Victor M Panaretos, Institute of Mathematics, Ecole Polytechnique Federale de Lausanne

Modular Statistical Inference in Single Particle Tomography

What can be said about an unknown density function on $\mathbb{R}^n$ given a finite collection of projections onto random and unknown hyperplanes? This question arises in single particle electron microscopy, a powerful method that biophysicists employ to learn about the structure of biological macromolecules. The method images unconstrained particles, as opposed to particles fixed on a lattice (crystallography) and poses a variety of problems. We formulate and study statistically the problem of determining a structural model for a biological particle given random projections of its Coulomb potential density, observed through the electron microscope. Although unidentifiable (ill-posed), this problem can be seen to be amenable to a consistent modular statistical solution once it is viewed through the prism of shape theory.