In addition to deriving fundamental mathematical results on various types of inverse problems, we develop reconstruction procedures that converge efficiently and can handle large data sets. Our main application fields are brain imaging, planetary small body research, forest and environmental sciences, and remote sensing. Our team is currently working on the following projects.
For more information, see the links below, the list of publications, and resources page.
Forest and ecological research with laser scanning
Keywords: terrestrial and UAV laser scanning, 3D point clouds, forest research and forest ecology, climate change and carbon counting, tree models, quantitative structure models (QSMs), surface reconstruction, optimisation, uncertainty quantification
Close-range laser scanner (LiDAR) allows measuring forest and individual tree structure in 3D, accurately and comprehensively. For example, it is possible to measure tree biomass and its distribution. Thus there is a large range of applications from forest research (forestry) and inventory to environmental and climate research and forest ecology.
Our goal is to develop mathematical and computational methods that can process and analyse close-range laser scanner data from forests to tree models and other useful information about the trees. These include methods to isolate the individual trees from the data and more generally segmenting the data into different classes such as wood, leaf, and ground points. We develop methods to reconstruct quantitative structure models (QSMs) of the woody structure of trees. Currently major area of research is uncertainty quantification in QSM reconstruction and tree measurements. We also study methods to model and measure leaf cover as distributions over QSMs. More information here.
Geoscience: Radar tomography
Keywords: asteroid interior, solar system research, volumetric inversion, regularization, finite element methods
In geosciences, inverting a full wavefield is crucial in various applications, including both seismic, and radar applications. Our focus is the development and analysis of finite element time domain (FETD) modelling and the associated inversion methods for electromagnetic wave propagation and scattering in radar tomography (RT) which can be used in imaging the interior structure of a small solar system body such as an asteroid. More information here.
Biomedical Science: Reconstructing the activity of the brain
Keywords: biomedicine, magnetoencephalography, volumetric inversion, hierarchical Bayesian approach, finite element methods
Modelling and inverting the electromagnetic field in the brain necessitates advanced forward simulation and inverse modelling. We focus on investigating source localization of brain activity for non-invasive brain imaging such as electro/magnetoencephalography (EEG/MEG) by applying and developing mathematical inverse modeling techniques. More information here.