CIF: Small: Collaborative Research: Signal Processing for Nonlinear Diffractive Imaging: Acquisition, Reconstruction, and Applications

在生物医学研究中，越来越需要在小于100nm的长度尺度上观察生物结构和过程。传统的光学系统不能有效地提供这样的信息，然而，由于臭名昭著的衍射极限。衍射极限的公式基本上依赖于假定的照明光和物体之间相互作用的线性。这个项目的目标是从现代信号处理的角度利用非线性来克服衍射极限。本项目将为非线性衍射成像奠定理论、算法和仪器基础。这个项目的成果可以为高散射介质的高分辨率成像开辟许多可能性，这些高散射介质在科学和医学中无处不在，包括组织学、细胞术、脑成像和药物发现。拟议的活动还将通过对学生进行信号处理、计算成像和光学等广泛主题的培训，以及通过将拟议研究的基本主题纳入研究人员教授的课程的相关课程开发工作，促进教育。本研究的重点是开发计算成像方法，充分利用两种非线性类型的编码信息：物体-光相互作用和对物体的先验假设。具体而言，工作将集中在：(a)数据采集的有效方案，(b) 3D重建的可扩展算法，以及(c)两个用于验证的新型应用平台。这项研究的结果将导致一个单一的，整体的信号处理框架，可以最大限度地提取非线性测量中编码的信息。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

There is a growing need in biomedical research to observe biological structure and processes on the length scales smaller than 100nm. Conventional optical systems cannot effectively provide such information, however, due to the infamous diffraction limit. The formulation of the diffraction limit fundamentally relies on the presumed linearity in the interaction between the illuminating light and the object. The goal of this project is to overcome the diffraction limit by exploiting nonlinearities from a modern signal processing perspective. This project will lay out theoretical, algorithmic, and instrumentation foundation for nonlinear diffractive imaging. The outcome of this project can open up many possibilities of high-resolution imaging in highly scattering media that are ubiquitous in science and medicine, including histology, cytometry, brain mapping, and drug discovery. The proposed activities will also promote education through the training of students in a wide range of topics within signal processing, computational imaging, and optics, and through related curriculum development efforts where the basic themes of the proposed research will be incorporated in courses taught by the investigators.The focus of this research is to develop computational imaging methods that fully harness the information encoded in two types of nonlinearities: object-light interactions and prior assumptions on the objects. Concretely, the work will focus on: (a) efficient schemes for data acquisition, (b) scalable algorithms for 3D reconstruction, and (c) two novel application platforms for validation. Results from this research will lead to a single, holistic signal processing framework that can maximally extract the information encoded in nonlinear measurements.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.