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SuCor: Susceptibility Distortion Correction via Parameter-Free and Self-Regularized Optimal Transport

Sreekar Chigurupati, Eleftherios Garyfallidis

Abstract

We present SuCor, a method for correcting susceptibility induced geometric distortions in echo planar imaging (EPI) using optimal transport (OT) along the phase encoding direction. Given a pair of reversed phase encoding EPI volumes, we model each column of the distortion field as a Wasserstein-2 barycentric displacement between the opposing-polarity intensity profiles. Regularization is performed in the spectral domain using a bending-energy penalty whose strength is selected automatically via the Morozov discrepancy principle, requiring no manual tuning. On a human connectome project (HCP) dataset with left-right/right-left b0 EPI pairs and a co-registered T1 structural reference, SuCor achieves a mean volumetric mutual information of 0.341 with the T1 image, compared to 0.317 for FSL TOPUP, while running in approximately 12 seconds on a single CPU core.

SuCor: Susceptibility Distortion Correction via Parameter-Free and Self-Regularized Optimal Transport

Abstract

We present SuCor, a method for correcting susceptibility induced geometric distortions in echo planar imaging (EPI) using optimal transport (OT) along the phase encoding direction. Given a pair of reversed phase encoding EPI volumes, we model each column of the distortion field as a Wasserstein-2 barycentric displacement between the opposing-polarity intensity profiles. Regularization is performed in the spectral domain using a bending-energy penalty whose strength is selected automatically via the Morozov discrepancy principle, requiring no manual tuning. On a human connectome project (HCP) dataset with left-right/right-left b0 EPI pairs and a co-registered T1 structural reference, SuCor achieves a mean volumetric mutual information of 0.341 with the T1 image, compared to 0.317 for FSL TOPUP, while running in approximately 12 seconds on a single CPU core.
Paper Structure (13 sections, 5 equations, 2 figures, 2 tables)

This paper contains 13 sections, 5 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Problem Formulation
  4. Column-Wise Optimal Transport
  5. Spectral Bending-Energy Regularization
  6. Automatic Parameter Selection
  7. Computational Complexity
  8. Experiments
  9. Data
  10. Evaluation Metrics
  11. Results
  12. Discussion
  13. Conclusion

Figures (2)

  • Figure 1: Multi-slice correction comparison. Columns show (left to right): uncorrected (LR+RL)/2 average, TOPUP, SuCor (ours), $T_1$ reference, $|$LR$-$RL$|$ before correction, and $|$LR$-$RL$|$ after SuCor correction. Three axial slices are shown at $z = 27$, $55$, and $83$.
  • Figure 2: Estimated displacement fields at $z = 55$. Top row: TOPUP field (Hz) and SuCor field (scaled to TOPUP units). Bottom row: cross-PE gradient magnitude $|\partial u / \partial y|$, showing that SuCor preserves sharper field transitions at tissue boundaries.