Upcoming astronomical surveys will produce petabytes of high-resolution images of the night sky, providing information about billions of stars and galaxies. Detecting and characterizing the astronomical objects in these images is a fundamental task in astronomy -- and a challenging one, as most of these objects are faint and many visually overlap with other objects. We propose an amortized variational inference procedure to solve this instance of small-object detection. Our key innovation is a family of spatially autoregressive variational distributions that partition and order the latent space according to a $K$-color checkerboard pattern. By construction, the conditional independencies of this variational family mirror those of the posterior distribution. We fit the variational distribution, which is parameterized by a convolutional neural network, using neural posterior estimation (NPE) to minimize an expectation of the forward KL divergence. Using images from the Sloan Digital Sky Survey, our method achieves state-of-the-art performance. We further demonstrate that the proposed autoregressive structure greatly improves posterior calibration.

翻译：即将开展的天文巡天项目将产生海量高分辨率夜空图像数据，其规模可达PB级别，为数十亿恒星与星系的研究提供信息支撑。在这些图像中检测并表征天体目标既是天文学的基础任务，也是极具挑战性的课题——绝大多数目标信号微弱，且视觉上常与其他目标相互重叠。本文提出一种摊销变分推断方法来解决此类小目标检测问题。我们的核心创新在于构建了一类空间自回归变分分布族，该分布族依据$K$色棋盘格模式对隐空间进行分区与排序。通过结构设计，该变分分布族的条件独立性关系与后验分布保持同构。我们采用卷积神经网络参数化变分分布，并运用神经后验估计技术，通过最小化前向KL散度的期望值对网络进行优化。基于斯隆数字巡天数据的实验表明，本方法达到了当前最优性能。我们进一步证明，所提出的自回归结构能显著提升后验分布的校准精度。