OP: Complex Media Optics and Imaging

恒星的闪烁是一种物理现象，每个人都会观察到，最欣赏的是一种迷人而美丽的现象。虽然从物理角度很好地理解了这一现象，但仍然没有从精确的数量角度严格地描述这一现象。这个项目涉及生物医学应用中出现的类似现象，在成像研究中，人们需要描述光场是如何“闪烁”的，并受到组织微结构的影响。高分辨率生物医学成像对于癌症的早期检测、药物效率的监测、计算机辅助手术以及对组织、器官和骨骼的总体健康状况的评估都是至关重要的。未来，对血糖水平、心率、血压和其他医学指标的监测可能是基于光学的，而通过聚焦光学能量来激活的新药可能会显著减少癌症或糖尿病治疗中的潜在副作用。生物组织通常是如此复杂，以至于人们只能以统计的方式描述其微观结构。在这个项目中，复杂的多尺度传播环境将被建模为一个在空间和时间上都变化的异质多尺度随机场。该项目将通过加强我们对光场如何受微结构影响的理解，支持生物医学成像中基于光学的新技术的发展。该项目还将支持开发其他成像和电波传播领域的新技术，如遥感和大气通信以及地球物理成像。在该项目中，将使用特定的标度关系来推导波场统计的渐近描述。这些描述将用于最佳过滤和成像技术的开发，这些技术可以利用新的光学技术提供的大量数据。这种对波场的描述将在光学和成像的一系列领域中有重要的应用，而这里的重点是定量生物医学成像。该项目旨在开发新的结果，使人们能够对复杂介质中的光波传播进行建模。这将涉及旁轴波的传播和亚扩散区的传播，此外，还涉及辐射传输和扩散区的传播。这一发展是基于对多尺度介质的随机建模，并使用标度极限来表征波场的统计特性。这项工作中的一个主要技术挑战是，在波的背景下，由于波的散射，信息向各个方向流动，而不是像在经典的随机过程背景下那样是一个演化问题。这种情况导致了一个无穷无尽的嵌入问题家族，这些问题在统计上是相互耦合的。该项目将分析和开发利用光谱波信息对光场进行多点观测的新型成像和过滤技术，使用与随机矩阵理论和统计估计技术一起开发的比例限制结果。

Scintillation of the stars is a physical phenomenon that everyone observes and most appreciate as a fascinating and beautiful phenomenon. Albeit well understood from a physical perspective, the phenomenon still is not rigorously described from a precise quantitative perspective. This project concerns an analogous phenomenon that arises in biomedical applications, where one needs to describe how the optical field "scintillates" and is affected by tissue microstructure in imaging studies. High-resolution biomedical imaging is fundamentally important for early cancer detection, monitoring of drug efficiency, computer assisted surgery, and for the evaluation of health of tissue, organs, and bones in general. Monitoring of glucose level, heart rate, blood pressure, and other medical indicators may in the future be optically based, and new drugs that are activated by focusing of optical energy may significantly reduce potential side effects in the treatment of cancer or diabetes. Biological tissue is typically so complicated that one can only describe the microstructure in a statistical fashion. In this project the complex multiscale propagation environment will be modeled as a heterogeneous multiscale random field varying in both space and time. The project will support the development of new optically based techniques in biomedical imaging by enhancing our understanding of how the optical field is affected by the microstructure. The project will also support the development of new techniques in other areas of imaging and wave propagation, such as remote sensing and communication through the atmosphere and in geophysical imaging. In the project, specific scaling relations will used to derive asymptotic descriptions of wave field statistics. The descriptions will be used in the development of optimal filtering and imaging techniques that can exploit the vast amount of data that new optical technology provides. Such a description of the wave field will have important applications in a range of areas in optics and imaging, while the focus here is on quantitative biomedical imaging. The project aims at developing new results that allow one to model optical wave propagation in complicated media. This will concern propagation both for paraxial waves and propagation in the sub-diffusive regime, moreover, propagation in the radiative transfer and diffusion regimes. The development is based on stochastic modeling of the multiscale medium and using scaling limits that allow one to characterize the statistics of the wave field. A main technical challenge in this work is the fact that in the context of waves, information flows in all directions due to wave scattering, rather than being an evolution problem as in the classic context of stochastic processes. This situation leads to an infinite family of imbedding problems that couple statistically. Novel imaging and filtering techniques that exploit spectral wave information for multi-point observations of the optical field will be analyzed and developed in the project, using the scaling limit results developed together with random matrix theory and statistical estimation techniques.