Today's high-resolution microscopes (sometimes called nanoscopes) provide an amazing insight into the nanostructure and dynamics of molecular systems. For example one can think of observing proteins that work at the single-molecule level, or whole cells with complex inner structure and dynamics.
Studying nanomaterial or biomedical samples together with biochemists or biophysicists often reveals interesting challenges in mathematical image processing. On the hand mathematical models can optimize the image acquisition process to obtain the "best" visual data. On the other hand image processing can allow for better analysis and understanding of chemical or biological properties in microscopy images.
The goal of this project is to study image processing techniques for the AFM (atomic force microscope) resp. the STM (scanning tunneling microscope). Both microscopes allow for incredibly high-resolution images (~0.1nm to aström).
The AFM belongs to the class of scanning probe microscopes where the information is gathered by "feeling" the surface with a cantilever and a tip. We will focus on combining non-raster scans and state of the art image inpainting techniques to achieve higher speed imaging of nanomaterial, desirably in real-time (video rate).
The STM (scanning tunneling microscope) is based on the concept of quantum tunneling. It is actually possible to image surfaces at the atomic level. Here we will focus on mathematical image analysis to get a quantitative understanding of the molecular structuring and orientation within the samples.
The outcome of this project will assist Paul Weiss' group (California NanoSystems Institute) and the group of Paul Ashby (Molecular Foundry, Berkeley National Lab) to better understand the dynamics and structure of nanomaterials.