Mathematical Problems and Adaptive Algorithms for Imaging in Random Media

随机介质成像的数学问题和自适应算法

• 批准号: 0907746
• 负责人: Liliana Borcea
• 金额: $ 29.33万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907746&HistoricalAwards=false
• 关键词: Mathematical; Problems; Adaptive; Algorithms; Imaging

BorceaDMS-0907746 The project is concerned with sensor array imaging in heterogeneous (cluttered) richly scattering media. It is motivated by applications in reflection seismology, ultrasonic nondestructive evaluation, ground-foliage penetrating radar, and synthetic aperture radar. Mathematically, the study is on inverse problems for the wave equation with rapidly fluctuating wave speed, due to numerous small heterogeneities in clutter. The goal is to locate (image) strong reflectors buried in clutter, using measurements of the scattered waves at remote arrays of sensors. Because the clutter inhomogeneities are not known and they cannot be estimated from the array data, they are modeled with random processes. The work is divided in three main themes: (1) Filtering random media effects for array imaging in heavy clutter. (2) Optimal subspace projection methods for selective illumination and imaging with array sensors in random media. (3) Robust and efficient imaging methods for persistent surveillance synthetic aperture radar. All problems are new and challenging, they involve theory, extensive numerical simulations, and algorithm development in realistic setups, motivated by applications. Sensor array imaging is an important technology in oil exploration, earthquake prediction, nondestructive evaluation of materials, radar, persistent surveillance of complex urban scenes, and elsewhere. Progress in sensor technology has improved dramatically the ability to collect new types of data and vast amounts of it. The current imaging technology is inadequate, specially in highly heterogeneous (cluttered), low visibility environments. The project is concerned with the development of new imaging methodologies that can adaptively mitigate the clutter effects and the uncertainty in the data, and can optimize sensor array illumination waveforms for achieving the best possible images.

Borceadms-0907746该项目与传感器阵列成像中的异质性（混乱）丰富的散射介质有关。 它是由反思地震学，超声波无损评估，地面透明雷达和合成孔径雷达的应用。 从数学上讲，由于杂物中许多小的异质性，这项研究是在波动方程的逆问题上。 目的是使用偏远的传感器阵列的散射波的测量来定位埋在混乱中的强反射器。 由于杂波不均匀性尚不清楚，并且无法从数组数据中估算它们，因此它们以随机过程进行建模。 该作品分为三个主要主题：（1）过滤沉重混乱中的阵列成像的随机介质效果。 （2）在随机介质中使用阵列传感器进行选择性照明和成像的最佳子空投影方法。 （3）持续监视合成孔径雷达的稳健有效的成像方法。 所有问题都是新的，具有挑战性的，它们涉及理论，广泛的数值模拟和算法开发在现实设置中，这是由应用程序动机的。 传感器阵列成像是石油探索，地震预测，材料无损评估，雷达，持续监视复杂城市场景以及其他地方的重要技术。 传感器技术的进步已显着提高了收集新类型数据和大量数据的能力。 当前的成像技术不足，特别是在高度异质（混乱），低的可见度环境中。 该项目与新成像方法的开发有关，这些方法可以适应数据中的混乱效应和不确定性，并且可以优化传感器阵列照明波形以实现最佳图像。