Students currently completing their PhDs in the inverse problems group.

Department of Mathematics and Statistics, University of Helsinki

Room: B421 (Exactum)

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

Email: andreas.hauptmann@helsinki.fi

As an applied mathematician with a focus on computational mathematics I am interested in inverse problems with real measurement data, in particular applications to medical imaging.

In my PhD thesis I investigate the problem of partial boundary data in electrical impedance tomography, a highly non-linear inverse problem that needs careful analysis of the underlying mathematics. My study is motivated by a computational point of view and seeks to recover the unknown conductivity from this incomplete data.

Furthermore, I am interested in dynamic imaging and regularization strategies. That is given a set of measurements at several time instances, we seek to compute a reconstruction that uses all time dependent information. These problems arise for instance in X-ray computed tomography of a moving object.

Department of Mathematics and Statistics, University of Helsinki

Room: B424 (Exactum)

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

Telephone: +358-9-191

Department of Mathematics and Statistics, University of Helsinki

Room: B407 (Exactum)

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

Telephone:

Email: zenith.purisha 'at' helsinki.fi

Sparse X-ray tomography problem is the main focus of my research. A new algorithm and some new implementations to get good reconstruction from the data has been implemented. Real data produced by CT/μCT machine are tested. B-spline and Markov Chain Monte Carlo (NURBS-MCMC) strategy is implemented successfully and the result is in a CAD-format.

Another project that I am now also working is in applying the state-or-arts and modern methods, e.g Barzilai Borwein, Chambolle Pock, & Shearlet for studying bone analysis whether the bone is healthy or osteoarthritis.

Department of Mathematics and Statistics, University of Helsinki

Room: A414 (Exactum)

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

Email: teemu.saksala(at)helsinki.fi

I'm interested in inverse problems on manifolds. In my Phd Thesis I study certain geometric inverse problems related to geophysical prospecting. The rough idea is that earthquakes produce seismic waves that propagate through the Earth and can be measured on different locations on the surface of Earht with instruments called geophones. Therefore it possible to measure travel time differences of seismic waves. Doing this kind of measurements, we can find indirect information about the inner structure of Earth.

Mathematically speaking we study an inverse problem of a wave equation on Riemannian manifold with Dirichlet or Neumann boundary values. The goal is to reconstruct the unknown wave speed in the interior of the manifold or equivalently the Riemannian metric tensor. That is a mathematical consept that corresponds to the material parameters of the soil and in this way tells us about the structure of Earth.

At the moment I work with my advisor Matti Lassas, Hangming Zhou, Tapio Helin and Lauri Oksanen. I'm planing to defend my thesis at the fall of 2017.

Department of Mathematics and Statistics, University of Helsinki

Room: B414, Exactum

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

E-mail: jonatan.lehtonen@helsinki.fi

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

Department of Mathematics and Statistics, University of Helsinki

Room: A422 (Exactum)

Address: P.O. Box 68 (Gustaf Hällströmin katu 2b)

FI-00014 University of Helsinki

E-mail: antti.kujanpaa@helsinki.fi

My research centers around inverse problems for the wave equation on Riemannian manifolds. The focus is on models of physical systems with moving medium such as a layer of gas or water. The main objective is to develop effective techniques for indirect determination of turbulence and flow of the fluid from scattering data of waves. Motivation for my research arises naturally from atmospheric imaging and radar technology.