Current activity and interests
- PDE-based image processing.
- Numerical analysis, especially computational linear algebra.
- Mathematical modelling, particularly in biology.
- The use of technology in teaching mathematics (see, for example,
the applets
I've written and used for teaching Calculus and Linear Algebra).
Current research projects
- Adaptive TV image restoration using exact solution theory.
- Comparing implicit vs. explicit time-marching in doing anisotropic diffusion
(TV Regularization is a model case of anisotropic diffusion).
- Developing a TV-minimizing median filter: basically,
combine the effectiveness of TV Regularization with the
speed of a median filter.
- Unifying TV image restoration and PDE-driven image restoration.
- Local variance-based adaptive TV regularization.
- Numerical considerations in TV regularization.
- Numerical methods for TV regularization.
I also am working on a few projects with a group at Los Alamos National Laboratory.
All of these projects involve TV Regularization in one form or another.
Other projects
- I'm currently combing through books dealing with the history and
evolution of math in the hopes of putting together a talk (of about
an hour in length) of some of the basic and common mathematical discoveries
that would be interesting to non-math people.