Image recovery from rotational and translational invariants

TL;DR

This paper presents a method to reconstruct images from features invariant to rotation and translation, using autocorrelation analysis, with applications in cryo-electron microscopy for small biomolecules.

Contribution

It introduces a novel framework for image recovery from invariant features, advancing the mathematical understanding and computational techniques in cryo-EM reconstruction.

Findings

Successful image reconstruction from invariant features in synthetic experiments

Reconstruction demonstrated to be robust to noise

Progress towards structure determination of small biomolecules

Abstract

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.