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Scalable Non-Cartesian Magnetic Resonance Imaging with R2D2

Yiwei Chen, Chao Tang, Amir Aghabiglou, Chung San Chu, Yves Wiaux

TL;DR

This work tackles scalable reconstruction for non-Cartesian MRI by decoupling data-consistency from denoisers through a residual-to-residual DNN series (R2D2), drawing on a Matching Pursuit perspective. The authors formalize the iteration $\boldsymbol{x}^i = \boldsymbol{x}^{i-1} + \mathbf{G}_{\boldsymbol{\theta}_i}(\boldsymbol{r}^{i-1}, \boldsymbol{x}^{i-1})$, with data residuals $\boldsymbol{r}$ computed from back-projected measurements and a normalized operator $\boldsymbol{\Phi}$. They propose two unrolled variants, R2D2-Net (NUFFT) and R2D2-Net (FFT), and show in radial 2D simulations that the scalable FFT version outperforms competitive baselines and the non-scalable NUFFT variant approaches, while still delivering high-quality reconstructions. The results indicate substantial gains over PnP and unrolled networks in terms of scalability and speed, with promising implications for 3D/4D dynamic MRI and multi-coil acquisitions. Future work will extend to complex-valued data, more advanced architectures, and larger-scale multi-coil settings to validate practical impact.

Abstract

We propose a new approach for non-Cartesian magnetic resonance image reconstruction. While unrolled architectures provide robustness via data-consistency layers, embedding measurement operators in Deep Neural Network (DNN) can become impractical at large scale. Alternative Plug-and-Play (PnP) approaches, where the denoising DNNs are blind to the measurement setting, are not affected by this limitation and have also proven effective, but their highly iterative nature also affects scalability. To address this scalability challenge, we leverage the "Residual-to-Residual DNN series for high-Dynamic range imaging (R2D2)" approach recently introduced in astronomical imaging. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of DNNs taking the previous iteration's image estimate and associated data residual as inputs. The method can be interpreted as a learned version of the Matching Pursuit algorithm. We demonstrate R2D2 in simulation, considering radial k-space sampling acquisition sequences. Our preliminary results suggest that R2D2 achieves: (i) suboptimal performance compared to its unrolled incarnation R2D2-Net, which is however non-scalable due to the necessary embedding of NUFFT-based data-consistency layers; (ii) superior reconstruction quality to a scalable version of R2D2-Net embedding an FFT-based approximation for data consistency; (iii) superior reconstruction quality to PnP, while only requiring few iterations.

Scalable Non-Cartesian Magnetic Resonance Imaging with R2D2

TL;DR

This work tackles scalable reconstruction for non-Cartesian MRI by decoupling data-consistency from denoisers through a residual-to-residual DNN series (R2D2), drawing on a Matching Pursuit perspective. The authors formalize the iteration , with data residuals computed from back-projected measurements and a normalized operator . They propose two unrolled variants, R2D2-Net (NUFFT) and R2D2-Net (FFT), and show in radial 2D simulations that the scalable FFT version outperforms competitive baselines and the non-scalable NUFFT variant approaches, while still delivering high-quality reconstructions. The results indicate substantial gains over PnP and unrolled networks in terms of scalability and speed, with promising implications for 3D/4D dynamic MRI and multi-coil acquisitions. Future work will extend to complex-valued data, more advanced architectures, and larger-scale multi-coil settings to validate practical impact.

Abstract

We propose a new approach for non-Cartesian magnetic resonance image reconstruction. While unrolled architectures provide robustness via data-consistency layers, embedding measurement operators in Deep Neural Network (DNN) can become impractical at large scale. Alternative Plug-and-Play (PnP) approaches, where the denoising DNNs are blind to the measurement setting, are not affected by this limitation and have also proven effective, but their highly iterative nature also affects scalability. To address this scalability challenge, we leverage the "Residual-to-Residual DNN series for high-Dynamic range imaging (R2D2)" approach recently introduced in astronomical imaging. R2D2's reconstruction is formed as a series of residual images, iteratively estimated as outputs of DNNs taking the previous iteration's image estimate and associated data residual as inputs. The method can be interpreted as a learned version of the Matching Pursuit algorithm. We demonstrate R2D2 in simulation, considering radial k-space sampling acquisition sequences. Our preliminary results suggest that R2D2 achieves: (i) suboptimal performance compared to its unrolled incarnation R2D2-Net, which is however non-scalable due to the necessary embedding of NUFFT-based data-consistency layers; (ii) superior reconstruction quality to a scalable version of R2D2-Net embedding an FFT-based approximation for data consistency; (iii) superior reconstruction quality to PnP, while only requiring few iterations.
Paper Structure (20 sections, 4 equations, 3 figures, 2 tables)

This paper contains 20 sections, 4 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. R2D2 approach
  4. DNN structure
  5. R2D2-Net
  6. Normalization procedures
  7. Related works
  8. Data Simulation
  9. Denoised GT images
  10. Radial sampling
  11. Density compensation
  12. Acceleration factor
  13. Noise
  14. Details of the data generation
  15. Experimental Results
  16. ...and 5 more sections

Figures (3)

  • Figure 1: Data simulation process. (a) Denoising the raw GT image; (b) Generating the simulated measurements and back-projected image.
  • Figure 2: Reconstructed images in the first row and corresponding differences compared to the GT image in the second row by different methods for one of the validation samples. Here, DR = 167 and AF = 16. SNR and logSNR values (dB) are displayed below.
  • Figure 3: The reconstruction performances of considered methods across (a), (b) the number of iterations, and (c), (d) the number of spokes. The scalable methods are denoted by continuous lines, while non-scalable methods are denoted by dotted lines.