About

It specializes in the theory, implementation and application of inversion methods. The objective is to create fundamentally new, efficient, and theoretically sound solutions to practical inverse problems, especially in following application areas:

• Medical imaging,
• Geophysics and space research,
• Remote sensing and modelling in enviromental and climate research.

The director of the Centre is Academy professor Matti Lassas (Univ. of Helsinki) and the vice-directors are research professor Johanna Tamminen (Finnish Meteorological Institute) and professor Mikko Kaasalainen (Univ. of Tampere). The Finnish Centre of Excellence of Inverse Modelling and Imaging is a network comprising research groups in the following institutions:

• University of Helsinki, Department of Mathematics and Statistics, Inverse Problems Group
• Aalto University, Department of Mathematics and Systems Analysis, Inverse Problems Research Group
• University of Eastern Finland, Department of Applied Physics, Computational Physics and Inverse Problems Research
• Finnish Meteorological Institute, Earth Observation Reseach, Greenhouse Gases and Satellite Methods
• University of Jyväskylä, Department of Mathematics and Statistics, Inverse Problems Research Group
• LUT University, Department of Mathematics and Physics, Inverse Problems
• University of Oulu, Department of Mathematical Sciences, Inverse Problems Research Group
• Tampere University, Department of Mathematics, Inverse Problems Group

Inverse Problems

Inverse problems appear in several fields, including medical imaging, image processing, mathematical finance, astronomy, geophysics, nondestructive material testing and sub-surface prospecting. Typical inverse problems arise from asking simple questions "backwards". For instance, the simple question might be "If we know precisely the structure of the inner organs of a patient, what kind of X-ray images would we get from her?" The same question backwards is "Given a set of X-ray images of a patient, what is the three-dimensional structure of her inner organs?" This is the inverse problem of Computerized Tomography, or CT imaging.

Usually the inverse problem is more difficult than the simple question that it reverses. For example, even though the Earth's gravitational field is governed by Newton's law of gravitation, the inverse problem of finding sub-surface structures from minor variations of the gravitational field on the surface is extremely hard. Successful solution of inverse problems requires specially designed algorithms that can tolerate errors in measured data.

Inverse problems research concentrates on the mathematical theory and practical interpretation of indirect measurements. The study of inverse problems is an active area of modern applied mathematics and one of the most interdisciplinary field of science.

Picture: Reconstruction of simulated cross-section of human chest from electrical impedance tomography data using a novel reconstruction method