FRG: Solutions for Inverse Problems

FRG：反问题的解决方案

• 批准号: 0101458
• 负责人: Joyce McLaughlin
• 金额: $ 101.09万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101458&HistoricalAwards=false
• 关键词: FRG; Solutions; Inverse; Problems

In the work proposed here, four researchers at Rensselaer Polytechnic Institute work in teams with postdocs and graduate students to solve inverse problems. The goal is to identify material properties or surface features from indirectly related data sets. Each problem is modeled as an elastic, electromagnetic, or acoustic medium and the mathematical model is strongly taken into account to develop solution techniques. Two of the four problems to be considered are: (1) find variations in stiffness in biological tissue so that regions that are abnormal (usually with 7 to 17 times stiffer than normal tissue) can be identified. The model is the equations of elasticity and measurement of low frequency propagating shear waves using Doppler ultrasound provide the data. Noise reduction, use of models with random media, determination of the minimum size of abnormal regions that can be identified, reconstruction algorithms and images are all targets of this investigation; and (2) create radar images from satellite or airborne radar equipment by developing solutions that correct for deviations from ideal flight paths, that correctly identify object positions (break left-right symmetry problems) and that can image objects that are moving. The problems involve establishing mathematical results, utilizing engineering expertise and development and implementation of numerical algorithms.In this work, four principal investigators, together with postdocs and graduate students, solve problems where noninvasive sensing is followed by the creation of images. To solve these problems, the researchers work in teams to combine mathematical analysis, engineering and numerical computation to achieve results. Two of the problems that will be addressed are: (a) elastography with ultrasound measurements of tissue movement created by a second low level propagated signal yields data that can distinguish the stiffer tissue of cancerous tumors from normal tissue. The goal, then, is to determine algorithms for computing the location of the stiff and normal regions, to find the minimum size of regions that can be identified, and to create images in 'real time';(b) airborne and satellite topographic and object sensing where signals reflected from the earth's surface are used to locate positions of objects and topographic features. The goal is to improve resolution and accuracy, to reduce the size of objects and features that can be identified and to correctly represent features that are partially hidden from view.

在这里提出的工作中，伦斯勒理工学院的四名研究人员与博士后和研究生合作解决逆问题。 目标是从间接相关的数据集中识别材料特性或表面特征。 每个问题都被建模为弹性、电磁或声学介质，并且在开发解决方案技术时会充分考虑数学模型。要考虑的四个问题中的两个是：(1) 发现生物组织中硬度的变化，以便识别异常区域（通常比正常组织硬 7 到 17 倍）。 该模型是弹性方程和使用多普勒超声测量低频传播剪切波提供的数据。 降噪、使用随机介质模型、确定可识别的异常区域的最小尺寸、重建算法和图像都是本次研究的目标； (2) 通过开发解决方案来纠正与理想飞行路径的偏差、正确识别物体位置（打破左右对称问题）以及对移动物体进行成像，从而从卫星或机载雷达设备创建雷达图像。 这些问题涉及建立数学结果、利用工程专业知识以及数值算法的开发和实施。在这项工作中，四名主要研究人员与博士后和研究生一起解决了无创传感随后创建图像的问题。 为了解决这些问题，研究人员通过团队合作，将数学分析、工程和数值计算相结合来取得成果。 将要解决的两个问题是：(a)利用第二低电平传播信号产生的组织运动的超声测量的弹性成像产生可以区分癌性肿瘤的较硬组织和正常组织的数据。 那么，目标是确定计算刚性区域和正常区域位置的算法，找到可识别区域的最小尺寸，并“实时”创建图像；（b）机载和卫星地形和物体感测，利用从地球表面反射的信号来定位物体的位置和地形特征。 目标是提高分辨率和准确性，减小可识别的对象和特征的大小，并正确表示部分隐藏在视图中的特征。