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 该项目涉及非均匀（杂乱）富散射介质中的传感器阵列成像。 它的动机是在反射地震学，超声波无损评价，地面植物穿透雷达和合成孔径雷达的应用。 在数学上，研究的是快速波动的波速，由于许多小的杂波的波动方程的反问题。 其目标是利用远程传感器阵列的散射波测量来定位（成像）掩埋在杂波中的强反射体。 由于杂波不均匀性是未知的，它们不能从阵列数据中估计，它们与随机过程建模。 本文的工作主要分为三个方面：（1）强杂波背景下阵列成像中随机介质效应的滤除。 (2)随机介质中阵列传感器选择照明与成像的最优子空间投影方法。 (3)持续监视合成孔径雷达的鲁棒高效成像方法。 所有的问题都是新的和具有挑战性的，它们涉及理论，广泛的数值模拟，并在现实的设置算法开发，由应用程序驱动。 传感器阵列成像是石油勘探、地震预测、材料无损评估、雷达、复杂城市场景的持续监视等领域的重要技术。 传感器技术的进步极大地提高了收集新类型数据和大量数据的能力。当前的成像技术是不够的，特别是在高度异构（杂乱），低可见度的环境中。 该项目关注的是新的成像方法的发展，可以自适应地减轻杂波的影响和数据的不确定性，并可以优化传感器阵列照明波形，以实现最佳的图像。