Detecting unknown objects in noisy data is a key task in many problems. A natural 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 talk, I will present an object detection algorithm that under the linear subspace model is asymptotically guaranteed to find all objects while making only a small percentage of false discoveries. We demonstrate our derivations for the problem of particle picking in cryo-electron microscopy.