2023

Biography

Zenith Purisha received the undergraduate and master degrees in Mathematics from Universitas Gadjah Mada, Indonesia, in 2008 and 2011, respectively. In 2018, she received Ph.D degree in Mathematics from University of Helsinki, Finland. She did a postdoctoral program from 2018 to 2020 in Department of Electrical Engineering and Automation (EEA), Aalto University, Finland. Currently, she is a lecturer in Mathematics Department, Faculty of Science at Universitas Gadjah Mada, Indonesia. She is a member of Computational Mathematics research group.

Her expertise is in the field of computational inverse problems with an application to tomographic reconstruction using real data.

Research interests

Zenith’s research is x-ray tomographic reconstruction using computational inversion methods from under-sampled data. Her initial research interest was tomographic inversion using NURBS (Non-Uniform Rational B-Splines) and Markov chain Monte Carlo (MCMC). Present focus is on iterative inversion methods using Gaussian processes and sparsity promoting regularization such as wavelet and shearlets. Her interest also includes dynamic x-ray tomography reconstruction using Kalman filter.

Students

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Publications:

1. Brücken, E., Bharthuar, S., Emzir, M., Golovleva, M., Gädda, A., Hostettler, R., Härkönen, J., Kirschenmann, S., Litichevskyi, V., Luukka, P. and Martikainen, L., Naaranoja, T., Nincă, I., Ott, J., Petrow, H., Purisha, P., Siiskonen, T., Särkkä, S., Tikkanen, J., Tuuva, T. and Winkler, A., 2020. Multispectral photon-counting for medical imaging and beam characterization. Journal of Instrumentation, 15(02), p.C02024.
2. Purisha, Z., Jidling, C., Wahlström, N., Schön, T.B. and Särkkä, S., 2019. Probabilistic approach to limited-data computed tomography reconstruction. Inverse Problems, 35(10), p.105004.
3. Leino, M.K., Ala-Laurinaho, J., Purisha, Z., Särkkä, S. and Viikari, V., 2019, May. Millimeter-wave imaging method based on frequency-diverse subarrays. In 2019 12th Global Symposium on Millimeter Waves (GSMM) (pp. 84-86). IEEE.
4. Hakkarainen, J., Purisha, Z., Solonen, A. and Siltanen, S., 2019. Undersampled dynamic X-ray tomography with dimension reduction Kalman filter. IEEE Transactions on Computational Imaging, 5(3), pp.492-501.
5. Purisha, Z., Karhula, S.S., Ketola, J.H., Rimpeläinen, J., Nieminen, M.T., Saarakkala, S., Kröger, H. and Siltanen, S., 2018. An automatic regularization method: An application for 3-D X-ray micro-CT reconstruction using sparse data. IEEE transactions on medical imaging, 38(2), pp.417-425.
6. Purisha, Z., Rimpeläinen, J., Bubba, T. and Siltanen, S., 2017. Controlled wavelet domain sparsity for x-ray tomography. Measurement Science and Technology, 29(1), p.014002.
7. Haario, H., Kallonen, A., Laine, M., Niemi, E., Purisha, Z. and Siltanen, S., 2017. Shape recovery for sparse‐data tomography. Mathematical Methods in the Applied Sciences, 40(18), pp.6649-6669.
8. Bubba, T.A., März, M., Purisha, Z., Lassas, M. and Siltanen, S., 2017, August. Shearlet-based regularization in sparse dynamic tomography. In Wavelets and Sparsity XVII (Vol. 10394, pp. 236-245). SPIE.
9. Purisha, Z. and Siltanen, S., 2016. Tomographic Inversion using NURBS and MCMC. In Forging Connections between Computational Mathematics and Computational Geometry (pp. 153-166). Springer, Cham.
10. Purisha, Z. and Siltanen, S., 2013, September. Tomographic reconstruction of homogeneous 2d geometric models with unknown attenuation. In IFIP Conference on System Modeling and Optimization (pp. 247-256). Springer, Berlin, Heidelberg.

Biography

Umi Mahnuna Hanung is a lecturer and researcher of Mathematics at Universitas Gadjah Mada (abbreviated as UGM) in Yogyakarta, Indonesia. She is a member of the Mathematical Analysis Group at the Department of Mathematics of UGM. Umi Mahnuna Hanung received her B.Sc. and M.Sc. in Mathematics from Universitas Brawijaya and Universitas Gadjah Mada directed by Professor M. Hasyim Baisoeni (with Dr. Noor Hidayat) and Professor Soeparna Darmawijaya, respectively. She has been pursuing a Ph.D. study in Mathematics at the University of Amsterdam, the Netherlands, and the Czech Academy of Sciences, the Czech Republic under the supervision of Professor Ale Jan Homburg, Professor Milan Tvrdy, and Professor Jan Wiegerinck. Umi Mahnuna Hanung has taught a variety of mathematics courses at Universitas Gadjah Mada, Universitas Islam Indonesia, and Universitas Islam Negeri Sunan Kalijaga, from first-year calculus to graduate-level classes in analysis. She has been a frequent presenter/talker at research conferences or seminars.

In the Department of Mathematics UGM, she joins the Mathematical Analysis Research Group and is also a member of a professional organization in Indonesia, namely the Indonesian Mathematical Society (IndoMS).

Research interests

Her interest in research is in Measure and Integral Theory, Differential Equations, and their Applications. Recently, she has pursued research on various kinds of the Stieltjes integral mainly using the gauge integration. The Stieltjes integrals have become more popular in differential equations, finite element method/numerical solutions, and other applications such as the approximation of the Fourier transform having implications in digital image processing, economic estimates, and acoustic phonetics, hysteresis, integral equations to game theory, financial market modeling, etc.

Students

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Selected Publications:

• U. M. Hanung, The Role of Harnack Extension in the Kurzweil-Stieltjes Sense: Integrating Functions over arbitrary Subsets, 2022, preprint. [https://arxiv.org/abs/2207.04426]
• U. M. Hanung and M. Tvrd´y, On the relationships between Stieltjes type integrals of Young, Dushnik and Kurzweil, Math. Bohem., 144 (4), pp.357–372, 2019. [http://dx.doi.org/10.21136/MB.2019.0015-19]
• G. A. Monteiro, U. M. Hanung and M. Tvrd´y, Bounded convergence theorem for abstract Kurzweil-Stieltjes integral, Monatshefte f¨ur Mathematik, 180 (3), pp.409–434, 2016. [https://doi.org/10.1007/s00605-015-0774-z]