CAM & DSI Joint Colloquium: Amit Singer

Single-Particle Electron Cryomicroscopy (cryo-EM) will soon become the leading technique for determining 3-D molecular structures at high resolution. In cryo-EM, the 3-D structure needs to be determined from many 2-D noisy tomographic projection images of the molecule taken at unknown viewing directions. The maximum likelihood approach has been very successful in determining large molecular structures, but struggles with small molecules for which the signal-to-noise (SNR) of the images is too low for accurate viewing direction estimation. Motivated by the challenge of reconstructing small molecules by cryo-EM, we have been investigating the method of moments as an alternative statistical and computational framework. In particular, the method of moments provides theoretical insight about the sample complexity, that is, the number of images required for reconstruction. No prior knowledge of cryo-EM or the method of moments is necessary for this talk.