Abstract:Deep generative models have emerged as state-of-the-art for solving inverse problems, but applying them to inverse problems for PDEs, like electrical impedance tomography (EIT) remains challenging. Because physical domains are naturally discretized as unstructured meshes rather than regular grids, standard convolutional architectures are often inadequate. In this paper, we propose a novel framework that extends diffusion posterior sampling (DPS) to graph-structured data. We develop an unconditional score-based diffusion model directly on a 2D triangular mesh to learn an accurate prior over the physical solution space. Furthermore, we introduce a regularized variant, RDPS, which incorporates explicit regularization terms, such as total variation and generalized Tikhonov, to complement the implicit diffusion prior and mitigate severe ill-posedness. Extensive experiments on synthetic and real 2D EIT datasets demonstrate that RDPS produces stable, physically plausible reconstructions. Our approach generalizes well to out-of-distribution inclusion geometries, is highly robust to measurement noise, and outperforms current state-of-the-art solvers (e.g., GPnP-BM3D, DP-SGS) in reconstruction accuracy and artifact reduction.
| Subjects: | Image and Video Processing (eess.IV); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| MSC classes: | 65N21, 65N75, 35R30, 62F15, 68T07 |
| Cite as: | arXiv:2605.19621 [eess.IV] |
| (or arXiv:2605.19621v1 [eess.IV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.19621 arXiv-issued DOI via DataCite (pending registration) |
From: Matteo Santacesaria [view email]
[v1]
Tue, 19 May 2026 09:57:10 UTC (42,357 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。