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.

Antti Hannukainen leads the Numerical Analysis team at Aalto University. The main expertise of the team is numerical analysis of partial differential equations, in particular, finite element methods and eigenvalue problems.

Andreas Hauptmann leads the team of Computational Mathematics and Inverse Problems in the Research Unit of Mathematical Sciences, University of Oulu. His main research topic concentrates on learned image reconstruction, which can be understood as the combination of classical analytic and model-based inversion techniques with modern methods from data-science, with the aim to overcome the “black-box” nature of many learning-based approaches. The application area is primarily within biomedical imaging and includes photoacoustic tomography and electrical Impedance tomography as well as established modalities such as X-ray imaging and magnetic resonance imaging.

Joonas Ilmavirta is an academy research fellow and an assistant professor of mathematics at Tampere University. He works on a number of different kinds of inverse problems, mostly on different kinds of ray tomography problems and problems related to geophysics.

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.

The research areas of the team of Prof. Kolehmainen are computational inverse problems and uncertainty quantification. The main part of the research is on development of mathematical models and computational inverse problems methods for image reconstruction in medical tomography imaging techniques such as X-ray tomography, diffuse tomography and MRI. The research team actively collaborates with system experts and clinical specialists on development of novel imaging techniques, which typically involve fusion of different types of imaging data and lead to large scale 3D or 4D imaging with sparse measurement data

Marko Laine is a research professor of weather model post-processing at FMI’s Meteorological Research Applications group. Marko’s research highlights include developing widely used MCMC toolbox for Matlab in his PhD thesis Adaptive MCMC methods with applications in environmental and geophysical models. 

Lauri Oksanen leads a research team that focuses on inverse problems for partial differential equations, their numerical analysis, and related geometric problems such as inversion of the geodesic ray transform.

The research of Associate Professor Pasi Raumonen concentrates on development of computational methods for forest and ecological research and forest remote sensing. The main measurement data are point clouds from laser scanners or photogrammetry which are used for analysis and model reconstruction to answer many forest inventory and ecology related questions such as estimation of biomass. The developed methods include segmentation of the data into individual plants or structural elements, topological and geometrical model reconstruction of the plants from the data, and feature extraction and classification methods from the data and the plant models.

Lassi Roininen holds the position of Associate Professor (tenure track) in applied mathematics in LUT University, Finland. He develops rigorous numerical and computational tools for inverse problems with applications in near-space remote sensing, subsurface imaging, and X-ray tomography.

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 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.