Inconsistent Stochastic Feasibility: the Case of Stochastic Tomography

Russell Luke (U Göttingen)

Mar 18. 2021, 15:30 — 16:15

X-FEL pulses are shot with high repetition rates on a stream of identical single biomolecules and the scattered
photons are recorded on a pixelized detector. These experiments provide a new and unique route to
macromolecular structure determination at room temperature, without the need for crystallization,
and at low material usage.  The main challenges in these experiments are the extremely low signal to noise
ratio due to the very low expected photon count per scattering image (10-50) and the unknown orientation
of the molecules in each scattering image.  The general strategy, developed by Helmut Grubmueller, is to extract phase-less Fourier densities from the scattering images via correlation and Bayesian approaches developed by Helmut Grubmueller, and then to reconstruct the molecular structure via phase retrieval methods developed by Luke.


Mathematically, this is a stochastic computed tomography problem where the goal is to reconstruct a
three-dimensional object from noisy two-dimensional images of a nonlinear mapping whose orientation
relative to the object is both random and unobservable. Our approach is a two-step
procedure for solving this problem.  In the first step, we compute a probability distribution associated with
the observed patterns (taken together) as the stationary measure of a Markov chain whose generator is
constructed from the individual observations. Correlation in the data and priors are used to further constrain the problem and accelerate convergence to a stationary measure. In the next step, with the stationary measure in hand,
we compute an expected marginal distribution of the molecular structure at each rotation
relative to a fixed reference orientation.

The focus of this talk is on computing the stationary measure of the Markov operator.


Further Information
Erwin Schrödinger Institute - virtual
Associated Event:
Tomographic Reconstructions and their Startling Applications (Online Workshop)
Wolfgang Drexler (Med U Vienna)
Peter Elbau (U Vienna)
Ronny Ramlau (RICAM, Linz)
Monika Ritsch-Marte (Med Uni Innsbruck)
Otmar Scherzer (U Vienna)
Gerhard Schütz (TU Vienna)