Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning

TL;DR

This paper demonstrates that deep learning can achieve near-perfect accuracy in noise-free tomographic inverse problems, specifically in computed tomography, by using an iterative end-to-end network and data-driven calibration.

Contribution

It introduces a novel deep learning approach that attains near-exact solutions for CT inverse problems, including a data-driven calibration for unknown forward models.

Findings

Achieves reconstructions close to numerical precision.

Outperforms classical compressed sensing methods.

Demonstrates state-of-the-art results on real-world datasets.

Abstract

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network scheme enables reconstructions close to numerical precision, comparable to classical compressed sensing strategies. Our results build on our winning submission to the recent AAPM DL-Sparse-View CT Challenge. Its goal was to identify the state-of-the-art in solving the sparse-view CT inverse problem with data-driven techniques. A specific difficulty of the challenge setup was that the precise forward model remained unknown to the participants. Therefore, a key feature of our approach was to initially estimate the unknown fanbeam geometry in a data-driven calibration step. Apart from an in-depth analysis of our methodology, we also demonstrate its state-of-the-art performance on the open-access real-world dataset LoDoPaB CT.