Joint Exit Wave Reconstruction and Nonrigid, Multimodal Registration of Transmission Electron Microscopy Image Series


Images taken with a Transmission Electron Microscope (TEM) have two main restrictions: they are distorted by a multitude of aberrations from the objective lens and correspond directly to the electron wave's amplitude, therefore lacking information about the phase. One widely used approach to avoid these restrictions is to post-process a series of TEM images typically taken with varying focus of the objective lens (focus series). This yields a reconstruction of the electron wave at the exit plane of the specimen, which is free from aberrations. Due to TEM instabilities and specimen drift, a registration of the images is performed in addition to the reconstruction of the exit wave.

The aim of this project is to incorporate both the exit wave reconstruction and the image registration into a single functional. Consequently a minimizer of this functional will yield a good approximation to the exit wave as well as the registration of the images. This avoids the limitations of existing methods for exit wave reconstruction, all of which solve the reconstruction problem separately from the registration problem. The basis for this work is the Maximum-Likelihood (MAL) functional, which is the core of the state-of-the-art non-linear approach for exit wave reconstruction described in [1]. Since the reconstruction of the exit wave by means of solving an energy minimization problem is necessarily an indirect approach, the relationship between the calculated and the real exit wave is unknown. The joint reconstruction and registration will improve the mathematical properties of the algorithm and allow for a mathematical analysis of the existence and possibly also the local uniqueness of minimizers, whereas current methods for exit wave reconstruction have only been validated by experiment. A further investigation of possible choices for regularizers for the exit wave will help in tailoring the analytical properties of the functional to give more reliable results. Additionally, the registration will be performed using piecewise rigid transformations, which can improve the registration quality for specimen that consist of several independently moving particles significantly. This is a generalization of existing methods for exit wave reconstruction, which only use rigid registration schemes.

The energy minimization algorithm for the functional will be implemented using the Quocmesh software library [2] and tested with synthetic and real data. The results will be verified in collaboration with national and international experts working on focal series exit wave reconstruction.

[1] W.M.J. Coene, A. Thust, M. Op de Beeck, D. Van Dyck. Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy. \textit{Ultramicroscopy}, 64:109-135, 1996.

[2] AG Rumpf, Institute for Numerical Simulation, University of Bonn. Quocmesh software library.