Sidharth Kumar^{1}, Asad Aali^{1}, and Jonathan I Tamir^{1,2,3}

^{1}Chandra Family Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX, United States, ^{2}Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, United States, ^{3}Department of Diagnostic Medicine, University of Texas at Austin, Austin, TX, United States

Score-based generative modeling has emerged as a powerful tool for modeling image priors and has recently been used to solve ill-posed inverse problems in various domains including MRI reconstruction. Here we extend the framework to reconstruct multi-contrast 3D fast spin-echo (FSE), i.e. T2 Shuffling data. This is achieved by constraining the posterior sampling reconstruction to a low-dimensional subspace and training a score model on images from this subspace. We demonstrate a proof-of-principal reconstruction of data with no model mismatch, i.e. generated from the forward model.

In recent parallel work, deep learning generative modeling has been used to model image priors separately from the measurement model and has been successfully applied to MRI reconstruction, showing great potential to reduce scan time beyond the abilities of compressed sensing

$$y=PFS\mathrm{\Phi}\alpha +w,\text{}w\sim \mathcal{N}(0,{\sigma}^{2}I),$$

$${\alpha}^{(t+1)}\leftarrow {\alpha}^{(t)}+{\eta}_{t}({s}_{\theta}({\alpha}^{(t)})+{\beta}_{t}{A}^{H}(y-A{\alpha}^{(t)}))+\sqrt{2{\eta}_{t}}{\zeta}_{t}\text{,}{\zeta}_{t}\sim \mathcal{N}(0,I),$$

This work was supported by NSF IFML 2019844 and NIH U24EB029240. We would like to thank Shreyas Vasanawala, Marc Alley, and Lucile Packard Children's Hospital for their assistance with scan data.

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Fig. 1 a) Illustration of the training process of the score model. The process involves randomly choosing a noise level at each step and adding that to the training samples. The perturbed samples are passed through the score network which predicts the gradient of the log prior. b) Posterior sampling procedure for basis coefficient estimation using score model prior from given y (under-sampled kspace data).

Fig. 2 Animation showing sampling from the learned prior. The score model is run independently with random initializations. This shows the score model's ability to generate images from the learned distribution. The model starts with gaussian noise and uses Annealed Langevin Dynamics to sample from the prior distribution.

Fig. 3 Animation of the posterior sampling reconstruction process. Images are shown at each iteration for the three basis coefficient images.

Fig. 4 Reconstructed basis coefficient images compared to the ground-truth T2Sh reconstruction and the difference image which is shown with a 10X scale. The score model output images match the ground truth images within acceptable NRMSE error values.

Fig. 5 Reconstructed time-series multi-contrast images as a function of the echo time. The first row represents the images reconstructed by the score-based posterior sampling, whereas the second row shows the T2Sh reconstruction acting as a ground-truth. The signal evolution as a function of the echo time index is shown in the bottom plot for two different tissue values (muscle and bone). Visually it can be observed that the score model output signal evolution is in very good agreement with T2Sh curves.