Image recovery from rotational and translational invariants
This work addresses the challenge of structure determination for small biomolecules in cryo-EM, representing an incremental step in improving reconstruction methods.
The authors tackled the problem of reconstructing an image from its rotationally and translationally invariant features, demonstrating through synthetic experiments that reconstruction is possible and robust to noise, with results applicable to cryo-electron microscopy.
We introduce a framework for recovering an image from its rotationally and translationally invariant features based on autocorrelation analysis. This work is an instance of the multi-target detection statistical model, which is mainly used to study the mathematical and computational properties of single-particle reconstruction using cryo-electron microscopy (cryo-EM) at low signal-to-noise ratios. We demonstrate with synthetic numerical experiments that an image can be reconstructed from rotationally and translationally invariant features and show that the reconstruction is robust to noise. These results constitute an important step towards the goal of structure determination of small biomolecules using cryo-EM.