Inverse problems


Inverse problems research concentrates on the mathematical theory and practical implementation of indirect measurements. Applications are found in numerous research fields involving scientific, medical or industrial imaging; familiar examples include X-ray computed tomography and ultrasound imaging. Inverse problems have a rich mathematical theory employing modern methods in partial differential equations, harmonic analysis, and differential geometry.

The inverse problems research group focuses on fundamental theoretical aspects of inverse problems such as the Calderón problem in electrical imaging and travel time tomography in seismic imaging. The group is part of the Finnish Centre of Excellence in Inverse Modelling and Imaging, is involved in activities of the Finnish Inverse Problems Society, and is supported by the European Research Council (ERC Starting/Consolidator Grants in 2012-2022).

Current events



Examples of research topics in the field are given on the research highlights webpage of the Centre of Excellence.

Recent publications

Recent publications of the group may be found on the TUTKA database and on the arXiv preprint server. The most up-to-date information is available on the members' personal web pages.

Selected publications
  • J. Ilmavirta: Coherent quantum tomography.
    SIAM Journal on Mathematical Analysis 48 (2016), no. 5, 3039–3064.
  • G. Paternain, M. Salo and G. Uhlmann: Spectral rigidity and invariant distributions on Anosov surfaces.
    Journal of Differential Geometry 98 (2014), no. 1, 147-181.
  • G. Paternain, M. Salo and G. Uhlmann: Tensor tomography on surfaces.
    Inventiones Mathematicae 193 (2013), no. 1, 229-247.
  • C. Kenig, M. Salo and G. Uhlmann: Inverse problems for the anisotropic Maxwell equations.
    Duke Mathematical Journal 157 (2011), no. 2, 369-419.
  • D. Dos Santos Ferreira, C. Kenig, M. Salo and G. Uhlmann: Limiting Carleman weights and anisotropic inverse problems. Inventiones Mathematicae 178 (2009), no. 1, p. 119-171.


The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme / ERC grant agreement no 307023.CoE_newlogo.jpgLOGO_ERC-FLAG_EU.jpg