Mathematical Problems and Adaptive Algorithms for Imaging in Random Media

BorceaDMS-0907746该项目涉及非均匀(杂波)富散射介质中的传感器阵列成像。它在反射地震学、超声波无损评估、地面树叶穿透雷达和合成孔径雷达中的应用受到了推动。在数学上，研究的是波速快速波动的波动方程的反问题，这是由于杂波中存在大量的微小不均匀。其目标是利用对远程传感器阵列上的散射波的测量，来定位(图像)隐藏在杂波中的强反射体。由于杂波的不均匀性是未知的，并且不能从阵列数据中估计，所以它们是用随机过程建模的。主要工作分为三个方面：(1)强杂波环境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性照明成像的最佳子空间投影方法。(3)稳健高效的持续监视合成孔径雷达成像方法。所有问题都是新的和具有挑战性的，它们涉及理论、广泛的数值模拟和受应用驱动的现实设置中的算法开发。传感器阵列成像是石油勘探、地震预报、材料无损评价、雷达、复杂城市场景持续监测等领域的一项重要技术。传感器技术的进步极大地提高了收集新型数据和海量数据的能力。目前的成像技术是不够的，特别是在高度不均匀(杂乱)、低能见度的环境中。该项目致力于开发新的成像方法，能够自适应地减少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，以获得尽可能好的图像。

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.