A Conditional Diffusion Model for Electrical Impedance Tomography Image Reconstruction

TL;DR

This work tackles the ill-posed inverse problem of Electrical Impedance Tomography by introducing CDEIT, a conditional diffusion model that reconstructs conductivity images from boundary voltages using a forward diffusion of the conductivity and a conditional reverse denoising process. The method employs a Transformer-based U-net to model the conditional denoiser and a sim-to-real normalization framework to enable application of simulated-training models to real data under varying geometry and excitation conditions. Experiments on simulated and real datasets show that CDEIT achieves state-of-the-art reconstruction quality on synthetic data and competitive performance on real data, with a notable improvement in PSNR and structural metrics and a tractable inference time via DDIM sampling. The work also provides an open-source implementation and a generalized normalization strategy that broadens the practical impact of diffusion-based EIT reconstruction in medical and industrial settings.

Abstract

Electrical impedance tomography (EIT) is a non-invasive imaging technique, capable of reconstructing images of the electrical conductivity of tissues and materials. It is popular in diverse application areas, from medical imaging to industrial process monitoring and tactile sensing, due to its low cost, real-time capabilities and non-ionizing nature. EIT visualizes the conductivity distribution within a body by measuring the boundary voltages, given a current injection. However, EIT image reconstruction is ill-posed due to the mismatch between the under-sampled voltage data and the high-resolution conductivity image. A variety of approaches, both conventional and deep learning-based, have been proposed, capitalizing on the use of spatial regularizers, and the paradigm of image regression. In this research, a novel method based on the conditional diffusion model for EIT reconstruction is proposed, termed CDEIT. Specifically, CDEIT consists of the forward diffusion process, which first gradually adds Gaussian noise to the clean conductivity images, and a reverse denoising process, which learns to predict the original conductivity image from its noisy version, conditioned on the boundary voltages. Following model training, CDEIT applies the conditional reverse process on test voltage data to generate the desired conductivities. Moreover, we provide the details of a normalization procedure, which demonstrates how EIT image reconstruction models trained on simulated datasets can be applied on real datasets with varying sizes, excitation currents and background conductivities. Experiments conducted on a synthetic dataset and two real datasets demonstrate that the proposed model outperforms state-of-the-art methods. The CDEIT software is available as open-source (https://github.com/shuaikaishi/CDEIT) for reproducibility purposes.

Figures (11)

• Figure 1: Overview of the proposed CDEIT framework, encompassing both the forward and the reverse processes. In the forward diffusion process, Gaussian noise is incrementally added to the conductivity image $\boldsymbol{\sigma}_0$ over $T$ time steps. In the reverse process, the denoising network $\mu_\theta(\cdot)$ progressively restores the spatial details of the original conductivity image, conditioned on the boundary voltages $\mathbf{U}$.
• Figure 2: 2D EIT forward model with 16 electrodes. When a current excitation is applied through a pair of electrodes, changes in the conductivity distribution of the target will result to changes in the voltages of the boundary electrodes.
• Figure 3: Framework of the denoising net $\boldsymbol{\sigma}_\theta(\boldsymbol{\sigma}_t,\mathbf{U},t)$.
• Figure 4: Transformer block and Swin-Transformer block. (a) global attention and windowed attention. (b) Time-involved Transformer blocks.
• Figure 5: Scale transformation modules. (a) Patch merging. (b) Upsampling by interpolation.