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.
