Object detection under the linear subspace model with application to cryo-EM images

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.