»Big data is full of existential questions«
We live in an age of data. We are confronted with massive amounts of it every day. In astronomy, for example, new telescope generations are recording huge data volumes in order to detect remote galaxies. The phenomenon we have come to call “big data” confronts us with the existential issue of how we can pick out relevant information from an enormous ocean of data. In my research, I develop efficient mathematical models to address this challenge. To give you a picture, I apply a mathematical lens to data that lets me see certain structures and patterns. I immerse myself in mathematics to create models and develop methods. In the process I apply various theories – applied harmonic analysis, frame theory, approximation theory, and compressed sensing, to name a few.
I am working to expand the new research field “com- pressed sensing” in Berlin, and we are currently in a very ex- citing phase. The potential applications seem to be endless at this point. For example in medicine, our findings could help reduce the time that patients need to spend lying in an MRI scanner. In this context, our approach is to reduce the number of sample values, while retaining the same image quality. And only collect data that matters. After sampling, to retrieve the image as a whole, we need to develop an algorithm that uses a modular system and then fills in the gaps with as few elements as possible. With sets of wavelets, we have already been able to achieve a time that is one sixth of the original time patients spent in the scanner, in other words just ten minutes, instead of an hour lying in an MRI. And we are now applying a further development called shearlets to reduce these ten minutes even further.
I can focus on mathematical problems for hours or even days on end when I want to prove a statement. It was like that at school and it’s still the same today. Once I find a solution, I am always quite excited to be the very first person to lay eyes on it. But it doesn’t take long until I am itching to pursue new questions or improve on what I have already developed. My perfectionism drives me to keep pushing ahead and make things even better.
The precision of mathematics is fascinating. It is the only scholarly field that can support its statements one hundred per cent. Mathematics is unique in that it gives us actual guarantees. The world of mathematics is a completely structured environment. And its methods work astonishingly well in reality. The natural world becomes much more understandable, once you have a reliable foundation.
Credits: Pablo Castagnola