Trevor Chan — MRI Reconstruction

Overview

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.

Chan, T.J. and Rajapakse, C.S., 2024, May. Learning the domain specific inverse NUFFT for accelerated spiral MRI using diffusion models. In 2024 IEEE International Symposium on Biomedical Imaging (ISBI) (pp. 1-5). IEEE.

(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, α = 1.23 sequence with an identical readout duration. (B) Snapshots of the image latent x_t and the gradient signal ∇x_t taken during a diffusion sampling process.

Example trajectories (A) and the corresponding readout gradients in k<sub>x</sub> and k<sub>y</sub> (B). All trajectories shown cover the frequency space of a 256×256 image and have a readout duration of 10.0 ms.

Example trajectories (A) and the corresponding readout gradients in k_x and k_y (B). All trajectories shown cover the frequency space of a 256×256 image and have a readout duration of 10.0 ms.

Given measurements y<sub>0</sub>, reconstruction follows a modified diffusion sampling process. At each timestep, a noisy latent x<sub>t</sub> is concatenated with a prior p<sub>0</sub> and passed to the denoising model to obtain x̃<sub>t−1</sub>. To enforce consistency with y<sub>0</sub>, we compute a frequency gradient ∇y<sub>t−1</sub> and solve for the image gradient using a modified iterative inverse NUFFT (section 3.3). A weighted sum of x<sub>t−1</sub> and ∇x<sub>t−1</sub> yields the corrected image x<sub>t−1</sub>. This is repeated until t = 0.

Given measurements y₀, reconstruction follows a modified diffusion sampling process. At each timestep, a noisy latent x_t is concatenated with a prior p₀ and passed to the denoising model to obtain x̃_t−1. To enforce consistency with y₀, we compute a frequency gradient ∇y_t−1 and solve for the image gradient using a modified iterative inverse NUFFT (section 3.3). A weighted sum of x_t−1 and ∇x_t−1 yields the corrected image x_t−1. This is repeated until t = 0.

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 α 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 α = 1, performs very poorly.