Postdoc in Computational Harmonic Analysis in Imaging
The research group in imaging within the department of mathematics is offering a two-year postdoc position based on a grant from the applied mathematics programme at the Swedish Foundation for Strategic Research. The position is part of a larger medical imaging project where the overall goal is to develop theory and algorithms for image reconstruction applicable to x-ray based medical imaging with under-sampled and/or highly noisy data. Imaging modalities involved are 3D spiral/helical CT, 4D SPECT/CT and PET/CT, C-arm 3D-CT, and spectral CT. The project also includes applications to x-ray and electron microscopy phase contrast imaging. Overall clinical goals are to significantly reduce the total dose of x-rays and/or acquisition time while maintaining a clinically useful image quality, alternatively to significantly improve image quality given a fixed total dose/acquisition time.
Research associated with the position includes development of theory and algorithms for analytic or learned dictionaries and their usage in tomographic reconstruction. For analytic dictionaries, the emphasis lies on constructing anisotropic representation systems, such as curvelets and shearlets, on bounded domains suitable for discretizing the wave front set. This also includes implementation of algorithms for computing these representations in the context of limited data 2D and 3D tomographic imaging problems. Research on trained dictionaries aims to integrate dictionary training with image reconstruction. A central topic is to perform dictionary training on indirect measurements, another is to efficiently handle larger dimensions and go beyond the small patches currently used in sparsity-based signal and image processing methods with trained dictionaries.
The research includes both theoretical development and implementation of numerical algorithms. The large-scale natures of the problems require algorithms that not only convergence fast but also have small memory footprint. Implementations of algorithms will be as software components integrated with ODL, a Python-based software framework for numerical functional analysis. Part of the research may include close collaboration with the medical technology companies Elekta and Philips, and with clinicians at Karolinska University Hospital in Stockholm.
There is a possibility to teach at 20% if the candidate wishes to do so.
We seek a candidate with a strong background in signal/image processing, computational harmonic analysis, and functional analysis. A PhD degree in mathematics, signal processing or computational physics that has been awarded (or planned to be awarded) before the commencement of the position is a requirement. Experience from sparse signal processing (compressive sensing) is highly beneficial. The candidate must also have experience from software development in scientific computing, preferably using Python and/or C/C++. Finally, a successful applicant must be strongly motivated, have the capability to work independently as well as in collaboration with members of the research group, and have good communication skills.