Data Completion for Electrical Impedance Tomography by Conditional Diffusion Models

TL;DR

This paper introduces a diffusion-based generative model to complete partial Dirichlet-to-Neumann measurements in Electrical Impedance Tomography, significantly reducing measurement requirements while maintaining reconstruction quality.

Contribution

It presents a novel conditional diffusion model for DtN data completion, enabling high-quality EIT reconstructions with only 1% of measurements, outperforming traditional matrix completion methods.

Findings

Diffusion completion achieves comparable reconstructions to full data with only 1% measurements.

Standard matrix completion needs at least 30% measurements for similar quality.

The method supports flexible configurations and can be integrated with existing EIT solvers.

Abstract

Data scarcity is a fundamental barrier in Electrical Impedance Tomography (EIT), as undersampled Dirichlet-to-Neumann (DtN) measurements can substantially degrade conductivity reconstructions. We address this bottleneck by completing partially observed DtN measurements using a diffusion based generative model. Specifically, we train a conditional diffusion model to learn the distribution of DtN data and to infer full measurement vectors given partial observations. Our approach supports flexible source receiver configurations and can be used as a plug in preprocessing step with off the shelf EIT solvers. Under mild assumptions on the polygon conductivity class, we derive nonasymptotic end to end bounds on the distributional discrepancy between the completed and ground truth DtN measurements. In numerical experiments, we couple the proposed diffusion completion procedure with a deep learning based inverse solver and compare its performance against the same solver with full measurement data. The results show that diffusion completion enables reconstructions comparable to the full data baseline while using only 1% of the measurements. In contrast, standard baselines such as matrix completion require 30% of the measurements to achieve similar reconstruction quality.