Mathematical Sciences: Numerical Methods for Parameter Estimation in Distributed Parameter Systems

9303222沃格尔研究人员将基于全变分的技术和并行计算相结合，开发了改进的参数估计方法。这项建议涉及分布参数系统中参数估计的计算方法。参数估计是根据对解的观察来确定系数函数的过程，通常用于偏微分方程组。科学计算和图像处理方面的最新进展使这一项目的工作成为可能。在图像处理领域，所谓的“全变差”技术的发展使重建的图像比以前可能的更加清晰。并行计算机的发展使复杂的二维和三维问题得以解决，而这些问题以前是很难解决的。参数估计研究的直接应用包括改进从电磁、热和声学数据重建图像。雷达和声纳可能是最广为人知的例子。其他包括非侵入性医学成像技术，如CAT扫描、超声波和磁共振成像(MRI)。地震数据处理是另一个重要的例子，它利用对穿过地球的扰动的记录来推断地球的内部结构。参数估计在数学模型的发展中也起着关键作用，即对物理现象的数学描述。这些模型被用来描述从有毒化学物质通过土壤的运输到艾滋病流行的传播的各种过程。***

9303222 Vogel The investigator combines Total Variation based techniques and parallel computing to develop improved parameter estimation methods. This proposal deals with computational methods for parameter estimation in distributed parameter systems. Parameter estimation is the process of determining coefficient functions, typically for partial differential equations, from observations of solutions. The work of this project was made possible by recent advances in scientific computing and image processing. In the field of image processing, the development of so-called ``Total Variation'' based techniques enables the reconstruction of much sharper images than was previously possible. The development of parallel computers allows the solution of complex 2- and 3-dimensional problems, which were previously intractable. Direct applications of research in parameter estimation include the improved reconstruction of images from electromagnetic, thermal, and acoustic data. Radar and sonar are perhaps the most well-known examples. Others include noninvasive medical imaging techniques such as CAT scans, sonograms, and Magnetic Resonance Imaging (MRI). Seismic data processing, where recordings of disturbances which have passed through the earth are used to infer the internal structure of the earth, is yet another important example. Parameter estimation also plays a key role in the development of mathematical models, i.e., mathematical descriptions of physical phenomena. These models are used to describe processes ranging from the transport of toxic chemicals through the soil to the spread of the AIDS epidemic. ***