Benjamin Berkels (RWTH Aachen University)

Title: From variational exit wave reconstruction to deep unrolling
Abstract: We first revisit the so-called exit wave reconstruction problem in the variational setting. Here, exit wave reconstruction means to reconstruct the complex-valued electron wave in a transmission electron microscope (TEM) right before it passes the objective lens, i.e., the exit wave, from a series of real-valued TEM images acquired with varying focus. This is a non-linear inverse problem that is a variant of the well known phase retrieval problem. We will show existence of minimizers, discuss practical gradient based optimization algorithms and show results on real data. Moreover, we will show how a regularizer for this non-linear inverse problem can be learned from data in the form of the Total Deep Variation. 
In the second part of the talk, we will turn to deep algorithm unrolling, a general strategy that allows to re-interpret iterative algorithms as deep neural networks with a very special structure inherited from the algorithm that is unrolled. In particular, unrolling allows to introduce data-driven learning to the unrolled algorithm. To this end, we will discuss the proximal gradient algorithm, which is suitable for unrolling and also applicable to exit wave reconstruction.