The methodological research of the LUT team has focused on approximative assimilation methods for high dimensional systems, both using dimension reduction methods and developing low-memory algorithms.  The applications include, in addition to weather forecasting,  satellite observations of the environment, forests and water systems, as well as remote tracking of flying objects. A recent direction is to develop rigorous statistical methods to quantify the variability and parameters of chaotic dynamical systems.

The research team of Professor Jari Kaipio focuses on the modelling of uncertainties in the underlying computational models, and how to recover from these. Examples include uncertain geometry of domains, unknown boundary conditions and auxiliary distributed parameters. The approaches that we use can be categorized as approximate Bayesian computation and, in particular, we employ the Bayesian approximation error approach. The current applications are related to geophysics, hydrology, biomedical engineering/physics, random fields, wave propagation, and scattering. The team consist of two senior researchers, Jari Kaipio and Timo Lähivaara, and several postdoctoral researchers and PhD students.

The group works in close collaboration with the inverse problems researchers in the Departments of Mathematics and Engineering Science of the University of Auckland.

Mikko Salo leads a research team that focuses on fundamental aspects of the mathematical theory of inverse problems. Topics of particular interest include inverse boundary value problems, such as the Calderón problem related to electrical imaging and the Gel'fand problem related to seismic imaging. The team also studies geometric inverse problems such as travel time tomography and the geodesic X-ray transform, with applications to imaging the Earth and other planets. The team is also supported by an ERC Consolidator Grant.

Associate Professor Aku Seppänen leads a research team, which develops and applies computational and statistical methods for solving inverse problems arising from (physical) science and engineering. The main applications are: 1) environmental monitoring and modeling (especially measuring atmospheric aerosols and remote sensing of forests), and 2) tomographic imaging (especially electrical impedance tomography, industrial process tomography, non-destructive material testing and structural health monitoring; special emphasis is on concrete and other cement-based materials and structures).

Professor Samuli Siltanen leads a research group concentrating on computational inversion methods for medical imaging, industrial applications, and art. There are three core topics.

  1. Reconstruction methods for X-ray tomography with limited data. In such imaging we record X-ray images of a patient or object along different directions of view and design a mathematical computer program for recovering the internal structure. Limited-data problems arise in medical imaging when the radiation dose to the patient needs to be kept very low, and in inspecting weldings in power plants when there are geometric restrictions for the view directions.
  2. Electrical imaging based on probing a patient or object with harmless electric currents. The main application area is to find out if a stroke victim is suffering from bleeding in the brain (hemorrhage) or from a blood clot preventing blood flow to the brain (ischemic stroke). The symptoms are the same in both cases, but the right treatment for ischemic stroke is dangerous to hemorrhagic patients. The imaging task is highly nonlinear and unstable, calling for special mathematical inversion techniques.
  3. Developing image processing methods that digital artists find useful for their work.

The team of Associate Professor Tanja Tarvainen investigates and develops computational methods for optical and ultrasonic inverse problems such as tomographic imaging and therapy. The tomographic methods include purely light based modalities such as diffuse optical tomography and coupled physics imaging such as photoacoustic tomography. In addition, modelling and computational methods for light transport and ultrasound propagation are studied, and prototype instrumentation for the techniques are developed. The team consist of two senior researchers, Tanja Tarvainen and Aki Pulkkinen, and several postdoctoral researchers and PhD students.

Research work of Professor Marko Vauhkonen concentrates on industrial and biomedical inverse problems. The most prominent area of his research includes development of diffuse tomographic imaging for industrial process. These imaging modalities can be used for example in monitoring of pipe flows, control of industrial processes and optimizing of process vessels. Studies in biomedical inverse problems include mainly PET, SPECT and fMRI imaging related to time-varying image reconstruction and motion artifact reduction.