Title: Estimation below the detection limit with application to cryo-EM

Cryo-electron microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology. In a cryo-EM experiment, tomographic projections of a molecule, taken at unknown viewing directions, are embedded in highly noisy images at unknown locations. These images are called micrographs. All current analysis pipelines first locate these projections (detection) and then reconstruct the 3-D structure from them. However, when low SNR levels hinder detection, standard techniques fail. Cryo-EM is a notable case of a statistical estimation problem with nuisance variables (e.g., locations and viewing directions of all projections) in a low SNR environment. In this talk, I will suggest the method of moments as an alternative to likelihood-based approaches commonly used for such problems. I will start by introducing a simplified mathematical model for cryo-EM. In this model, several unknown images appear multiple times at unknown locations in noisy micrographs. I will demonstrate how the method of moments allows estimating directly the sought images in any SNR level, without intermediate detection, provided that sufficiently many micrographs are recorded. Then, I will claim that the same principles carry through to cryo-EM and the 3-D structure could, in principle, be reconstructed directly from the micrographs. This is especially important for small molecules, which can be particularly hard to detect. Finally, I will outline the challenges that lay ahead to turn this approach into a competitive alternative to state-of-the-art algorithms.