Adaptive and Nonlinear Methods in Signals and Imaging

这项研究项目是研究自适应和非线性方法来解决某些大型的、经常是不适定的反问题，其中的解可能不连续地依赖于数据。所涉及的具体应用涉及大规模自适应滤波计算，例如在有源噪声控制中，以及非线性和自适应图像增强计算。该项目在毛伊岛高性能计算中心使用一台400节点的IBM SP2。这个特殊的设施专门从事图像和信号处理应用。该项目包括以下主题：-用于估计和滤波的快速稳定的自适应算法，以及灵敏度分析，以及在信号处理中的应用。-非线性和自适应图像增强方法，包括涉及偏微分方程的总变异最小化方法，基于自适应多级分割的方法，以及这两种方法的组合。-将数值计算和符号计算结合起来。-算法的并行化。该项目有强大的教育和区域联盟研究部分，并包括代表人数不足的少数群体的参与。

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.