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Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction

Pierre-Antoine Comby, Benjamin Lapostolle, Matthieu Terris, Philippe Ciuciu

TL;DR

A fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising deep neural network (DNN) and introduces an annealed Half-Quadratic Splitting algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms.

Abstract

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while robust across varying acquisition settings, struggle to maintain good reconstruction quality at high acceleration factors ($\ge$ 8). Recent advances in deep learning have improved reconstruction quality, but purely data-driven methods are prone to overfitting and hallucination effects, notably when the acquisition setting is varying. Plug-and-Play (PnP) approaches have been proposed to mitigate the pitfalls of both frameworks. In a nutshell, PnP algorithms amount to replacing suboptimal handcrafted CS priors with powerful denoising deep neural network (DNNs). However, in MRI reconstruction, existing PnP methods often yield suboptimal results due to instabilities in the proximal gradient descent (PGD) schemes and the lack of curated, noiseless datasets for training robust denoisers. In this work, we propose a fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising DNN. Furthermore, we introduce an annealed Half-Quadratic Splitting (HQS) algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms. When combined with preconditioning techniques, our approach achieves state-of-the-art results, providing a robust and efficient solution for high-quality MRI reconstruction.

Robust plug-and-play methods for highly accelerated non-Cartesian MRI reconstruction

TL;DR

A fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising deep neural network (DNN) and introduces an annealed Half-Quadratic Splitting algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms.

Abstract

Achieving high-quality Magnetic Resonance Imaging (MRI) reconstruction at accelerated acquisition rates remains challenging due to the inherent ill-posed nature of the inverse problem. Traditional Compressed Sensing (CS) methods, while robust across varying acquisition settings, struggle to maintain good reconstruction quality at high acceleration factors ( 8). Recent advances in deep learning have improved reconstruction quality, but purely data-driven methods are prone to overfitting and hallucination effects, notably when the acquisition setting is varying. Plug-and-Play (PnP) approaches have been proposed to mitigate the pitfalls of both frameworks. In a nutshell, PnP algorithms amount to replacing suboptimal handcrafted CS priors with powerful denoising deep neural network (DNNs). However, in MRI reconstruction, existing PnP methods often yield suboptimal results due to instabilities in the proximal gradient descent (PGD) schemes and the lack of curated, noiseless datasets for training robust denoisers. In this work, we propose a fully unsupervised preprocessing pipeline to generate clean, noiseless complex MRI signals from multicoil data, enabling training of a high-performance denoising DNN. Furthermore, we introduce an annealed Half-Quadratic Splitting (HQS) algorithm to address the instability issues, leading to significant improvements over existing PnP algorithms. When combined with preconditioning techniques, our approach achieves state-of-the-art results, providing a robust and efficient solution for high-quality MRI reconstruction.

Paper Structure

This paper contains 20 sections, 1 theorem, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Plug-and-Play algorithms for MRI
  3. MR image reconstruction
  4. Plug-and-play algorithms
  5. Complex-valued denoisers for MRI
  6. Proposed approach
  7. Denoised dataset generation
  8. Unsupervised preprocessing of multicoil data
  9. Proposed algorithm
  10. Preconditioning matrices
  11. Experimental results and discussion
  12. Simulated non-Cartesian acquisition
  13. Training of the denoising prior
  14. Image reconstruction results
  15. Preconditioning boosts image quality
  16. ...and 5 more sections

Key Result

Proposition 1

Assume that there exists a convex function $g$ such that $\operatorname{D}_\sigma= \operatorname{prox}_g$. Furthermore, assume that $P = \operatorname{Id}$ and that for all $k$, $\gamma_k = \gamma$ and $\sigma_k = \sigma$ in eq:dpir. Then:

Figures (3)

  • Figure 1: Effect of the unsupervised preprocessing on the training dataset. Top row shows a non-preprocessed sample of the fastMRI multicoil dataset, obtained with virtual coil combination procedure described in parker2014phase; bottom row shows the preprocessed image.
  • Figure 2: Top row: Reconstruction results for \ref{['eq:MRI_multicoil']} for HQS and PNP algorithms with no (Id) or static (F1) Preconditioner at AF=4 (top) and AF=16 (bottom). PSNR/SSIM metrics are shown inside each image. Bottom right inset depicts the residual maps (5$\times$ magnified).
  • Figure 3: Evolution of the PSNR across iterations for various PnP algorithms at AF=16. Dashed lines correspond to variations of the \ref{['eq:pnp_pgd']} algorithm, while solid lines correspond to variations of the \ref{['eq:dpir']} algorithm.

Theorems & Definitions (1)

  • Proposition 1