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NCTS Differential Geometry Seminar
16:00 - 17:00, November 2, 2017 (Thursday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Geometric Measure Theory and Data: The Role of Minimisers
Simon Morgan (Imperial College London)


Many data processing operations involve energy minimisation tasks. These energies balance the desire for high regularity of solutions with the desire for fidelity in closely representing the original data input.
For example de-noising and smoothing in signal and image processing, inverse problem image reconstruction in compressive sensing and medical imaging. Geometric measure theory helps establish existence and regularity properties of minimisers in these contexts. More advanced energy functionals, tailored to specific applications, can require more generalisable techniques. Additionally, we will show an optimal transport minimisation problem with a basis in geometric measure theory and applications to bio-medical data, and some related geometry research problems.


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