T2 Shuffling Fast 3D Spin-Echo Reconstruction with Score-Based Generative Modeling

Sidharth Kumar

1

, Asad Aali

1

, Jonathan I Tamir

1,2,3

1

Chandra Family Department of Electrical and Computer Engineering,

2

Oden Institute for Computational Engineering and Sciences,

3

Department of Diagnostic

Medicine, University of Texas at Austin, Austin, TX, United States

Target Audience: MRI researchers interested in image reconstruction and deep learning.

Introduction: Volumetric fast spin-echo (3DFSE) is desirable for multi-planar

reformatting, but it has not been routinely used clinically due to T2-decay induced

blurring

1-3

. Recently, a method called T2 Shuffling (T2Sh) has been proposed which

generates images along the FSE signal relaxation curve, thus reducing blur and providing

multi-contrast images

4

. While this approach has been shown to be noninferior to clinical

2D FSE

5,6

, it still requires scan times in excess of 7 minutes

5

. Recently deep learning-

based score models have been applied to MRI with promising reconstruction results with

under-sampling, exceeding the performance of traditional compressed sensing methods.

7

In this work, we train the score model to learn a prior that is used to reconstruct T2Sh

data through posterior sampling

8

. We use the basis coefficient images from the low-rank

T2Sh reconstruction to train the score model and apply posterior sampling to

retrospectively accelerated data with no model mismatch. We show performance over

different acquisition signal-to-noise (SNR) levels in this setting. Finally, we show

preliminary results of our approach for experimentally acquired under-sampled T2Sh

data.

Methods: For this work, we trained the score model on 5000 basis coefficient knee

images, which were acquired with IRB approval and informed consent/assent. As the

score model is only trained on basis images, it is agnostic to MRI sampling and hence it

can be customized to different sequence parameters. The T2Sh forward model is as follows:

! " #$%&' ( )*+++) , -+

.

/* 0

!

1

2

where

' 3 4

"

are the basis coefficient images,

& 3

5

#×"

is the basis,

%+

is the coil sensitivity maps,

$

is the Fourier transform operator,

#+

is the

k-space sampler, and

)+

is Gaussian noise.

6+

is the FSE echo train length (ETL) and

7+

is the

number of basis coefficients. We define the forward operator as

8 " #$%&

. The MRI

reconstruction is done using posterior sampling which uses Annealed Langevin Dynamics

7

as follows:

9

%&'

: 9

%

+( ;

%

<

=

(

.

9

%

2

( >

%

?

)

.

@ A ?9

%

2

B

( C.D;

%

2+E

%

+* E

%

, F./*G2+

where

'

*

are the estimated basis coefficient images at step t,

H

*

is the learning rate,

I

+

is the score

model output,

J

*

+

is the weight of the data consistency term,

8

,

is the adjoint of the forward

operator, and

K

*

is the annealing noise. For the first set of experiments, the under-sampled

k-space data is generated from the forward model as a proof of principle to show that the

score model-based posterior sampling can reconstruct coefficient images, noting that this is

an inverse crime

9

. For this set of results, we treat T2Sh reconstruction as a “ground truth.”

In the second set of results, we incorporate varying SNR levels in the forward model and

compare the reconstruction results. For the third set of

results, we run the posterior sampling on experimental

under-sampled T2Sh k-space data.

Results and Discussion: Fig. 2 shows the reconstructed

basis coefficient images after posterior sampling using

the prior provided by the score model. The reconstructed

coefficient images and the ground truth coefficients agree

very well as corroborated by the low normalized root

mean squared error (NRMSE). Fig. 3 shows the effect of

different SNR levels. Noise is added to the under-

sampled k-space data corresponding to different SNR

values. It can be observed that as SNR increases, the

NRMSE for all 3 coefficients decreases. Fig. 4 shows the comparison between the output from

T2Sh and the score-based posterior sampling on the experimental data. Coefficient images seem

to qualitatively match both methods except for the 3

rd

coefficient image. For future work, we

will focus on improving score model posterior sampling to handle variation in SNR across the

basis images and experimental k-space data.

References: 1. Busse, MRM 60(3), 2008. 2. Mugler, JMRM 39(4), 2014. 3. Busse, MRM 55(5) 2006. 4. Tamir,

MRM 77(1) 2017. 5. Tamir, JMRI 49(7), 2019 6. Bao, MRM 74(2), 2015 7. Jalal, NeurIPS, 2021. 8. Song, NeurIPS,

2020. 9. Shimron, PNAS, 119(13), 2022.

1

Fig 1. A) Overview of the training process of

the score model. Training involves choosing

random noise levels at different steps and

adding them to the training samples and

making the score model predict the gradient.

B) Basis coefficient estimation using posterior

sampling from a given k-space measurements

y.

Fig 2. Reconstructed basis coefficient images

and ground truth coefficient images along with

difference image with 10X zoom.

Fig. 3. NRMSE vs SNR for reconstructed

basis coefficient images.

Fig. 4. Score model and T2Sh output images

on experimental k-space data.