My research interests are in computational methods in medical imaging and numerical methods for differential equations.
I am interested in the image reconstruction problem arising in single photon emission computed tomography (SPECT), in particular the dynamic reconstruction problem. These are ill-posed problems. Their solution requires the inclusion of additional information, and the solution is usually computed by an iterative process.
I work on a number of aspects of high-order methods for solving differential equations, in particular spectral collocation and radial basis function methods. Such methods are highly accurate, but often exhibit more severe stability restrictions, lead to full rather than sparse matrices, and are more sensitive to roundoff errors. Many problems require adaptive solution methods.