Mathematical Problems in Imaging in Random Media

随机介质成像的数学问题

• 批准号: 0604008
• 负责人: Liliana Borcea
• 金额: $ 27.8万
• 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: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2010-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0604008&HistoricalAwards=false
• 关键词: Mathematical; Problems; Imaging; Random; Media

We consider inverse problems for the acoustic wave equation, where the goal is to image strong reflectors in a medium from measurements of the scattered echoes at a remote array of transducers. In known and smooth environments, imaging is done well with coherent migration type imaging techniques. We are concerned with imaging in cluttered media, with rapid and unknown fluctuations of the sound speed, which we model with random processes. The research is focused on theoretical and numerical studies of statistically stable imaging methods in such media, in regimes of significant interaction of the waves with the inhomogeneities in the clutter. Explicitly, we consider a coherent interferometric imaging approach that uses statistical smoothing techniques for suppressing the unwanted clutter effects and emphasizing the coherent part of the data, which can then be processed to get robust images that are independent of the realization of the clutter. The research has the following main parts: (1) Theoretical studies of both statistical stability and resolution of coherent interferometric imaging in random media, for particular wave scattering regimes. (2) Development of algorithms that are capable of estimating adaptively the needed amount of smoothing, without any a priori knowledge of the statistics of the clutter. (3) Theoretical and numerical studies of optimal illumination strategies for achieving the best possible resolution of coherent interferometric images. (4) Coupling of the coherent interferometric imaging of strong reflectors with the estimation of the background (average) sound speed in the medium. This will be done in the context of a mine detection problem. (5) Theoretical and numerical studies of statistically stable imaging techniques for noisy acoustic waveguides. brbrWe study robust array imaging techniques in cluttered media that arise naturally in applications such as ground or foliage penetrating radar, nondestructive evaluation of aging concrete structures, medical ultrasound, imaging in noisy ocean waveguides, etc. These media consist of a smooth part, which is known or can be estimated, and a fluctuating part, which is due to the presence of small inhomogeneities that are not known and that cannot be estimated. When the interaction of the waves with the clutter is weak, there is a lot of coherence in the scattered echoes, and classic migration (radar) imaging techniques work well. However, these techniques fail in richly scattering environments, in the sense that they give speckled images that are difficult to interpret and that change unpredictably from one clutter to another. Our goal is to develop a robust imaging framework for such scattering environments and to quantify the effect of the inhomogeneities in the clutter on the resolution of the images. The study brings together a combination of ideas from statistics, asymptotic stochastic analysis, numerical simulations, and signal processing and considers specific problems in the following applications: (1) Ultrasound, nondestructive evaluation of aging concrete structures. (2) Land mine detection. (3) Imaging through foliage. (4) Imaging in noisy ocean waveguides. We are presently collaborating with experimentalists on all these applications and an important part of the study will be the testing of our imaging techniques on experimental data.

我们考虑了声波方程的反问题，其中的目标是通过在远程传感器阵列处的散射回声测量介质中的强反射器成像强反射器。 在已知和光滑的环境中，成像通过相干迁移型成像技术做得很好。 我们关注混乱的介质中的成像，声速的快速和未知的波动，我们以随机过程进行建模。 该研究的重点是此类媒体中统计稳定成像方法的理论和数值研究，在波浪与混乱中的不均匀性的显着相互作用方面。 明确地，我们考虑了一种连贯的干涉成像方法，该方法使用统计平滑技术来抑制不必要的混乱效应并强调数据的相干部分，然后可以对其进行处理以获得与杂物的实现无关的强大图像。 该研究具有以下主要部分：（1）在随机培养基中，针对特定波散射方案在随机介质中相干干涉成像的理论研究。 （2）开发能够自适应估算所需的平滑量的算法，而无需先验地了解混乱的统计数据。 （3）最佳照明策略的理论和数值研究，以实现最佳分辨率的相干干涉图像。 （4）强反射器的相干干涉成像与介质中背景（平均）音速的估计。 这将在矿山检测问题的背景下完成。 （5）嘈杂的声学波导的统计稳定成像技术的理论和数值研究。 Brbrwe研究在混乱的介质中使用的健壮阵列成像技术自然出现在诸如地面或叶子穿透雷达，对衰老混凝土结构的无损评估，医疗超声，嘈杂的海洋波导中的成像等。 估计的。 当波浪与混乱的相互作用很弱时，散射的回声有很多连贯性，经典的迁移（雷达）成像技术效果很好。 但是，这些技术在丰富的散射环境中失败了，从某种意义上说，它们给出了难以解释的斑点图像，并且从一个混乱变成了另一个杂物。 我们的目标是为这种散射环境开发强大的成像框架，并量化混乱中不均匀性对图像分辨率的影响。 该研究汇集了统计学，渐近随机分析，数值模拟以及信号处理的思想组合，并考虑了以下应用中的特定问题：（1）超声，对老化混凝土结构的无损评估。 （2）地雷检测。 （3）通过叶子成像。 （4）在嘈杂的海洋波导中进行成像。 我们目前正在与实验者在所有这些应用程序上进行合作，研究的重要部分将是对实验数据的成像技术的测试。