You are all cordially invited to the AMLab seminar on **Thursday June 20th** at **16:00** in **C3.163**, where **Karen Ullrich **will give a talk titled **“Differentiable probabilistic models of scientific imaging with the Fourier slice theorem”**. Afterwards there are the usual drinks and snacks!

**Abstract: **Scientific imaging techniques such as optical and
electron microscopy and computed tomography (CT) scanning are used to
study the 3D structure of an object through 2D observations. These
observations are related to the original 3D object through orthogonal
integral projections. For common 3D reconstruction algorithms,
computational efficiency requires the modeling of the 3D structures to
take place in Fourier space by applying the Fourier slice theorem. At
present, it is unclear how to differentiate through the projection
operator, and hence current learning algorithms can not rely on gradient
based methods to optimize 3D structure models. In this paper we show
how back-propagation through the projection operator in Fourier space
can be achieved. We demonstrate the validity of the approach with
experiments on 3D reconstruction of proteins. We further extend our
approach to learning probabilistic models of 3D objects. This allows us
to predict regions of low sampling rates or estimate noise. A higher
sample efficiency can be reached by utilizing the learned uncertainties
of the 3D structure as an unsupervised estimate of the model fit.
Finally, we demonstrate how the reconstruction algorithm can be extended
with an amortized inference scheme on unknown attributes such as object
pose. Through empirical studies we show that joint inference of the 3D
structure and the object pose becomes more difficult when the ground
truth object contains more symmetries. Due to the presence of for
instance (approximate) rotational symmetries, the pose estimation can
easily get stuck in local optima, inhibiting a fine-grained high-quality
estimate of the 3D structure.