Permanent Faculty
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Per Christian Hansen, Professor
Keywords: uncertainty quantification, inverse problems, matrix computation, regularization methods
Per Christian Hansen is a VILLUM Investogator and his research focuses on computational methods for the solution of large mathematical and engineering problems. His main research area concerns the numerical solution of inverse problems in, e.g., tomography and iamge deblurring. His work on numerical methods for regularization is internationally recognized. His h-index is 48 (March 2019) and he is a SIAM Fellow. Per Christian Hansen is professor of Scientific Computing at the Department of Informatics and Mathematical Modelling. He was awarded the Danish Dr. Techn. doctoral degree in 1996 from DTU in the area of numerical analysis. He has spent several research visits at American universities, such as Stanford University, UCLA, Emory University, and Tufts University. Per Christian Hansen teaches numerical algorithms and inverse problems. He has published 4 books on numerical methods and inverse problems and more than 100 scientific papers in international journals. read more
Yiqiu Dong, Associate ProfessorKeywords: numerical linear algebra, matrix computation, inverse problems, variational methods, regularization methods, mathematical image processing, tomography reconstruction, optimization
My main research topic is imaging related inverse problems. The main tool that I use is variational methods, i.e., combining Bayesian statistics and regularisation techniques to propose suitable minimisation problems that mathematically describe the inverse problems and its desired solutions. Then, I apply as well as develop advanced optimisation algorithms for solving the proposed minimisation problems. Recently I have also begun to introduce uncertainty quantification technique into inverse problems. read more
Kim Knudsen, Associate professorKeywords: Applied mathematical analysis, Inverse Problems, Partial Differential Equations, Functional Analysis, Medical Imaging, Tomography, Biomathematics, Mathematical Biology, Uncertainty Quantification, Scientific Computing
Kim Knudsen has a background in applied mathematical analysis, which concerns the mathematical modelling, analysis and numerical computations for real world physical phenomena. During the last 20 years he has contributed significantly to the reconstruction problem in Electrical Impedance Tomography by advancing the theory in the partial data problem and by developing and investigating so-called direct reconstruction methods in 2D and 3D. In recent years his interest has been devoted to the theoretical and computational understanding of Hybrid Data Tomography, e.g. Acousto-Electric Tomography and Magnetic Resonance Electrical Impedance Tomography. Besides his works on Inverse Problems, Kim Knudsen has worked on mathematical biology within aquatic sciences. read more
Mirza Karamehmedovic, Associate ProfessorKeywords: analysis, differential equations, partial differential equations, pseudodifferential boundary problems, inverse problems, inverse scattering, inverse source problems, Uncertainty Quantification
I use the theory of partial differential equations and of pseudodifferential operators to characterize general inverse scattering and inverse source problems in terms of solution regularity, as well as stability in the presence of noise. A 'byproduct' of the analysis are, for example, new results concerning the mapping properties of special classes of pseudodifferential operators. On the numerical side, I construct and apply numerical methods for the approximate solution of industrially relevant inverse scattering problems. Here, I have lately begun to include elements of PDE-based Uncertainty Quantification and rudimentary machine learning. Spectral and regularity analysis of solutions of boundary problems. Numerical solution of inverse problems for PDE. Uncertainty Quantification. read more
PhDs, Postdocs and Research Assistants
Coming soon.