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Fast Controllable Diffusion Models for Undersampled MRI Reconstruction

Wei Jiang, Zhuang Xiong, Feng Liu, Nan Ye, Hongfu Sun

TL;DR

The paper tackles undersampled MRI reconstruction using unsupervised diffusion models and addresses the slow sampling bottleneck and limited adaptability of prior methods. It introduces Predictor-Projector-Noisor (PPN), a DDIM-based sampling strategy that enforces k-space data consistency and re-noises at higher levels to keep trajectories within noisy manifolds, enabling fast, high-fidelity reconstructions without paired data or retraining. Empirically, PPN outperforms state-of-the-art controllable diffusion methods across BraTS and fastMRI datasets, achieving superior PSNR/SSIM at multiple accelerations while requiring far fewer diffusion steps. This approach enhances clinical practicality by delivering robust, acquisition-parameter-agnostic reconstructions with substantial speedups and without supervised training on specific undersampling patterns.

Abstract

Supervised deep learning methods have shown promise in undersampled Magnetic Resonance Imaging (MRI) reconstruction, but their requirement for paired data limits their generalizability to the diverse MRI acquisition parameters. Recently, unsupervised controllable generative diffusion models have been applied to undersampled MRI reconstruction, without paired data or model retraining for different MRI acquisitions. However, diffusion models are generally slow in sampling and state-of-the-art acceleration techniques can lead to sub-optimal results when directly applied to the controllable generation process. This study introduces a new algorithm called Predictor-Projector-Noisor (PPN), which enhances and accelerates controllable generation of diffusion models for undersampled MRI reconstruction. Our results demonstrate that PPN produces high-fidelity MR images that conform to undersampled k-space measurements with significantly shorter reconstruction time than other controllable sampling methods. In addition, the unsupervised PPN accelerated diffusion models are adaptable to different MRI acquisition parameters, making them more practical for clinical use than supervised learning techniques.

Fast Controllable Diffusion Models for Undersampled MRI Reconstruction

TL;DR

The paper tackles undersampled MRI reconstruction using unsupervised diffusion models and addresses the slow sampling bottleneck and limited adaptability of prior methods. It introduces Predictor-Projector-Noisor (PPN), a DDIM-based sampling strategy that enforces k-space data consistency and re-noises at higher levels to keep trajectories within noisy manifolds, enabling fast, high-fidelity reconstructions without paired data or retraining. Empirically, PPN outperforms state-of-the-art controllable diffusion methods across BraTS and fastMRI datasets, achieving superior PSNR/SSIM at multiple accelerations while requiring far fewer diffusion steps. This approach enhances clinical practicality by delivering robust, acquisition-parameter-agnostic reconstructions with substantial speedups and without supervised training on specific undersampling patterns.

Abstract

Supervised deep learning methods have shown promise in undersampled Magnetic Resonance Imaging (MRI) reconstruction, but their requirement for paired data limits their generalizability to the diverse MRI acquisition parameters. Recently, unsupervised controllable generative diffusion models have been applied to undersampled MRI reconstruction, without paired data or model retraining for different MRI acquisitions. However, diffusion models are generally slow in sampling and state-of-the-art acceleration techniques can lead to sub-optimal results when directly applied to the controllable generation process. This study introduces a new algorithm called Predictor-Projector-Noisor (PPN), which enhances and accelerates controllable generation of diffusion models for undersampled MRI reconstruction. Our results demonstrate that PPN produces high-fidelity MR images that conform to undersampled k-space measurements with significantly shorter reconstruction time than other controllable sampling methods. In addition, the unsupervised PPN accelerated diffusion models are adaptable to different MRI acquisition parameters, making them more practical for clinical use than supervised learning techniques.
Paper Structure (9 sections, 6 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 9 sections, 6 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. methodology
  3. Preliminary: Diffusion Models
  4. MRI Inverse Problems
  5. Predictor-Projector-Noisor (PPN) method
  6. experiments
  7. Ablation study
  8. Results
  9. Conclusion

Figures (3)

  • Figure 1: Illustration of a proposed PPN generation step.
  • Figure 2: MRI reconstructions for BraTS menze2014multimodal_brats1bakas2017advancing_brats2 and fastMRI knee and brain zbontar2018fastMRI at 8× acceleration, 50 NFEs.
  • Figure 3: Performance vs. NFEs for 4× accel. reconstruction on BraTS menze2014multimodal_brats1bakas2017advancing_brats2. Shaded areas represent standard deviations.