Detecting multiple unknown objects in noisy data is a key problem in many scientific fields, such as electron microscopy imaging. A common model for the unknown objects is the linear subspace model, which assumes that the objects can be expanded in some known basis (such as the Fourier basis). In this paper, we develop an object detection algorithm that under the linear subspace model is asymptotically guaranteed to detect all objects, while controlling the family wise error rate or the false discovery rate. Numerical simulations show that the algorithm also controls the error rate with high power in the non-asymptotic regime, even in highly challenging regimes. We apply the proposed algorithm to experimental electron microscopy data set, and show that it outperforms existing standard software.

翻译：在噪声数据中检测多个未知目标是许多科学领域（如电子显微镜成像）的关键问题。针对未知目标的常见模型是线性子空间模型，该模型假设目标可在某些已知基（如傅里叶基）下展开。本文提出了一种目标检测算法，该算法在线性子空间模型下能够渐近保证检测到所有目标，同时控制族系错误率或错误发现率。数值模拟表明，该算法即使在高度挑战性的非渐近条件下，也能以高统计功效控制错误率。我们将所提出的算法应用于实验电子显微镜数据集，并证明其性能优于现有标准软件。