Inverse problems aim to recover information, such as internal structures, from a set of measurements. For instance, in tomographic applications we may probe biological tissue with X-rays, while measuring the loss of intensity as an X-ray projection image, but to obtain a tomographic image of the inside we need to solve an inverse problem. Providing a more detailed image of the structures, which is essential to make accurate diagnostic decisions.
Inverse problems are a rich area of study and can range from microscopic medical imaging and non-destructive testing to macroscopic geophysical exploration. While the theoretical study of inverse problems is primarily of mathematical nature, solving an inverse problem is undoubtedly highly interdisciplinary, involving physics, engineering, as well as computer science. My research team in Computational Mathematics and Inverse Problems at the University of Oulu is aligned at this intersection, to provide a link between theory and practice.
Our research is currently concentrated on what we call learned image reconstruction, which can be understood as the combination of classical mathematical techniques to solve an inverse problem with modern approaches from data-science, with the aim to overcome the “black-box” nature of many learning-based approaches.
Webpage: www.hauptmann-research.net