This research project is to investigate adaptive and nonlinear methods for the solution of certain large and often ill-posed inverse problems, where the solution may not depend continuously on the data. The particular applications addressed concern large scale adaptive filtering computations, such as in active noise control, and nonlinear and adaptive image enhancement computations. The project is using a 400 node IBM SP2 at the Maui High Performance Computing Center. This particular facility specializes in image and signal processing applications. The project includes the following topics: - Fast and stable adaptive algorithms for estimation and filtering, along with sensitivity analysis, with applications in signal processing. - Nonlinear and adaptive image enhancement methods, including Total Variation minimization involving partial differential equations, adaptive multi-level segmentation-based methods, and a combination of these two approaches. - Coupling numeric and symbolic computations. - Parallelization of the algorithms. The project has strong educational and REU research components, and includes participation by underrepresented minorities.
