Bo Zhao1,2, Borjan Gagoski2,3, Justin P. Haldar4, Elfar Adalsteinsson5, Ellen Grant3,6, and Lawrence L. Wald1,2
1Athinoula A. Martinos Center for Biomedical Imaging, Chalestown, MA, United States, 2Harvard Medical School, Boston, MA, United States, 3Boston Children's Hospital, Boston, MA, United States, 4Electrical Engineering, University of Southern California, Los Angeles, CA, United States, 5Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, United States, 6Radiology, Harvard Medical School, Boston, MA, United States
Synopsis
HAlf-fourier
Single-shot Turbo spin Echo (HASTE) acquisition is widely used in fetal MR
imaging due to its T2 contrast and motion robustness, but speed and
T2-blurring remain a problem for fully sampled acquisitions. In the
work, we describe a new reconstruction approach based on low-rank and subspace
modeling of local k-space neighborhood to accelerate HASTE acquisition. The
proposed approach decreases the echo-train length with improved image quality
and noise robustness compared to conventional reconstruction. It is compatible
with the vendor-provided acquisition. The effectiveness and utility of the
proposed approach is evaluated with both retrospectively and prospectively undersampled
fetal imaging data.
Introduction
Accelerated
HAlf-fourier Single-shot Turbo spin Echo (HASTE) acquisition is widely used in
fetal MRI1, since it provides good T2 contrast, and
improves motion robustness. Conventional reconstruction approach accelerates HASTE acquisition with a hybrid half-Fourier2 and GRAPPA3
reconstruction. While widely used in clinical practice, it enables only a low
to medium acceleration factor before severe noise amplification occurs. Recently,
we introduced a low-rank model-based approach to accelerate HASTE4,
which utilizes the linear predictability of local k-space neighborhood
associated with limited image support. The proposed approach provides better
image quality and noise robustness, and is compatible with the standard HASTE
acquisition scheme. In this abstract, we extend the early work to investigate an
alternative low-rank model, which models slowly-varying image phase. To enhance
the computational efficiency, we further incorporate a subspace constraint into
the reconstruction process. We demonstrate the effectiveness of the proposed
approach on both retrospectively undersampled data and
prospectively-undersampled data. Theory
Early work has shown that an
approximately low-rank matrix can be constructed by collecting patches of k-space
data, if the underlying image has a slow-varying image phase5. Here
we form such a data matrix, denoted as S∈CM×N. Moreover, to account for correlation
between multi-coil data6, we further form the matrix SP=[S1,S2,⋯,SL]∈CM×LN. Here, by enforcing the
low-rank property, i.e., rank(SP)≤r, we can formulate a matrix completion problem that enables reconstruction from sub-Nyquist data. Although
directly solving the matrix completion problem often provides good accuracy, it
often results in an expensive computational problem. To enhance the
computational efficiency, we further introduce a null space constraint7,
which pre-estimates the null space of SP from the full-sampled
calibration/training data. Figure 1 shows the singular
value decays respectively from SP and the calibration data, which follow a very similar
trend. More specifically, let the
column of Vs span the null space of SP. Enforcing both the low-rank constraint and the subspace constraint, we can
formulate the following image reconstruction problem: ˆz=arg minz∥Ps(T(d)+Tc(z))Vs∥22 where T is the linear operator that
maps the sampled k-space data into the complete k-space data vector, while
filling unsampled k-space locations with zeros; Tc is the linear operator
performing the complementary operation; and Ps maps the complete k-space
data to the data matrix SP. Note that with the subspace
constraint, the reconstruction problem reduces to a sparse linear least-squares
problem, which can be efficiently solved by a number of numerical algorithms
(e.g., the iterative LSQR algorithm).
Methods
We first evaluated the performance of the
proposed approach with retrospectively-undersampled data. Here we compared the
proposed approach with the conventional reconstruction. More specifically, under
an IRB approved protocol, we performed the HASTE acquisition on one healthy pregnant
woman at a 3T Siemens Skyra scanner, equipped with 20 coils. Here FOV = 360×360
mm2, slice thickness = 3.5 mm, and matrix size = 256×512. We
performed a half-Fourier acquisition covering the 5/8 of the k-space, and then
performed a factor of 4 undersampling in the outer k-space. The data
acquisition scheme is illustrated in Figure 2. With this acquisition scheme,
the net acceleration factor is 3. We compared the proposed approach with the
reference obtained from the fully-sampled data, and the conventional approach using the GRAPPA and half-Fourier reconstruction. To evaluate the utility of the proposed
approach, we further performed prospectively-undersampled HASTE acquisition of
three imaging slices and reconstructed the data using the proposed approach. Results
Figure 3
shows the results from the retrospectively-undersampled experiments. As can be
seen, the proposed method provides improved image quality compared to the
conventional reconstruction approach. In particular, it reduces the noise
amplification, while well preserving the anatomical structure of the fetal
brain. Figure 4 shows the results from the prospectively-undersampled
experiments. As can be seen, the proposed approach consistently provides
high-quality reconstructions for all the imaging slices. Conclusion
In this abstract, we
developed a new imaging approach to accelerate HASTE acquisition for fetal MRI.
The proposed approach enforces the low-rank modeling of local k-space
neighborhood, and further incorporates the subspace constraint to simplify the
computational problem. We demonstrated the effectiveness of the proposed
approach with both retrospectively-undersampled data and
prospectively-undersampled data.Acknowledgements
This work was support in
part by NIHR01EB017337 and NIH-U01HD087211.References
[1] A.
Gholipour, J. A. Estroff, C. E. Barnewolt, R. L. Robertson, P. E. Grant, B.
Gagoski, S. K. Warfield, O. Afacan, S. A. Connolly, J. J. Neil, A. Wolfberg,
and R. V. Mulkern. “Fetal MRI: A technical update with educational aspirations,”
Concepts Magn. Reson. Part A, vol. 43, pp. 237-266, 2014.
[2] D. C. Noll, D. G. Nishmura, and A.
Macovski, “Homodyne detection in magnetic resonance imaging,” IEEE Trans. Med.
Imag. vol. 10, pp. 154-163, 1991.
[3] M. A. Griswold, P. M. Jakob, R. M. Heidemann, M. Nittka, V. Jellus, J. Wang, B. Kiefer, and A.
Haase. “Generalized
autocalibrating partially parallel acquisitions (GRAPPA),” Magn. Reson. Med.,
vol. 47, pp. 1202-1210, 2002.
[4] B.
Zhao, Borjan Gagoski, Elfar Adalsteinsson, P. Ellen Grant, and Lawrence L. Wald,
“Accelerated HASTE-Based Fetal MRI with Low-Rank Modeling”, In: Proc. Int. Soc.
Magn. Reson. Med. 2016; p. 4820.
[5] J.
P. Haldar, “Low-rank modeling of local k-space neighborhoods (LORAKS),” IEEE
Trans. Med. Imag., vol. 33, pp. 668-681, 2014.
[6] J. P. Haldar and J. Zhuo, “P-LORAKS:
Low-rank modeling of local k-space neighborhoods with parallel imaging data,”
Magn. Reson. Med. vol.75, pp. 1499-1513, 2016.
[7] J.
P. Haldar, “Autocalibrated LORAKS for fast constrained MRI reconstruction”, in
Proc. IEEE Int. Symp. Biomed. Imaging, pp. 910-913, 2015.