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Wednesday, 22-03-2017

Research


Image Processing and Optimization for Quantitative Biomedicine

4D image processing, sparsity, learning methods, optimal control, microscopy

I am working together with Prof. Andrea Bertozzi, Prof. Stanley Osher and Prof. Martin Burger on several projects in inverse problems, 4D image processing, optimal transport and optimal control. I received my PhD in Germany in the Department of Mathematics at the University of Münster. Applications range from dynamic biomedical imaging (e.g. live fluorescence microscopy and tomography) to crime modeling and realtime atomic force microscopy.

Projects:

  • Sparse image reconstruction via learning and higher-order regularization

                                                                        

Alternative Scan Algorithms and Image Processing in High Speed Atomic Force Microscopy

 

Collaborators: Dr. Paul Ashby, Dr. Dominik Ziegler (Molecular Foundry, Berkeley National Lab), Prof. Andrea L. Bertozzi, Travis Meyer (Math, UCLA)

                                                                        

  • 4D imaging and flow estimation

  • Optimal control with PDEs and convex optimization

                                                                        

Sparse optimal control of chemotaxis

In this project we study sparse optimal control methods for predictive policing in crime modeling (social sciences). Underlying parabolic PDEs are aggregation equations related to chemotaxis and Keller-Segel type equations. Our control models could also be applied to chemotaxis in cell migration (biomedicine).

Collaborators: Prof. Andrea L. Bertozzi, Prof. Martin B. Short, Joseph R. Zipkin (Mathematics, UCLA) and Prof. Jeffrey Brantingham (Anthropology, UCLA)

Improved augmented Lagrangian and Bregman methods

In this project we study inexact (preconditioned) Uzawa methods, respectively augmented Lagrangian methods, for saddle point problems arising in convex constrained imaging problems.

Collaborators: Dr. Klaus Frick (Stochastics, Göttingen) and Prof. Martin Burger