Mathematical Problems and Adaptive Algorithms for Imaging in Random Media

该项目关注的是传感器阵列在非均匀（杂乱）高散射介质中的成像。它在反射地震学、超声无损评价、探地雷达和合成孔径雷达等方面的应用推动了它的发展。在数学上，由于杂波中存在许多小的非均质性，研究的是波速快速波动波动方程的逆问题。目标是利用远程传感器阵列的散射波测量来定位（图像）隐藏在杂波中的强反射器。由于杂波的不均匀性是未知的，也不能从阵列数据中估计出来，所以用随机过程来建模。该工作分为三个主要主题：(1)在重杂波条件下滤波随机介质效应用于阵列成像。(2)随机介质中阵列传感器选择照明和成像的最优子空间投影方法。(3)持久监视合成孔径雷达鲁棒高效成像方法。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，并在实际设置的算法开发，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、复杂城市场景持续监测等领域的重要技术。传感器技术的进步极大地提高了收集新类型和大量数据的能力。目前的成像技术是不够的，特别是在高度异构（杂乱）、低能见度的环境中。该项目涉及开发新的成像方法，可以自适应地减轻杂波效应和数据中的不确定性，并可以优化传感器阵列照明波形，以获得最佳图像。

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.