What is it like to study Inverse Problems and Imaging in the MAST programme?
There are many applications for this study track. As an example, say you want to monitor the lungs of a patient, something that was done throughout COVID. To accomplish this, you’ll need to get a picture inside someone that you cannot directly look into with general tools. The mathematics in our field can be used to solve this issue. We also have something similar in our courses, where you do actual X-ray measurements and imaging on objects such as seashells.
Most of our courses are very traditional, but a number are somewhat unconventional in that they can be completed through project work instead of exams. We often emphasize the programming components, so, for example, writing a mathematical software could be a way to pass the course. Most of our courses are more computational and applied than other mathematics classes.
Who should consider these studies?
These studies are good for people who are interested in applied and computational mathematics. I also think studies would be very suitable for people who want to go into clustering for purposes outside of academics, although there is some interesting theory in the field that you could study. Overall, I think it gives an excellent basis for doing actual computations in industry.
Additionally, one nice thing about this field is how close it is to physics. All our models come from physics, and we work on inferring parameters from them. If you have a minor in physics or are interested in it, this field might be a great fit for you.
What kind of career paths does studies in inverse problems and imaging open up?
I would say it opens up many different careers. You can, for instance, stay in academia and do mathematical research using tools from analysis, geometry, numerical analysis, and computational sciences. However, studies in inverse problems and imaging are great if you want to do something outside academia. You can learn numerical computational methods working with actual data programming, medical imaging with X-rays, acoustic simulations, epidemiological modeling, or radar development in the defense industry. Even smaller companies in Finland desire the skills from this study track.
What do you find most interesting about this field of research?
To me, this field’s questions are very mathematically intriguing. They are often quite difficult to solve because they tend to be nonlinear and unstable. As a result, you really need to think carefully—not just about solving them theoretically but also about implementing your ideas as numerical algorithms.
However, there’s also a practical side to this work. We address real-world problems, such as medical imaging, where we screen or monitor patients. While the theoretical aspects are fascinating, the industrial impact of this work is also significant. For some people, especially those less inclined toward theory, that might be the main attraction of this field.
I’ve put a lot of effort into the computational courses I created from scratch, and I enjoy teaching them. These courses are also very suitable for a wide range of students. Even for those not specifically interested in inverse problems, the skills they teach are broadly applicable.