CRII: CIF: Coordinate-based Neural Networks for Inverse Problems in Computational Imaging

该奖项全部或部分由2021年美国救援计划法案（公法117-2）资助。现代图像处理在很大程度上依赖于图像的像素表示。然而，在计算成像的上下文中，使用像素表示需要进行近似，这可能会使图像估计过程产生偏差，从而对图像质量产生负面影响。该项目旨在通过一种基于神经网络的新型图像表示来克服这些限制，这种图像表示与标准计算成像模型更兼容。主要的研究目的是开发一种理论，量化的预期精度的计算成像技术，使用这些神经网络图像表示，并获得有效的估计算法适用于实际的高分辨率成像问题。这项研究在科学和工程的所有领域都有可预见的应用，其中计算成像起着至关重要的作用，包括医学成像和诊断，安全筛选，地震成像和环境monitoring.This项目研究使用一类神经网络，称为基于坐标的神经网络（CBNNs），在计算成像的图像重建问题。CBNN将图像表示为将空间坐标映射到图像强度的连续域函数。由于常见的成像前向模型，如连续Radon或傅立叶变换，可以更准确地实现CBNN，他们有可能提高基于模型的迭代重建技术的准确性。该项目的具体目标包括：（1）从有限的线性投影测量和相关非凸优化问题的恢复保证中为CBNN的独特可识别性开发采样理论，以及（2）开发用于加速CBNN训练的有效算法，该算法可扩展到实际成像场景。该理论和算法将通过压缩传感磁共振成像和低剂量/稀疏视图计算机断层扫描等真实的数据在大规模应用中得到验证。该奖项反映了NSF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。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Modern image processing relies heavily on pixel representations of images. However, in the context of computational imaging, working with pixel representations requires making approximations which may bias the image-estimation process and therefore negatively impact image quality as a result. This project seeks to overcome these limitations through a new type of image representation based on neural networks that is more compatible with standard computational imaging models. The main research aims are to develop a theory quantifying the expected accuracy of computational imaging techniques using these neural-network image representations, and to derive efficient estimation algorithms applicable to practical high-resolution imaging problems. This research has foreseeable applications in all areas of science and engineering where computational imaging plays a critical role, including medical imaging and diagnostics, security screening, seismic imaging, and environmental monitoring.This project investigates the use of a class of neural networks, known as Coordinate-Based Neural Networks (CBNNs), for image-reconstruction problems in computational imaging. A CBNN represents an image as a continuous domain function mapping spatial coordinates to image intensities. Because common imaging-forward models, such as continuous Radon or Fourier transforms, can be implemented more accurately for CBNNs, they have the potential to improve the accuracy of model-based iterative reconstruction techniques. Specific objectives of this project include (1) developing a sampling theory for the unique identifiability of CBNNs from a finite set of linear projection measurements and recovery guarantees for the associated non-convex optimization problem, and (2) developing efficient algorithms for accelerated training of CBNNs that scale to practical imaging scenarios. The theory and algorithms will be demonstrated on large-scale applications with real data, including compressed sensing magnetic-resonance imaging and low-dose/sparse-view computerized tomography.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.