Speaker
Description
We 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 focus series of real-valued TEM images. This is a non-linear inverse problem that is a variant of the well known phase retrieval problem. First, we discuss a classical variational approach to this setting. Here, existence of minimizers can be established in the functional space setting and numerical minimization is usually done with gradient descent based approaches. Applying the proximal gradient algorithm to a specific simplified version of this problem leads to an iterative algorithm well suited for deep unfolding. The latter is a technique that recasts iterative algorithms into neural networks and allows to introduce data-driven learning to a large class of classical iterative model-based approaches, creating new hybrid methods. By extending a proof technique Behboodi, Rauhut and Schnoor proposed for a similar unfolded network but with a linear forward operator to our non-linear forward operator, we can show a generalization error bound for the resulting network. A key ingredient for the extension to our non-linear setting is to ensure and exploit firmly non-expansiveness.
