PhD Candidates.

# PhD Candidates

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: B218b (Physicum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: tommi.heikkila 'at' helsinki.fi

#### Research Interests

My research interest is in dynamic tomography, more specifically in the underlying theory and computational methods which allow for the reconstruction of objects which are changing during the measurement process. The data from dynamic target is generally sparse to shorten the measurement time which makes for an ill-posed problem. My current research focuses on regularization methods which link consecutive measurements together in order to gain more information about the unknown target.

Dynamic tomography has a wide range of applications from medicine to material sciences. For example it can be used to observe the perfusion of nutrients in plant stems.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: A415 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: markus.juvonen@helsinki.fi

#### Research Interests

I am interested in image processing in general and anything that combines mathematics with photography and visualization.

The main focus of my research is the development of a patch-based image restoration approach that will create visually more realistic and natural reconstructions made locally out of real image data.

Another research topic is the automation of image restoration by learning the model and the optimal parameters from the given image data.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: A422 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

E-mail: antti.kujanpaa@helsinki.fi

#### Research Interests

Geometric Inverse Problems, Microlocal Analysis

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: B323 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: salla.latva-aijo 'at' helsinki.fi

#### Research Interests

I am interested in dynamic and spectral X-ray tomography and its applications. I focus on developing and improving iterative reconstruction algorithms, especially algorithms for extremely sparse and time-dependent data, like the modified level set method. Attenuation of materials is dependent of the energy of X-rays. This energy dependency makes it possible to get more information out from the reconstructed tomographic images with using multiple X-ray energies. My aim is to apply the Level Set method to material decomposition and extend the MLS method to work with two or more level set functions, both in terms of computational implementation and theoretical convergence.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: B414, Exactum

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

E-mail: jonatan.lehtonen@helsinki.fi

#### Research Interests

My primary interest is in applying mathematics to real-world problems, which naturally led me to the field of inverse problems. My PhD thesis focuses on atmospheric tomography, an inverse problem related to next-generation telescopes.

A well-known issue with ground-based telescope imaging is that atmospheric turbulence (fluctuations of the refractive index) perturbs the phase of incoming light waves, resulting in degraded resolution and blurred images. In atmospheric tomography, the basic idea is to reconstruct the turbulence profile in real time based on measurements of aberrations in the phase of incoming light waves from known light sources, e.g. natural stars or artificial laser stars. The turbulence profile can then be used to correct for the effect of turbulence on images in real time

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: A415 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: alexander.meaney 'at' helsinki.fi

#### Research Interests

I am interested in the mathematics and physics of medical imaging. My current research is focused on inverse problems and tomographic reconstruction algorithms in X-ray imaging. The range of my scientific activities varies from working with X-ray imaging hardware to computational mathematics and theoretical research.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: A329 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: siiri.rautio 'at' helsinki.fi

#### Research Interests

I am interested in applying deep learning to medical imaging, mainly to computed tomography. My research focuses on combining deep learning and analytical inverse problems methods in order to develop more interpretable deep learning algorithms with high-quality results. Currently, many deep learning methods can be described as a ‘black box’, which reduces their credibility from the viewpoint of an end user, eg. a doctor performing medical diagnosis. By basing the algorithm on well-studied, rigorous mathematical methods and releasing only a part of it to learning leads to the results being more reliable and interpretable.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: C315 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: anna.suomenrinne-nordvik 'at' helsinki.fi

#### Research Interests

My research interests are applications related to biological systems, especially infectious diseases. This includes mathematical modeling and data analysis to gain insight on issues such as the non-observable properties of diseases and disease prevention measures.

I am currently working on a multi-strain HPV model and inference on cervical cancer screening data. Screening data gives indirect measurements on the prevalence of HPV and on the progression of infections towards cancer within the body. There are only a handful of strains that cause cancer, and my focus is on correctly identifying those and their rate of progression.

#### Contact Information

Department of Mathematics and Statistics, University of Helsinki

Room: C435 (Exactum)

Address: P.O. Box 68 (Pietari Kalmin katu 5)

FI-00014 University of Helsinki

Email: Lauri.Ylinen 'at' helsinki.fi

#### Research Interests

I am interested in inverse problems for heat equation and fractional diffusion equations, and more generally in inverse problems in spectral geometry. I am also interested in dynamical systems modelling injection locking. I have also done work in inverse problems related to X-ray imaging.