Topics of interest
Mathematical methods in image processing, inverse problems in imaging, variational methods, inverse problems in single particle tracking.
List of papers
- M. Muszkieta, J. Janczura, "A compressed sensing approach to interpolation of fractional Brownian trajectories for a single particle tracking experiment", Appl. Math. Comput., 446:127900, 2023.
- M. Muszkieta,"Automated image restoration and segmentation using Mumford-Shah-like regularization and topological asymptotic expansion", J. Math. Imaging Vision, 64:646–661, 2022.
- J. Janczura, K. Burnecki, M. Muszkieta, A. Stanislavsky, A. Weron, "Classification of random trajectories based on the fractional Lévy stable motion", Chaos, Solitons & Fractals, 154:111606, 2022.
- M. Muszkieta, J. Janczura, A. Weron, "Simulation and tracking of fractional particles motion. From microscopy video to statistical analysis. A Brownian bridge approach", Appl. Math. Comput., 396:125902, 2021.
- A. Aspri, E. Beretta, O. Scherzer, M. Muszkieta, "Asymptotic expansions for higher order elliptic equations with an application to quantitative photoacoustic tomography", SIAM J. Imag. Sci., 13(4):1781-1833, 2020.
- Y. Giga, M. Muszkieta, P. Rybka, "A duality based approach to the minimizing total variation flow in the space H^{-s}", Jpn J Ind Appl Math., 36(1), 261-286, 2019.
- 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 Probl. Imaging, 2(10):499–517, 2016.
- P. B. Mucha, M. Muszkieta, P. Rybka, "Two cases of squares evolving by anisotropic diffusion", Adv. Differ. 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 Probl. 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.
- 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.
- 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.
- M. Muszkieta, "Optimal edge detection by topological asymptotic analysis", Math. Mod. Meth. Appl. Sci. 19(11):2127-2143, 2009.
- M. Muszkieta, "Nonlinear diffusion filtering of images using the topological gradient approach to edges detection", PhD Thesis, 2007, Technische Universität Kaiserslautern.
Teaching in Summer Semester 2025/2026
Consultations
Thursdays, room A.3.25 C-19, time 13:00-15:00
Fridays, room A.3.25 C-19, time 13:00-15:00
Courses
Matematyka
Perturbation Methods