DDMA works with Bill Allard on geometric measure theory, differential geometry, PDEs, and numerical techniques.

Current work is on image de-noising using Total Variation Regularization. Image de-noising methods may be considered to fall into two classes. The first class consists of off the shelf gradient descent methods that are modified in an ad-hoc manner to produce results of dubious quality.

The second set of methods is probably convergent to the correct solution; however the convergence is weak and the current methods are extremely slow. Dr. Allard is investigating algorithms for the computation of these de-noisings based on their geometry. Such an algorithm would be similar in concept to those used to solve conservation laws and to construct distance functions.

In related work Dr. Allard is finishing writing the code for a boundary finder which computes very accurately the location and other geometric entities associated with a curve given only the pixels which lie inside the curve. He is also looking at extending this work to three dimensions