Monika Muszkieta

Topics of interest

Mathematical methods in image processing, inverse problems in imaging, applications of variational calculus, inverse problems in a 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):419–517, 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.

Dr Monika Muszkieta

Topics of interest

List of papers

Teaching in Summer Semester 2022/2023

Consultations