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Super-resolution of 4D flow MRI through inverse problem explicit solving

Aurélien de Turenne, Rémi Cart-Lamy, Denis Kouamé

Abstract

Four-dimensional Flow MRI enables non-invasive, time-resolved imaging of blood flow in three spatial dimensions, offering valuable insights into complex hemodynamics. However, its clinical utility is limited by low spatial resolution and poor signal-to-noise ratio, imposed by acquisition time constraints. In this work, we propose a novel method for super-resolution and denoising of 4D Flow MRI based on the explicit solution of an inverse problem formulated in the complex domain. Using clinically available magnitude and phase images, we reconstruct synthetic complex-valued spatial signals. This enables us to model resolution degradation as a physically meaningful truncation of high-frequency components in k-space, and to recover high-resolution velocity fields through a fast, non-iterative 3D Fourier-based solver. The proposed approach enhances spatial resolution and reduces noise without the need for large training datasets or iterative optimization, and is validated on synthetic datasets generated from CFD simulations as well as on a 4D Flow MRI of a physical phantom.

Super-resolution of 4D flow MRI through inverse problem explicit solving

Abstract

Four-dimensional Flow MRI enables non-invasive, time-resolved imaging of blood flow in three spatial dimensions, offering valuable insights into complex hemodynamics. However, its clinical utility is limited by low spatial resolution and poor signal-to-noise ratio, imposed by acquisition time constraints. In this work, we propose a novel method for super-resolution and denoising of 4D Flow MRI based on the explicit solution of an inverse problem formulated in the complex domain. Using clinically available magnitude and phase images, we reconstruct synthetic complex-valued spatial signals. This enables us to model resolution degradation as a physically meaningful truncation of high-frequency components in k-space, and to recover high-resolution velocity fields through a fast, non-iterative 3D Fourier-based solver. The proposed approach enhances spatial resolution and reduces noise without the need for large training datasets or iterative optimization, and is validated on synthetic datasets generated from CFD simulations as well as on a 4D Flow MRI of a physical phantom.

Paper Structure

This paper contains 10 sections, 11 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. METHODS
  3. Acquisition process
  4. Forward model
  5. Inverse problem solving
  6. RESULTS
  7. Datasets
  8. Simulated dataset results
  9. Phantom dataset results
  10. Conclusion

Figures (3)

  • Figure 1: Comparison between the HR reference, LR input, bicubic interpolation, 4DFlowNet, and our method for a $\times 4$ super-resolution task on synthetic data. The velocity magnitude (cm/s) is shown within the flow mask.
  • Figure 2: Quantitative evaluation on synthetic data ($\times 4$). PSNR and RMSE computed within the flow mask over all time frames. Our method achieves the best reconstruction fidelity.
  • Figure 3: Comparison between the LR input, 4DFlowNet, and our method on a physical flow phantom for a $\times 2$ super-resolution task. The in-plane velocity component (cm/s) is shown within the flow mask.