Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction

German Shâma Wache, Chaithya G R, Asma Tanabene, Sebastian Neumayer

Abstract

While highly accelerated non-Cartesian acquisition protocols significantly reduce scan time, they often entail long reconstruction delays. Deep learning based reconstruction methods can alleviate this, but often lack stability and robustness to distribution shifts. As an alternative, we train a rotation invariant weakly convex ridge regularizer (WCRR). The resulting variational reconstruction approach is benchmarked against state of the art methods on retrospectively simulated data and (out of distribution) on prospective GoLF SPARKLING and CAIPIRINHA acquisitions. Our approach consistently outperforms widely used baselines and achieves performance comparable to Plug and Play reconstruction with a state of the art 3D DRUNet denoiser, while offering substantially improved computational efficiency and robustness to acquisition changes. In summary, WCRR unifies the strengths of principled variational methods and modern deep learning based approaches.

Weakly Convex Ridge Regularization for 3D Non-Cartesian MRI Reconstruction

Abstract

While highly accelerated non-Cartesian acquisition protocols significantly reduce scan time, they often entail long reconstruction delays. Deep learning based reconstruction methods can alleviate this, but often lack stability and robustness to distribution shifts. As an alternative, we train a rotation invariant weakly convex ridge regularizer (WCRR). The resulting variational reconstruction approach is benchmarked against state of the art methods on retrospectively simulated data and (out of distribution) on prospective GoLF SPARKLING and CAIPIRINHA acquisitions. Our approach consistently outperforms widely used baselines and achieves performance comparable to Plug and Play reconstruction with a state of the art 3D DRUNet denoiser, while offering substantially improved computational efficiency and robustness to acquisition changes. In summary, WCRR unifies the strengths of principled variational methods and modern deep learning based approaches.

Paper Structure

This paper contains 29 sections, 1 theorem, 23 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Learned regularizers
  4. Unrolled models
  5. Plug-and-play
  6. Method
  7. Rotation-invariant fields-of-experts
  8. Parametrization
  9. Potentials
  10. Convolutions
  11. Training
  12. MRI reconstruction
  13. Training and validation data
  14. Non-cartesian sampling trajectory
  15. Benchmark setup
  16. ...and 14 more sections

Key Result

Proposition 1

If the $\psi_j$ are $1$-weakly convex and $\|\mathbf W\| = 1$, then $\mathcal{R}$ in reg is also $1$-weakly convex.

Figures (8)

  • Figure 1: Illustration of WCRR: The (rotated) inputs are processed by a filter bank $\{\mathbf W_1, \ldots, \mathbf W_J\}$. The extracted features are penalized based on the potentials $\{\psi_1, \ldots, \psi_J\}$. Usually, the filters extract high-frequency information.
  • Figure 2: Overview of the training and reconstruction pipeline. The WCRR is trained on a Gaussian denoising task, and then used for MRI reconstruction. This involves only tuning of the scalar hyperparameters $\sigma$ and $\lambda$ of the reconstruction model on a (small) validation set. The coil sensitivity maps are estimated using the ESPiRIT algorithm uecker2014espirit on the central 24x24 k-space data (simulating ACS acquisition).
  • Figure 3: (A) 3D GoLF-SPARKLING trajectory with GRAPPA acceleration. The green portion highlights the central Cartesian readouts, and the blue one depicts the non-Cartesian SPARKLING parts. Slices with $\mathbf{k_x} = 0$, $\mathbf{k_z} = 0$, and $\mathbf{k_y} = 0$ are given in (B), (C) and (D), respectively.
  • Figure 4: WCRR convergence curves for reconstructing the 12-coil volume e14091s3_P67584.7.h5. (Left) Relative error between consecutive iterates (tolerance). (Middle) Energy functional. (Right) Masked PSNR. The dashed vertical line highlights where Algorithm \ref{['nmapg']} terminates with tolerance 5.0e-3.
  • Figure 5: Box plots of the quantitative results (masked PSNR/masked SSIM) across volumes in the test sets.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Proposition 1
  • proof