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


In this paper, we reveal the formal algebraic structure underlying the intrinsic reconstitution algorithm, introduced by Singer and Shkolnisky in [S], for determining three dimensional macromolecular structures from images obtained by an electron microscope. Inspecting this algebraic structure, we obtain a conceptual explanation for the admissibility (correctness) of the algorithm and a proof of its numerical stability. In addition, we explain how the various numerical observations reported in that work follow from basic representation theoretic principles.


Ronny Hadani

Department of Mathematics
The University of Texas at Austin
Austin, TX 78712

Amit Singer

Department of Mathematics and PACM
Princeton University
Princeton, NJ 08544