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

Marquette University, Milwaukee WI

Investigators

Abstract

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.