Signal Processing/ECE Seminar: Estimation in multireference alignment and cryo-electron microscopy
Cryo-electron microscopy (cryo-EM) is a biological technique where we obtain noisy 2D projections of a molecule, at unknown viewing directions, from which we want to recover the 3D structure of the molecule, while in multi reference alignment, a signal is observed by the action of a random circular translation and the addition of Gaussian noise. In both these models, the observations result from a group action on the signal, corrupted with noise. The group actions can typically be determined in the high signal-to-noise ratio (SNR) regime, by "aligning" observations, but as the SNR approaches the low SNR regime, which is the prevalent regime in cryo-EM, methods based in alignment fail. In this regime, we show that methods which use features invariant under the group action are optimal. This follows from a relation between an information theoretic lower bound and the invariant features which appears in the low SNR regime.