The inverse problems research at the Department of Applied Physics has strong ties with the Finnish Center of Excellence in Inverse Problems. The associated research consortium has been the leading group, among other topics, in the modelling of model uncertainties and especially the Bayesian approximation error approach, which provides computationally efficient implementations of inversion algorithms. In addition, the consortium is well known for the theory and applications of non-stationary inverse problems, that is, problems in which the unknown changes rapidly in time. The applications include various biomedical, industrial, geophysical and environmental problems.
Biomedical inverse problems
We develop computational methods and modelling for inverse problems in the field of medical imaging and biomedical research. The research topics include, for example, developing novel tomographic techniques and advancing computational methods for existing modalities.
- Optical Imaging of biological tissue utilising visible or near-infrared light
- Development of joint inversion methods for multimodality medical imaging
- Focused ultrasound therapy
- Development of EIT biomedical applications for classification of stroke
Industrial inverse problems
Industrial applications include various different opportunities for utilizing the advanced computational inverse problems techniques. The most prominent area of research includes development of diffuse tomographic imaging for industrial process and non-destructive testing. These imaging modalities can be used for example in monitoring of pipe flows or testing of concrete structures or designing and optimizing of process vessels.
- Tomography for imaging processes for example in chemical, pharmaceutical, oil, gas and mining industries
- Development of tools for non-destructive testing and structura health monitoring
- Designing and building of different types of diffuse tomographic imaging devices
- Thermal diffusion tomography for material characterization
Inverse problems in geophysics and atmospheric sciences
Our research on environmental applications covers geophysical and atmospheric inverse problems, and estimation of forest resources. We aim at solving grand challenges related to natural resources and climate change.
- Computational modelling of forward and inverse problems related to geophysics and hydrology
- Data analysis in aerosol physics and modeling of climate change
- Computational methods for remote sensing of forests
Theoretical studies on inverse problems
The research has several foci: computational models for observations, typically partial differential equations, modelling the underlying unknowns and uncertainties, and computing estimates for the inverse (parameter estimation) problems.