Stefan Manfred Spann^{1}, Christoph Stefan Aigner^{1}, Matthias Schloegl^{1}, Andreas Lesch^{1}, Kristian Bredies^{2}, Stefan Ropele^{3}, Daniela Pinter^{3}, Lukas Pirpamer^{3}, and Rudolf Stollberger^{1,4}

3D imaging sequences such as GRASE or RARE-SoSP are the preferable choice for acquiring ASL images. However, a tradeoff between the number of segments and blurring in the images due to the T2 decay has to be chosen. In this study we propose a reconstruction algorithm based on total generalized variation for reducing the number of segments and therefore the acquisition time of one image. We incorporate the averaging procedure in the reconstruction process instead of reconstructing each image individually. This allows exploiting temporal redundancy and spatial similarity for improving the reconstruction quality of ASL images.

Four healthy volunteers were scanned at a
3T MR system (Prisma, Siemens Healthcare, Germany) using pseudo-continuous ASL
labeling with a 3D GRASE readout.^{9} The following imaging parameters were used: matrix
= 64x64x46, 46 slices with 10% slice oversampling, 3mm isotropic resolution, TR/TE=4000/16 ms, EPI-factor=21, TF=17, PLD=1800ms, 9 segments,
4 C/L-pairs resulting in an acquisition time of 4min 48s for the whole k-space. K-space
data were retrospectively under sampled as illustrated in Figure 1, using 21
phase encodings in ky which corresponds to an EPI factor of 21. In slice
direction every second line is acquired yielding two segments and a third
additional segment covering the center of k-space is used for each average (21
central lines of the 17 central slices).
For baseline evaluations a synthetic
CBF-map was generated.^{10} Zero mean complex Gaussian
noise was added to the C/L-raw-data. For the synthetic dataset 3D coil
sensitivity profiles were simulated using Biot-Savart’s law. For in-vivo
datasets coil sensitivity profiles were estimated using the method proposed by
Walsh.^{11}
The image reconstruction is done solving the
following minimization problem using primal dual algorithm^{12}:

$$\min_{u_c, u_l} \frac{\lambda_c}{2}\left\|(MFC\mathbf{1}u_c - U_c^{\delta})\right\|_2^2 + \frac{\lambda_l}{2}\left\|(MFC\mathbf{1}u_l - U_l^{\delta})\right\|_2^2 + \gamma_1(s)TGV_{\alpha1,\alpha0}(u_l) + \gamma_2(s)TGV_{\alpha1,\alpha0}(u_c - u_l)$$

where
$$$u_c\,$$$and$$$\,u_l$$$ are the 3D reconstructions, $$$\lambda_c$$$ is the
regularization parameter for the control data and set to 11, $$$\lambda_l$$$ is
the regularization parameter for the label data and set to 15. The parameter s
controls the weighting between the two TGV terms and is calculated as described
in^{13}, $$$ U_c^{\delta}\,$$$and$$$\,U_l^{\delta}$$$ are the acquired 4D
C/L-images, $$$\alpha1\,$$$and$$$\,\alpha0\ $$$ are fixed model parameters.^{8}
The $$$\mathbf{1}$$$-operator generates a number of identical
copies of $$$u_c\,$$$and$$$\,u_l$$$
over the temporal dimension. $$$C$$$ are the coil sensitivity maps, $$$M$$$
is a mask containing the undersampling pattern and $$$F$$$ is the Fourier
operator.

This work was funded by the Austrian Science Fund "SFB 3209-18".

NVIDIA Corporation Hardware grant support.

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Figure 1: K-space acquisition pattern: The
number of phase encodings ky is 21 which corresponds to an undersampling of 3
in phase direction. In slice direction each second line is acquired leading to
two segments for the whole k-space. Additionally, for each average one segment
is used to acquire the center of the k-space (21 central lines of the 17
central slices) resulting finally in 3 segments.

Figure 2: Synthetic generated PWIs, PWIs using
standard reconstruction with 9 and 3 segments and PWIs reconstructed from 3
segments using the proposed algorithm. For reconstruction of all PWIs 4
averages are used.

Figure 3: Standard PWI reconstruction from
one subject using the fully sampled data (9 segments) compared to PWI
reconstructed using the proposed algorithm with 3 segments (US = 3).

Figure 4: Exemplary PWIs from 3 subjects
using standard reconstruction from the fully sampled data (9 segments) compared
to the proposed method with 3 segments.