Research Summary

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, in medical imaging it is necessary to produce images for which you were 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.

I enjoy doing research, but must admit that it is not my main priority. I love the problem solving associated with my area of research, and I love analyzing the results. It became very clear to me, however, during my sabbatical two years ago that I needed huge blocks of time to devote solely to my research if I was going to make meaningful contributions to the field. This is just not possible for me during the school year, and I am not in a position to devote my summers entirely to research. Thus, I decided to forego the grant proposal route and work independent of outside funding, during whatever time I could find. I was able to work with two Transy students, David Leatherman and Brad Jones, during the summer of 1998, thanks to university funding available to them. I also worked with numerical analyst A. C. R. Newbery, who has provided the inspiration for the latest version of our algorithm. But recent discoveries we have made have convinced me that our work will best be continued in the hands of a professor at U.K., who has several very large grants. Not only does he have the manpower available to continue our work, but he has the connections with industry that are necessary to have the algorithm seriously considered. It is disappointing to not be able to see it through to its conclusion, but I have much satisfaction in knowing that I have been involved during the most important stage: the formulation, testing, and refining of the algorithm. I have constructed several major proofs connected with the algorithm, which should prove useful to the team that continues with it. In addition, I have demonstrated that the algorithm is able to drive a pen plotter, so it theoretically could drive any machining tool. The potential uses are very exciting. That is the main reason I have not completely given up the project yet, so may yet continue to make some contributions, as the new team allows.