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Better than the eye

According to an old saying, nothing sees better than the eye. Today, this saying no longer holds true.

“Mathematics has proved to be the new eyes. It helps see into places where we would not otherwise be able to see,” says Lassi Päivärinta, Director of the Finnish Centre of Excellence in Inverse Problems.

The Centre of Excellence is unique in the world in this research field. An inverse problem is defined as a problem of providing as perfect information as possible from a research target by means of mathematical models. This problem-solving method can be likened to a child’s development, which is an ongoing process forming a complete picture of the world through isolated observations.

What kind of things do inversion problems involve?

“The entirety of life,” says Päivärinta.

For example, ultrasound and X-ray imaging are solutions to inversion problems.

The unit combines many applied fields from medicine and dental surgery to geophysics, space studies and practical industrial processes. Accurate images may be needed of internal organs, unhealthy teeth, flowing water or an asteroid. Depending on the methods, the core of inversion problems is how to get all available information from measurements.

“Mechanics and technology are easy, but mathematics is difficult,” says Päivärinta, explaining why the Centre of Excellence is so necessary.

The research gathers information on, for example, electromagnetic waves. Unlike the X-ray, electrical current does not proceed via air and its route is dependent on an unknown medium in a complex way. The role of mathematics is to systematise information gathered, and to develop methods of measuring that would make interpretation easier.

One of the methods developed within inversion research is electric impedance tomography. Its advantages are that it is inexpensive and safe. As an imaging method it is also more accurate than, for example, X-ray.

Text: Ulla Mether
Photo: Veikko Somerpuro
Translation: Valtasana Oy