Learning the Domain Specific Inverse NUFFT for Accelerated Spiral MRI using Diffusion Models

TL;DR

This work tackles accelerating spiral MRI by combining diffusion-model-based reconstruction with non-Cartesian sampling. It introduces a multi-conditioning score-based method for the inverse NUFFT, augmented by frequency-guided sampling and trajectory optimization. Retrospective experiments on the NYU FastMRI dataset show optimized spiral trajectories and SSIM gains up to about $0.15$ over baselines, with ultra-fast readouts of $0.02$ s for a $256\times256$ image. The approach leverages multicoil data, diffusion priors, and trajectory design to enable extreme acceleration potentially suitable for real-time 3D MRI, though prospective validation with custom sequences is needed.

Abstract

Deep learning methods for accelerated MRI achieve state-of-the-art results but largely ignore additional speedups possible with noncartesian sampling trajectories. To address this gap, we created a generative diffusion model-based reconstruction algorithm for multi-coil highly undersampled spiral MRI. This model uses conditioning during training as well as frequency-based guidance to ensure consistency between images and measurements. Evaluated on retrospective data, we show high quality (structural similarity > 0.87) in reconstructed images with ultrafast scan times (0.02 seconds for a 2D image). We use this algorithm to identify a set of optimal variable-density spiral trajectories and show large improvements in image quality compared to conventional reconstruction using the non-uniform fast Fourier transform. By combining efficient spiral sampling trajectories, multicoil imaging, and deep learning reconstruction, these methods could enable the extremely high acceleration factors needed for real-time 3D imaging.

Figures (5)

• Figure 1: Example trajectories (A) and the corresponding readout gradients in $k_x$ and $k_y$ (B). All trajectories shown cover the frequency space of a 256x256 image and have a readout duration of 10.0 ms.
• Figure 2: Given measurements $y_0$, reconstruction follows a modified diffusion sampling process. At each timestep, a noisy latent $x_t$ is concatenated with a prior $p_0$ and passed to the denoising model to obtain $\tilde{x}_{t-1}$. To enforce consistency with $y_0$, we compute a frequency gradient $\nabla y_{t-1}$ and solve for the image gradient using a modified iterative inverse nufft (section \ref{['equation:modified_nufft']}). A weighted sum of $x_{t-1}$ and $\nabla x_{t-1}$ yields the corrected image $x_{t-1}$. This is repeated until $t=0$.
• Figure 3: Representative reconstruction results for a single 2D 16 coil image. Retrospective k-space data was sampled with an optimized 23 interleave sequence with a total readout duration of 0.02 s. Rows 1 and 2 show the RSS-reconstructed images and log-scaled k-space magnitudes for the ground truth, inverse nufft, and proposed model reconstructions. Below are the individual coil magnitude and phase images for the fully sampled image, the inverse nufft reconstructions, and the model predictions.
• Figure 4: We performed a grid hyperparameter search over a 2D trajectory space. We fixed readout duration at 0.02 seconds and varied the number of interleaves from 1 to 125 and alpha from 1 to 4. Based on structural similarity of the model-reconstructed images, we found multiple trajectories that yield improved image quality. In comparison, the naive Archimedean spiral, corresponding to 1 interleave and $\alpha=1$, performs very poorly.
• Figure 5: (A) Effect of sampling trajectory optimization, model reconstruction without frequency guidance, and model reconstruction with frequency guidance. For the non-optimized trajectory, we used a single interleave Archimedean spiral with a readout duration of 0.02 s. The optimized trajectory uses a 23 interleave, $\alpha=1.23$ sequence with an identical readout duration. (B) Snapshots of the image latent $x_t$ and the gradient signal $\nabla x_t$ taken during a diffusion sampling process.