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Joint Supervised and Self-Supervised Training with Acquisition-Robust Techniques for Accelerated 4D Flow MRI Reconstruction
Mengyuan Xue, Bochun Mei
TL;DR
Long acquisition and reconstruction times motivate prospective undersampling, while reference-based training requires fully sampled examples that acceleration is intended to avoid. FlowVN-JSSL jointly trains on reference-bearing and reference-free data, directly supervises velocity phase, and adds acquisition-robust techniques to an independently processed, eight-stage variational network. Across R=10–50, the proposed model has 38–50% lower RelErr and 7.0–8.7° lower angular error than the other learned method; on unseen sites, versus baseline, it gains 0.063 SSIM, lowers RelErr by 31%, and lowers AngErr by 17.7°.
Problem
Long acquisition and reconstruction times motivate prospective undersampling, while reference-based training requires fully sampled examples that acceleration is intended to avoid.
Source: §1 · pp. 1–2Method
FlowVN-JSSL jointly trains on reference-bearing and reference-free data, directly supervises velocity phase, and adds acquisition-robust techniques to an independently processed, eight-stage variational network.
Source: §1 · p. 2, §2.2 · p. 3Results
Across R=10–50, the proposed model has 38–50% lower RelErr and 7.0–8.7° lower angular error than the other learned method; on unseen sites, versus baseline, it gains 0.063 SSIM, lowers RelErr by 31%, and lowers AngErr by 17.7°.
Source: §3.1 · pp. 6–7Takeaways & Limitations
The same frozen model transfers to unseen sites and organs without retraining or per-domain fine-tuning.
Source: §3.1 · p. 7, §4 · p. 9At R=50, splitting the already-undersampled acquisition leaves the self-supervised consistency loss with only about 0.4% of k-space.
Source: §4 · p. 9
Abstract
from arXiv · showhide
4D flow MRI measures time-resolved, three-directional blood velocity but requires long acquisition times, and its diagnostic signal is carried by the phase difference \emph{between} velocity encodings, not by image magnitude. Recent work has developed a per-encoding variational network to address image reconstruction in this field. In this work, we incorporate a joint supervised and self-supervised training regime and utilize both magnitude and velocity data during supervision. At the same time, we add multiple acquisition-robust and conditioning strategies based on the acceleration factors. On the CMRx4DFlow~2026 aortic dataset (1.5 and 3T), our model lowers RelErr by $38$--$50\%$ and AngErr by $7.0$--$8.7^\circ$ against a training-matched baseline across $R{=}10$--$50$, improving on every held-out subject at every acceleration. Our model also shows strong generalization ability to transfer on out-of-distribution data by employing the joint training scheme, with an increase of $7.2\%$ in SSIM and decrease of $38\%$ and $31\%$ in AngErr and RelErr respectively.
1 Introduction
4D flow MRI provides time-resolved velocity measurements, but long acquisition and reconstruction times motivate prospective undersampling. FlowVN-JSSL combines supervised and self-supervised learning with direct velocity-phase supervision and acquisition-robust techniques.
1 Introduction
- The CMRx4DFlow 2026 challenge targets accelerated reconstruction across more than 400 clinical cases, multiple centers, field strengths, vendors, and acceleration factors R=10–50.The data use 3D Cartesian k-t Gaussian undersampling.Source: §1 · p. 1
- Self-supervised methods such as SSDU use held-out acquired k-space as a consistency target, while joint training combines this with supervised learning on reference-bearing data.The joint regime can also train on target data without reference images.Source: §1 · p. 2
- FlowVN-JSSL directly supervises velocity phase and adds acquisition-robust techniques, including coil-map refinement, coil/noise/phase-ramp augmentation, and acceleration conditioning across R=10–50.Against a training-matched FlowVN baseline, it improves magnitude and velocity fidelity at every acceleration and transfers to unseen sites and organs without adaptation.Source: §1 · p. 2
2 Methods
The methods formulate 4D flow reconstruction around four separately processed velocity encodings, with velocity carried by phase differences relative to a reference. An eight-stage variational network is trained jointly on reference-bearing and reference-free data, with augmentation and magnitude- and velocity-focused objectives.
2.1 Problem formulation
- Velocity is encoded as the phase difference between each directional encoding and the flow-compensated reference, while reconstruction is scored on magnitude and relative phase.The measurements are undersampled with 3D Cartesian k-t Gaussian masks per encoding at R=10–50.Source: §2.1 · p. 2
2.2 Network architecture
- The eight-stage physics-driven variational network alternates learned image-domain regularization with data consistency and processes each encoding independently using shared weights.The four encodings do not meet in learned layers, so measured k-space data consistency preserves their relative phase.Source: §2.2 · p. 3, Figure 1 · p. 3
- A lightweight complex CNN refines coil maps once before the cascade, with zero-initialized output and unit-RSS renormalization.The refinement can absorb site- and array-dependent map error rather than fixing the reconstruction to an ESPIRiT estimate.Source: §2.2 · p. 3
2.3 Training objective and evaluation
- Joint supervised/self-supervised training minimizes the unweighted sum of supervised and self-supervised losses computed from independent, mutually exclusive datasets.The self-supervised stream follows SSDU, holding out 20% of acquired k-space for consistency and using one random encoding per step.Source: §2.3 · pp. 3–4
- The supervised objective penalizes image, multi-scale structural similarity, k-space, angular, and velocity errors, with velocity terms weighted by ground-truth speed.The direction loss penalizes angle between predicted and reference velocity vectors; the wrapped velocity loss handles the ±π boundary, and both downweight noise-dominated low-velocity voxels.Source: §2.3 · p. 4
- Supervised-stream augmentation adds k-space noise, coil-map jitter, and a readout phase ramp, while winsorized k-space-RMS scaling is applied to both streams.The augmentations require fully sampled sources or true-map targets, which the self-supervised stream lacks.Source: §2.3 · pp. 4–5
3 Experiments and Results
Across acceleration factors, the proposed model improves velocity and magnitude metrics over the learned baseline and transfers to unseen sites and organs without adaptation. Ablations identify gains from both acceleration conditioning and joint supervised/self-supervised training.
3 Experiments and Results
- The aortic cohort contains 138 subjects across six center/scanner domains, split disjointly into six self-supervised, 119 supervised, and 13 held-out subjects; the FlowVN baseline uses the same split and hyperparameters.Under-represented Philips subjects were sampled twice per epoch to counter the cohort’s GE predominance.Source: §3 · p. 5
3.1 Quantitative and qualitative results
- Across R=10–50, SSIM is 0.021–0.032 higher and RelErr is 38–50% lower between the learned methods; the AngErr margin widens from 7.0° at R=10 to 8.7° at R=50.The proposed model is more accurate on every held-out subject at every R on both velocity metrics.Source: §3.1 · p. 6, Figure 3 · p. 7
- At R=30, the proposed and baseline networks are visually comparable in magnitude, while the proposed model performs better on the velocity-based AngErr and RelErr maps.Fig. 2 shows four approaches for one held-out peak-systole frame.Source: §3.1 · p. 6, Figure 2 · p. 6
- On cross-site data, the frozen model gains 0.063 SSIM, lowers RelErr by 31%, and lowers AngErr by 17.7° against the baseline; it also leads on every cross-organ metric.There is no retraining or per-domain fine-tuning; the cross-organ angular margin is 7.16°.Source: §3.1 · p. 7
3.2 Ablation studies
- Acceleration conditioning and the dual-domain Lksp term reduce velocity metrics individually and together yield around a 10% RelErr reduction and 3° AngErr reduction against baseline, trading magnitude for velocity accuracy.The ablation adds mechanisms incrementally; step sizes, optimizer, and scheduler are fixed, with single-seed runs.Source: §3.2 · p. 8, Table 2 · p. 8
- JSSL reduces RelErr from 0.501 to 0.376 and AngErr from 33.04° to 28.18°, while raising SSIM by 0.013; at R=50, it lowers AngErr to 35.01°.The final ablation increment bundles JSSL with velocity-specific losses and the reference-free stream, preventing strict isolation of the joint objective.Source: §3.2 · p. 8
4 Discussion and Conclusion
The discussion attributes velocity gains to direct supervision of relative phase, while describing stronger transfer across anatomy than across acquisition systems. The conclusion reports reconstruction across acceleration factors and transfer to unseen sites and organs without adaptation.
4 Discussion and Conclusion
- Direct relative-phase supervision with Lang and wrapped, ±π-correct Lvel weights ground-truth velocity to avoid noise-dominated voxels contaminating gradients.The discussion notes that per-encoding processing alone shows no velocity gain.Source: §4 · p. 8
- The frozen model transfers better across anatomy than acquisition systems: anatomy changes content but not the measurement model, whereas site shifts alter acquisition statistics.The discussion says cross-site loss concentrates in magnitude and RelErr, while angular error is essentially unchanged.Source: §4 · p. 8
- At R=50, splitting the undersampled acquisition leaves the consistency loss at approximately 0.4% of k-space, bounding reference-free supervision where accuracy is hardest.The final ablation increment also bundles JSSL, velocity-specific losses, and the reference-free stream, leaving some variables uncontrolled.Source: §4 · p. 9
- The same frozen model transfers to unseen sites and organs without adaptation, after training with joint supervision and direct velocity-phase supervision.The conclusion also reports reconstruction across various acceleration factors.Source: §4 · p. 9