Sampsa Pursiainen: Mathematics to solve numerical inverse problems
“Mathematical inverse problems concern identifying unknown parameters on the basis of measured or otherwise observed data. For example, the 3D structure of biological tissue can be reconstructed from projection measurements, or the unknown parameters of a finance model can be determined based on observed market data.”
According to Pursiainen, inverse problems are often computationally demanding and can involve several uncertainties that affect measurements.
“Analytical techniques that have traditionally been used to solve inverse problems can sometimes be inadequate, because they are limited to simplified models. Numerical methods, in this regard, often are more efficient and capable of handling large amounts of data and complex models.”
Pursiainen is particularly interested in inverse problems related to topics in biomedicine and geosciences. He has applied inversion mathematics, for example, in brain source imaging, transcranial electrical stimulation where brain activity is modulated, and microwave tomography.
“Managing uncertainty is key to solving inverse problems. Measurements often contain inaccuracies that can be caused by the circumstances, for example, but by quantifying uncertainty, we can prevent incorrect solutions.”