Diff-INR: Generative Regularization for Electrical Impedance Tomography

TL;DR

Diff-INR, a novel method that combines generative regularization with Implicit Neural Representations (INR) through a diffusion model, achieves state-of-the-art reconstruction accuracy in both simulation and experimental data.

Abstract

Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse problem, which complicates accurate results. To tackle this, we propose Diff-INR, a novel method that combines generative regularization with Implicit Neural Representations (INR) through a diffusion model. Diff-INR introduces geometric priors to guide the reconstruction, effectively addressing the shortcomings of traditional regularization methods. By integrating a pre-trained diffusion regularizer with INR, our approach achieves state-of-the-art reconstruction accuracy in both simulation and experimental data. The method demonstrates robust performance across various mesh densities and hyperparameter settings, highlighting its flexibility and efficiency. This advancement represents a significant improvement in managing the ill-posed nature of EIT. Furthermore, the method's principles are applicable to other imaging modalities facing similar challenges with ill-posed inverse problems.

Figures (7)

• Figure 1: Architecture of the proposed method with diffusion regularization. The coordinates of FE nodes and pixel centers are initially encoded using RFF and then fed into the INR to estimate conductivity in both mesh and pixel domains. Data-fidelity loss $\mathcal{L}_\text{data}$ is computed using the EIT forward model, while the regularization loss $\mathcal{L}_\text{reg}$ is calculated based on generative regularization employing a pre-trained diffusion model. The INR is then iteratively optimized with the reconstruction loss $\mathcal{L}_\text{rec}$ using the Adam optimizer until convergence.
• Figure 2: Samples in 2D shape datasets for pretraining the diffusion model.
• Figure 3: Simulation results using a human thorax phantom under different noise levels.
• Figure 4: Results of experimental data reconstruction using TV, INR+TV and Diff-INR.
• Figure 5: Image corresponding to $x_t$, $\epsilon_\phi(x_t, t)$, and $[\epsilon_\phi(x_t, t) - \epsilon]$ across various diffusion time steps.