Improved Temporal Resolution TWIST Reconstruction using Annihilating Filter-based Low-rank Hankel Matrix

Eun Ju Cha^{1}, Kyong Hwan Jin^{1}, Dong-Wook Lee^{1}, Eung Yeop Kim^{2}, Seung-Hong Choi^{3}, and Jong Chul Ye^{1}

^{}Two sets of 3D DCE data, one for brain
and the other for carotid and cerebral vessel imaging, were obtained using
Siemens 3T Verio scanners. The TWIST sampling pattern for brain is shown in
Fig. 2(a). The imaging parameters are as following: repetition time (TR) 2.81
ms, echo time (TE) 1.04 ms, 192x252x40 matrix size, 32 coils and 60 time
frames. 1-D GRAPPA with 25 autocalibration lines was used. The TWIST sampling
pattern for carotid and cerebral vessels is shown in Fig. 2(c). The imaging
parameters are as follows: TR 2.5 ms, TE 0.94 ms, 159x640x80 matrix size, 16
coils and 30 time frames. 2D GRAPPA with 24x24 ACS regions was used. In
addition, the partial Fourier was applied, so only 63% of data was acquired. The
view sharing for GRAPPA for brain and carotid imaging are illustrated in Fig. 2(a)(c), respectively; whereas the corresponding view sharing scheme for ALOHA are shown in Fig. 2(b)(d).

The reduced view sharing in ALOHA causes
irregular sampling pattern, so GRAPPA cannot be used for reconstruction.
Furthermore, the conventional compressed sensing (CS)^{4} cannot be applied due to
severe aliasing artifacts. Therefore, we employed the ALOHA , where the cost
function is given by $$ \begin{eqnarray} \min_{\mathcal{Y}}&&
\|\mathcal{Y}\|_* \\ \mbox{subject to} &&\mathcal{Y} =
\begin{bmatrix}
\mathscr{H}\{\widehat{\mathbf{M}}_1\}~\cdots~\mathscr{H}\{\widehat{\mathbf{M}}_C\}
\end{bmatrix}, \end{eqnarray} \\
\hat{m}_i(\mathbf{k})=\hat{\phi}(\mathbf{k})\hat{y}_i(\mathbf{k}),\quad
\mathbf{b} \in \Omega,$$ where $$$\widehat{\mathbf{M}}_i$$$ is a matrix
constituted from samples of $$$\hat m_i(\mathbf{k})$$$, and
$$$\hat{\phi}(\mathbf{k})$$$ represents the wavelet spectrum that is used for
weighting. $$$\hat{y_i}(\mathbf{k})$$$ denotes the k-space measurement from the
$$$i$$$-th coil, and $$$\Omega$$$ is the k-space indices. We used ADMM
algorithm for minimization of this interpolation method^{3, 5}.

1. Laub, Gerhard, Randall Kroeker. syngo TWIST for dynamic time-resolved MR angiography. Magnetom Flash. 2006;34(3):92-95.

2.Griswold, Mark A., et al. Generalized autocalibrating partially parallel acquisitions (GRAPPA). Magnetic resonance in medicine. 2002;47(6):1202-1210.

3. Jin, Kyong Hwan, Dongwook Lee, and Jong Chul Ye. A general framework for compressed sensing and parallel MRI using annihilating filter based low-rank Hankel matrix. arXiv preprint arXiv:1504. 2015;00532.

4. Jung, Hong, et al. k-t FOCUSS: A general compressed sensing framework for high resolution dynamic MRI. Magnetic Resonance in Medicine. 2009;61(1):103-116.

5. Jin, Kyong Hwan, Jong Chul Ye. Annihilating filter based low rank Hankel matrix approach for image inpainting. 2015;24(11):3498-3511.

Fig 1. Three steps of the pyramidal
decomposition in ALOHA reconstruction.

Fig 2. View sharing scheme. The center and periphery of
k-space data are indicated by A and B, respectively. (a) Standard scheme for 1D
GRAPPA reconstruction. (b) Proposed scheme of brain data for ALOHA. (c)
Standard scheme for 2D GRAPPA reconstruction. (d) Proposed scheme of carotid
and vessel data for ALOHA.

Fig 3. (Upper) Low resolution image of brain data without view sharing. (Middle)
GRAPPA reconstruction. (Bottom) ALOHA reconstruction. Enlarged yellow boxes
indicate flow of contrast agent.

Fig 4. (a) Subtracted MIP images
of carotid and cerebral vessel using standard (upper) and ALOHA (bottom)
reconstruction. Yellow arrows indicate the differences. (b) Plots of relative
temporal intensity of superior sagittal sinus and distal internal carotid
artery in reconstruction.

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

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