PhD defence by Christian Schou Oxvig


22.06.2017 kl. 13.00 - 16.00


Algorithms for Reconstruction of Undersampled Atomic Force Microscopy images

An atomic force microscope is capable of measuring the topography of a surface on a nano meter scale by moving a cantilever with a tiny tip at its end across the surface. The flexibility in the choice of the scan pattern, that the cantilever follows, allows for undersampling of the surface, i.e. measuring only a part of the surface. In order to display an image of the entire surface, algorithms for reconstructing the missing parts are required. Such algorithms provide a description of the computations needed to estimate the topography of the entire surface being imaged. If the time it takes to do the computations is small compared to the time saved by only acquiring a part of the surface, a speed-up in the entire imaging process is achievable. An image acquisition speed-up may potentially enable applications such as surface “pre-viewing”, video-rate imaging, or super resolution imaging.

We describe and discuss algorithms for reconstructing undersampled atomic force microscopy images or other similar types of high dimensional signals. In particular, our contributions relate to the design of algorithms that not only exploit sparsity but structured sparsity. That is, algorithms that exploit the structure in prior information about an image to guide the reconstruction of the image. We show that such structure may be used to improve the estimate of the full topography surface compared to the estimate obtained by algorithms relying only on sparsity.

Since our proposed algorithms are primarily evaluated empirically through simulations, a major part of our work has been devoted to ensuring correctness and reproducibility of our computational results. Towards this end, we present our proposed methods for storing experiment metadata and applying best practices to obtain reproducible and correct computational results.

Assessment Committee
Associate Professor Zheng-Hua Tan, Aalborg University, Denmark (Chairman)
Senior Principal Research Scientist Petros T. Boufounos, Mitsubishi Electric Research laboratories, USA
Professor Lars Kai Hansen, Technical University of Denmark

Professor Torben Larsen, Aalborg University, Denmark
Associate Professor Thomas Arildsen, Aalborg University, Denmark

Associate Professor Lars Bo Larsen, Aalborg University, Denmark

After the defence there will be a reception at Fredrik Bajers Vej 7, B4-211


Free of charge


Signal and Information Processing, Department of Electronic Systems


Aalborg University, Fredrik Bajers Vej 7B 3-104