Representation theoretic patterns in three dimensional Cryo-Electron Microscopy I - The intrinsic reconstitution algorithm

TL;DR

This paper provides a mathematical framework for cryo-electron microscopy, proving the correctness and stability of the intrinsic reconstitution algorithm and explaining numerical observations through representation theory.

Contribution

It offers a rigorous proof of the intrinsic reconstitution algorithm's correctness and stability, connecting numerical results to representation theoretic principles.

Findings

Proof of correctness of the intrinsic reconstitution algorithm

Numerical stability established for the algorithm

Explanation of numerical observations via representation theory

Abstract

In this paper, we describe and study a mathematical framework for cryo-elecron microscopy. The main result, is a a proof of the admissability (correctness) and the numerical stability of the intrinsic reconstitution algorithm which was introduced by Singer and Shkolnisky in [7]. In addition, we explain how the various numerical observations reported in that work, follow from basic representation theoretic principles.