Rigorous Uncertainty Quantification for Helmholtz-based EPT: Application to Uncertainty-Guided Post-processing

We provide a ground-truth-free uncertainty metric for Helmholtz-based EPT. The uncertainty maps can be thresholded to identify reliable voxels for analysis, while our uncertainty-guided filter further improves accuracy and reduces boundary artifacts. All code is openly available on GitHub.Motivation: Assessing the reliability of Electrical Properties Tomography is challenging in clinical settings where no ground truth is available.Goals: To develop a framework that quantifies voxel-wise uncertainty from the measured data, and to use this metric to guide a post-processing filter for improved accuracy.Approach: We use a bivariate error-propagation strategy accounting for the full covariance terms to generate uncertainty maps. A novel filter then improves reconstructions by selectively weighted-averaging only the lowest-uncertainty neighboring voxels.Results: Our uncertainty metric strongly correlated (r > 0.8) with reconstruction error in simulations. The uncertainty-guided filter consistently achieved lower errors than the standard median filter in post-processing.