## Research Interests for William K. Allard

**Research Interests:** *Scientific computing, particularly distributed computing; differential geometry; geometric measure theory; partial differential equations.*
1. My main research effort will be to continue my collaboration with the Data Driven Modeling and Analysis group at LANL. This group works for the most part in the area of image processing.
2. I will continue to work as an investigator on Tom Kepler's NIH contract. My contribution is to provide analyis and parallel computing support for simulations.

**Recent Publications**
- W.K. Allard, Guanglian Chen, Mauro Maggioni,
*W.K. Allard, G. Chen, M. Maggioni Multiscale Geometric Methods for Data Sets II: Geometric Wavelets*,
to appear in ACHA
(2011)
- W.K. Allard,
*A boundary approximation algorithm for planar domains*
(Preprint, 2009) [pdf]
- Allard, WK,
*Total variation for image denoising: III. Examples*,
Siam Journal on Imaging Sciences, vol. 2
(2009) [pdf]
- Allard, WK,
*Total variation regularization for image denoising, geometric theory*,
Siam Journal on Mathematical Analysis, vol. 39 no. 4
(December, 2007),
pp. 1150-1190, ISSN 0036-1410 [Gateway.cgi], [doi] [abs]
- Allard, WK,
*Total variation regularization for image denoising: I. Geometric theory
using total variation regularization; II Examples.*,
Siam Journal on Mathematical Analysis, vol. 39 no. 4
(November, 2007) [~wka] [abs]