@inproceedings{55d837c9c83e4facb6bab253c03908a3,
title = "Learning a projection operator onto the null space of a linear imaging operator",
abstract = "Image reconstruction algorithms seek to reconstruct a sought-after object from a collection of measurements. However, complete measurements such that an object can be uniquely reconstructed are seldom available. Analysis of the null components of the imaging system can guide both physical design of the imaging system and algorithmic design of reconstruction algorithms to more closely reconstruct the true object. Characterizing the null space of an imaging operator is a computationally demanding task. While computationally efficient methods have been proposed to iteratively estimate the null space components of a single or a small number of images, full characterization of the null space remains intractable for large images using existing methods. This work proposes a novel learning-based framework for constructing a null space projection operator of linear imaging operators utilizing an artificial neural network autoencoder. To illustrate the approach, a stylized 2D accelerated MRI reconstruction problem (for which an analytical representation of the null space is known) was considered. The proposed method was compared to state-of-the-art randomized linear algebra techniques in terms of accuracy, computational cost, and memory requirements. Numerical results show that the proposed framework achieves comparable or better accuracy than randomized singular value decomposition. It also has lower computational cost and memory requirements in many practical scenarios, such as when the dimension of the null space is small compared to the dimension of the object.",
keywords = "Autoencoder, Inverse problem, Medical image reconstruction, Null space",
author = "Joseph Kuo and Jason Granstedt and Umberto Villa and Anastasio, {Mark A.}",
note = "Funding Information: This work was supported in part by NIH awards EB020604, EB023045, NS102213, EB028652, and NSF Award DMS1614305. Publisher Copyright: {\textcopyright} COPYRIGHT SPIE. Downloading of the abstract is permitted for personal use only.; Medical Imaging 2021: Physics of Medical Imaging ; Conference date: 15-02-2021 Through 19-02-2021",
year = "2021",
doi = "10.1117/12.2582263",
language = "English (US)",
series = "Progress in Biomedical Optics and Imaging - Proceedings of SPIE",
publisher = "SPIE",
editor = "Hilde Bosmans and Wei Zhao and Lifeng Yu",
booktitle = "Medical Imaging 2021",
}