**Department of Mathematics **(Applied Mathematics)

#### Joined SFU in August 2014

High-dimensional approximation is becoming imperative in the data-rich era. Dr. Adcock’s research tackles problems related to the recovery of complex, high-dimensional objects from limited datasets in the realms of modern science, medicine, and engineering. He seeks to develop new algorithms using the theory of a signal processing technique called compressed sensing (CS), as well as optimal approximation algorithms. His work is interdisciplinary, with applications in medical imaging, intelligent signal processing, machine learning, uncertainty quantification, and the numerical solution of partial differential equations.

*What early experiences influenced you to pursue a career in science?*

My dad is a statistician and I have an older brother who was always very interested in computing and science. I also benefited from some really great math teachers in high school – that's what really swung me in the direction of studying mathematics at university.

*What is the best part of the work you do? The downside?*

I work on computational math so I am interested in practical problems coming from science and engineering applications. I enjoy the interplay between the applications and forming the mathematics that I do, so the theorems that I prove inform the applications. For me, the most satisfying thing is when you can see the mathematics in something, it is very powerful and it provides new insight into these applications, even though the mathematics may seem rather abstract on the face of it.

Working on applications, sometimes I can see certain phenomena occurring but cannot explain them mathematically, and that is frustrating. There is an aspect of the work where at some point you have to stop and move on to something else and maybe come back in six months time when you have a new idea on how to tackle the problem.

*Your algorithms have diverse applications. Which one affects you personally or motivates you the most?*

I suppose the one that has proved to be the most intriguing is medical imaging. MRI is an application that can be reduced to what seems, on the face of it, a simple mathematical problem, but then there is a lot of richness to the application that you can add on top of it.

*What limitations in medical applications will your new algorithms overcome?*

In MRI one of the biggest limitations concerns the amount of time a patient sits in the machine. Motion artifacts corrupt the data so it would be advantageous to reduce the imaging time. You can go quite a long way with engineering medical devices to make them more efficient, but that can only take you so far, and then you have to look at the mathematical algorithmic side to improve the technology further.

About 10 years ago a new area of research called compressed sensing sprung up. This new area of mathematics says that under the right conditions you can recover images from far fewer measurements than you classically think you need. I've been working on building compressed sensing-based algorithms for applications like MRI where the goal is to reduce the number of measurements you need to acquire and reduce the time someone needs to sit in the scanner. There are a lot of people who work on aspects of applying compressed sensing to MRI. What I'm trying to do is develop new mathematics to further improve compressed sensing algorithms and optimize their performance in applications such as MRI.