对于需要校正影响数据的仪器和电离层效应的现有相关校准方法也是如此。无线电干涉成像的另一个主要限制是缺乏适当的方法来量化图像估计的不确定性。Wiaux和他的合作者进行了十年的开创性研究，表明优化理论是设计新的无线电干涉成像算法的一个强大而通用的框架。在优化框架中，目标函数被定义为数据保真度项和促进给定先验信号模型的正则化项的和。我们的研究假设是，目前出现在优化和深度学习界面的算法结构可以在宽带宽视场偏振环境下，为精确、稳健、可扩展的无线电干涉成像提供预期的算法生成挑战。在这种情况下，将开发一种新的方法，该方法基于将数据分解为块，并将图像立方体分解为小的、规则的、重叠的3D面。特定于面的正则化术语和特定于块的数据保真度术语都将通过所谓的近端分割优化方法并行处理，从而同时解锁图像和数据大小瓶颈。将先验信息注入到facet水平的逆成像问题中也有可能更好地促进局部空间光谱相关性，最终提供目标图像精度。首先考虑基于高级正则化的复杂先验模型，同时促进稀疏性，相关性和正性等，在第二阶段将被使用深度神经网络的学习先验所取代，目的是进一步提高精度和可扩展性。facet和神经网络将从成像模块渗透到鲁棒性的校准和不确定度量化。我们的算法将在高性能计算（HPC）机器上验证高达10TB的图像大小。将在医学成像方面进行1GB图像大小的技术转让，特别是3D磁共振和超声成像，以证明其更广泛的适用性。

Aperture synthesis by interferometry in radio astronomy is a powerful technique allowing observation of the sky with antennae arrays at otherwise inaccessible angular resolutions and sensitivities. Image formation is however a complicated problem. Radio-interferometric measurements provide incomplete linear information about the sky, defining an ill-posed inverse imaging problem. Powerful computational imaging algorithms are needed to inject prior information into the data and recover the underlying image.The transformational science envisaged from radio astronomical observations for the next decades has triggered the development of new gigantic radio telescopes, such as the Square Kilometre Array (SKA), capable of imaging the sky at much higher resolution, with much higher sensitivity than current instruments, over wide fields of view. In this context, wide-band image cubes will exhibit rich structure and reach sizes between 1 Terabyte (TB) and 1 Petabyte (PB), while associated data volumes will reach the Exabyte (EB) scale. Endowing SKA and pathfinders with their expected acute vision requires image formation algorithms capable to transform the data and provide the target imaging precision (i.e. resolution and dynamic range), while simultaneously being robust (i.e. addressing calibration and uncertainty quantification challenges), and scalable to the extreme image sizes and data volumes at stake.The commonly used imaging algorithm in the field, dubbed CLEAN, owes its success to its simplicity and computational speed. CLEAN however crucially lacks the versatility to handle complex signal models, thereby limiting the achievable resolution and dynamic range of the formed images. The same holds for the existing associated calibration methods that need to correct for instrumental and ionospheric effects affecting the data. Another major limitation in radio-interferometric imaging is the absence of a proper methodology to quantify the uncertainty around the image estimate.A decade of research pioneered by Wiaux and his collaborators suggests that the theory of optimisation is a powerful and versatile framework to design new radio-interferometric imaging algorithms. In the optimisation framework, an objective function is defined as sum of a data-fidelity term and a regularisation term promoting a given prior signal model. Our research hypothesis is that algorithmic structures currently emerging at the interface of optimisation and deep learning can take the challenge of delivering the expected generation of algorithms for precision robust scalable radio-interferometric imaging, in a wide-band wide-field polarisation context.A novel approach will be developed in this context, based on the decomposition of the data into blocks and of the image cube into small, regular, overlapping 3D facets. Facet-specific regularisation terms and block-specific data-fidelity terms will all be handled in parallel through so-called proximal splitting optimisation methods, thereby unlocking simultaneously the image and data size bottlenecks. Injecting prior information into the inverse imaging problem at facet level also offers potential to better promote local spatio-spectral correlation, and eventually provide the target image precision. Sophisticated prior models based on advanced regularisation simultaneously promoting sparsity, correlation, positivity etc., will firstly be considered, to be substituted by learned priors using deep neural networks in a second stage with the aim to further improve precision and scalability. Facets and neural networks will percolate from the imaging module to calibration and uncertainty quantification for robustness. Our algorithms will be validated up to 10TB image size on High Performance Computing (HPC) machines. A technology transfer at 1GB image size will be performed in medical imaging, specifically 3D magnetic resonance and ultrasound imaging, as proof of their wider applicability.