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。现代图像处理严重依赖于图像的像素表示。然而，在计算成像的背景下，处理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，该神经网络与标准计算成像模型更加兼容。主要研究目标是发展一种理论，量化使用这些神经网络图像表示的计算成像技术的预期精度，并推导出适用于实际高分辨率成像问题的有效估计算法。这项研究在计算成像发挥关键作用的所有科学和工程领域都有可预见的应用，包括医学成像和诊断、安全筛查、地震成像和环境监测。该项目研究了一类神经网络的使用，称为基于坐标的神经网络（CBNNs），用于计算成像中的图像重建问题。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。由于常见的成像正演模型，如连续Radon或傅里叶变换，可以更准确地实现cbnn，因此它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)开发一种采样理论，用于从有限的线性投影测量集中识别cbnn的唯一可识别性，并为相关的非凸优化问题提供恢复保证，以及(2)开发用于加速cbnn训练的有效算法，以适应实际成像场景。理论和算法将在实际数据的大规模应用中进行演示，包括压缩感知磁共振成像和低剂量/稀疏视图计算机断层扫描。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。

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.