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

点击翻译按钮获取中文摘要

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.