Research Summary
(From Personal Statement)

The area of my research deals with imaging (scientific visualization of data) and design. During the last two years especially, I have made significant progress toward a potentially valuable solution to a problem. The problem is how to accurately produce an image of something for which you have only partial data. For example, x-ray tomography is used to produce images for which it is only able to obtain scattered data points. The computer must be used to "fill in the blanks" in such a way as to make a usuable image. How the blanks are filled in is the role of the computer scientist. Curiously, the same algorithms can sometimes be used for design of objects as well. Recently, I was made aware of the fact that our algorithm may have even more important applications in the area of speech recognition. My software has proved very successful so far in accurately reproducing sound waves when only a few data points on the wave were saved. This could be important because audio files are very large, even after using compression algorithms. Our algorithm indicates that the actual points that need to be saved are much fewer than anyone thought.