About me
I obtained my Ph.D. degree in applied mathematics at Technical University in Kaiserslautern in 2007 under the supervision of Prof. H. Neunzert.
During my studies, I was working at Image Processing Department of Fraunhofer Institute for Industrial Mathematics.
Since the summer semester 2008, I am involved in a work on the new european program of master studies
Mathematics for Industry
at Wroclaw University of Science and Technology under patronage of ECMI.
Research
Area of my interest is in construction and analysis of mathematical models for image processing. The main focus of interest is on methods using partial differential equations
and calculus of variations. Currently, the following topics are investigated by me:
- topological asymptotic analysis of the Mumford-Shah functional
- derivation of a systematic approach to edge detection
- construction and analysis of computational methods to total variation-like flows
Topics of interest
Mathematical methods in image processing, inverse problems in imaging, topological asymptotic analysis, application of variational calculus, numerical analysis
List of papers
- "Discontinuity detection with higher order topological gradients", in preparation.
- Y. Giga, M. Muszkieta, P. Rybka, "A duality based approach to the minimizing total variation flow in the space H^{-s}", Japan Journal on Industrial and Applied Mathematics, 2018, accepted.
- E. Beretta, M. Muszkieta, W. Naetar, O. Scherzer, "A variational method for quantitative photoacoustic tomography with piecewise constant coeffcients", Radon Series on Computational and Applied Mathematics, vol. 18, Variational Methods, edited by M. Bergounioux, G. Peyré, Ch. Schnörr, J.-B. Caillau, T. Haberkorn, De Gruyter, Berlin/Boston, 2016.
- M. Muszkieta, "A variational approach to edge detection", Inverse Problems and Imaging, 2(10):419–517, 2016.
- P. B. Mucha, M. Muszkieta, P. Rybka, "Two cases of squares evolving by anisotropic diffusion", Advances in Differential Equations, 20(7-8):773-800, 2015.
- E. Beretta, M. Grasmair, M. Muszkieta, O. Scherzer, "A variational algorithm for the detection of line segments", Inverse Problems and Imaging, 8(2):389-408, 2014.
- M. Grasmair, M. Muszkieta, O. Scherzer, "An approach to the minimization of the Mumford-Shah functional using Γ-convergence and topological asymptotic expansion", Interfaces and Free Boundaries, 15(2):141-166, 2013.
- M. Muszkieta, "Optimal edge detection by topological asymptotic analysis", Math. Mod. Meth. Appl. Sci. 19(11):2127-2143, 2009.
- K. Burnecki, M. Muszkieta, G. Sikora, A. Weron "Statistical modelling of subdiffusive dynamics in the cytoplasm of living cells: A FARIMA approach", EPL 98, 10004, 2012.
- W. Tarnawski et al. "A robust algorithm for segmenting and tracking clustered cells in time-lapse fluorescent microscopy". IEEE J. Biomedical and Health Informatics, 2013.
Recent invited talks
- "The forward-backward scheme for the minimizing total variation flow in H^{-s}", Workshop "Advanced Developments for Surface and Interface Dynamics - Analysis and Computation"
Banff, Canada, The Banff International Research Station, 19.06.2018
- "A duality based approach to the minimizing total variation flow in the space H^{-s}", International conference "Towards Regularity", IM PAN Warszawa, 09.09.2016
- "The total variation flow in H^{-s}", Mini-symposium on "PDE and Real Analysis", University of Tokyo, 12.07.2016
- "Discontinuities detection using higher order topological gradients", Workshop "Inverse Problems in the Alps", Obergurgl University Center, Austria, 18.03.2016
- "A duality based approach to total variation flow in H^{-s}", Workshop "Anisotropy 2015", IM PAN Warszawa, 16.10.2015
- "Duality based approaches to total variation-like flows with applications to image processing", Seminar on Mathematics for various disciplines, University of Tokyo, 08.09.2015
Recent scientific visits
- Vienna University, 15-20.02.2015, (invited by O. Scherzer)
- Uniwersytet Warszawski, 03-05.02.2015, 10-11.05.2018 (invited by P. Rybka)
- Politecnico di Milano, 08-19.09.2014, (invited by E. Beretta)
- University of Tokyo, 18.06-16.07.2016, 30.08-26.09.2015, 02.03-14.03.2014, 06.06-09.07.2013 (invited by Y. Giga)