Research Interests

My main research interests are associated with inverse problems. In my PhD thesis I specialized in inverse problems connected with complex (polymeric) fluids. This research was heavily involved with computational techniques for the signal processing of data from oscillatory shear flow experiments. In particular, I developed a fresh approach to numerical deconvolution, which is applicable to the deconvolution of noisy data where there is a strong level of ill-posedness in the associated inverse problem. In my PhD I confined attention to an exponentially ill-posed inverse problem in fluid mechanics, which also has an analogue in the relaxation of dielectric materials. However, the methodology I have developed can be used more generally, and I am keen to explore the potential impact of my work in other application areas of signal and image processing.

I am extremely interested in inverse problems in imaging science, and in particular, brain imaging, which is a vital tool in understanding how the human brain works and how diseases and malfunctions of the brain affect health, behaviour, and well-being. I am keen to exploit current trends in the mathematical underpinning of imaging science to achieve transformational change in brain imaging, and help to form a strong collaboration between the School of Mathematics and CUBRIC (Cardiff University Brain Research Imaging Centre).

Research Group

Applied Mathematics