Shot-Coil Compression for Accelerated K-Space Reconstruction in Interleaved EPI DWI

Zijing Dong^{1}, Fuyixue Wang^{1}, Xiaodong Ma^{1}, Erpeng Dai^{1}, Zhe Zhang^{1}, and Hua Guo^{1}

For
large coil arrays, the computation time of parallel imaging methods becomes
longer due to the large datasets. To overcome the computation burden, coil
compression techniques have been developed which can
remove the redundancy in highly correlated multi-coil data. For multishot diffusion
imaging, conventional
coil compression methods that compress data only in coil dimension still result
in relatively long reconstruction time due to a large number of shots. Since
there are correlations between the data of different shots, we performed data
compression along both shot and coil dimensions as an extension of geometric-decomposition
coil compression (GCC) ^{3} method for multishot diffusion imaging. As
shown in Fig. 1, the proposed method is
divided into three steps,

1. Shift the k-space data of different shots to the same sampling pattern. The same operation is then performed to the corresponding 2D navigator of each shot.

2. Reshape the data to combine the coil and
shot dimensions, then we get a new encoding dimension of
$$$N_{c}\times N_{s}$$$, where
$$$N_{c}$$$ is the number of coils,
$$$N_{s}$$$ is the number of shots. 2D navigator data are used to solve the following minimization problem and obtain the compression matrix $$$A$$$ ^{3}.

$$minimize(A_{x}) \; \sum_{x,k_{y}}\parallel (A_{x}^HA_{x}-I)d_{x}(k_{y}) \parallel$$

$$subject \, to \; A_{x}A_{x}^H=I$$

Here, $$$A_{x}$$$ is the compression matrix of the encoding dimension ($$$N_{c}\times N_{s}$$$) at spatial location $$$x$$$ and $$$d_{x}(k_{y})$$$ is the k-space data from all dimensions at spatial location $$$x$$$ and k-space coordinate $$$k_{y}$$$ .

3. Compress the aligned shot-coil encoding dimension using the compression matrix $$$A$$$.

After compression, the data size is largely reduced and SYMPHONY ^{1} is
used to reconstruct the diffusion images.

A simulation was designed to compare the shot-coil compression method with the conventional GCC method. A 32-channel non-diffusion weighted 8-shot dual spin-echo EPI image was used as a reference. Spatially random phases (third-order) were added to 8-shot data respectively, to simulate the motion-induced phase variations in diffusion weighted images. The matrix size of the data was 240×232. 240×16 ACS data in the center of k-space were used to calculate the compression matrix. Compression rate is defined as the ratio of original and compressed encoding dimensions. The proposed method was compared with the conventional GCC method at various compression rates. Single kernel GRAPPA SYMPHONY was used to reconstruct the simulated data.

In-vivo brain DTI data was also acquired to validate the feasibility of the proposed method. The multishot diffusion tensor images were acquired from a
healthy volunteer on a Philips 3T scanner (Philips Healthcare, Best, The
Netherlands) with the following parameters: number of shot=8, FOV=240×240 mm^{2}, slice thickness=4 mm, TR/TE=2500/77 ms,
in-plane image resolution=1×1 mm^{2}, the number of diffusion
directions=12 with b value=800 s/mm^{2}, navigator size=240×25, Number of Signals Averaged (NSA)=2.

1. Xiaodong M, Zhe Z, et al. High Resolution Spine Diffusion Imaging using 2D-navigated Interleaved EPI with Shot Encoded Parallel-imaging Technique (SEPARATE). In Proceedings of the 23th Annual Meeting of ISMRM, Montreal, Canada, 2015. p. 2799.

2. Liu W, Zhao X, Ma Y, et al. DWI using navigated interleaved multishot EPI with realigned GRAPPA reconstruction. Magnetic Resonance in Medicine, 2015.

3. Zhang T, Pauly J M, Vasanawala S S, et al. Coil compression for accelerated imaging with Cartesian sampling. Magnetic Resonance in Medicine, 2013, 69(2): 571-582.

FIG. 1. The schematic diagram of the proposed method using a 2-shot
3-channel acquisition as an example.

FIG. 2. The
nRMSEs of the proposed method and the conventional coil compression at
different compression rates.

FIG. 3. Reconstructed images and the corresponding
error maps(×10) by SYMPHONY with and
without compression. The nRMSEs between reconstructed images and the reference are
shown at the right-bottom of each error map.

FIG. 4. Diffusion weighted images (a) and FA maps (b) of two slices. The high
resolution FA maps reconstructed by the proposed method with compression rate
of 16 are close to those by SYMPHONY without compression.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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