New Diffusion Method Solves Electrical Impedance Tomography on Unstructured Meshes
Overcomes limitations of regular grids for PDE-based inverse problems using graph neural diffusion...
Inverse problems in electrical impedance tomography (EIT) aim to reconstruct internal conductivity distributions from boundary voltage measurements. These problems are notoriously ill-posed and nonlinear, and physical domains are typically discretized as unstructured meshes, not regular grids—making standard convolutional diffusion models unsuitable.
A team led by Giovanni S. Alberti proposes a new framework that extends diffusion posterior sampling (DPS) to graph-structured data. They build an unconditional score-based diffusion model directly on a 2D triangular mesh, learning an accurate prior over the physical solution space. To handle severe ill-posedness, they introduce RDPS—a regularized variant incorporating explicit terms like total variation and generalized Tikhonov regularization alongside the implicit diffusion prior.
Extensive experiments on synthetic and real 2D EIT datasets demonstrate that RDPS produces stable, physically plausible reconstructions. The method generalizes well to out-of-distribution inclusion geometries, shows high robustness to measurement noise, and outperforms state-of-the-art solvers (GPnP-BM3D, DP-SGS) in reconstruction accuracy and artifact reduction. This work bridges deep generative models with PDE-constrained inverse problems on arbitrary meshes.
- Extends diffusion posterior sampling (DPS) to graph-structured data on 2D triangular meshes for PDE-based inverse problems.
- Introduces RDPS with explicit regularization (total variation, generalized Tikhonov) to complement the implicit diffusion prior.
- Outperforms GPnP-BM3D and DP-SGS on synthetic and real EIT data, with robust noise handling and out-of-distribution generalization.
Why It Matters
Enables high-quality medical and industrial imaging from sparse measurements using graph-based diffusion, overcoming grid limitations.