Neural Correction Operator: A Reliable and Fast Approach for Electrical Impedance Tomography

TL;DR

This paper introduces the neural correction operator framework for electrical impedance tomography, combining iterative reconstruction with deep learning correction to improve accuracy, robustness, and speed in solving ill-posed inverse problems.

Contribution

It proposes a novel two-operator approach that enhances neural inverse map learning with an initial iterative estimate and a learned correction, outperforming existing methods.

Findings

Significantly improved reconstruction quality over traditional and neural methods.

Robustness to measurement noise demonstrated in experiments.

Achieves substantial computational speedup compared to conventional techniques.

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive medical imaging method that reconstructs electrical conductivity mediums from boundary voltage-current measurements, but its severe ill-posedness renders direct operator learning with neural networks unreliable. We propose the neural correction operator framework, which learns the inverse map as a composition of two operators: a reconstruction operator using L-BFGS optimization with limited iterations to obtain an initial estimate from measurement data and a correction operator implemented with deep learning models to reconstruct the true media from this initial guess. We explore convolutional neural network architectures and conditional diffusion models as alternative choices for the correction operator. We evaluate the neural correction operator by comparing with L-BFGS methods as well as neural operators and conditional diffusion models that directly learn the inverse map over several benchmark datasets. Our numerical experiments demonstrate that our approach achieves significantly better reconstruction quality compared to both iterative methods and direct neural operator learning methods with the same architecture. The proposed framework also exhibits robustness to measurement noise while achieving substantial computational speedup compared to conventional methods. The neural correction operator provides a general paradigm for approaching neural operator learning in severely ill-posed inverse problems.