Peizhou Huang^{1}, Jingyuan Lyu^{2}, Hongyu Li^{3}, Yongsheng Chen^{4,5}, Saifeng Liu^{4}, Chaoyi Zhang^{3}, Ukash Nakarmi^{3}, E. Mark Haacke^{4,5}, and Leslie Ying^{1,3}

In many clinical applications, the three dimensional (3D) MRA plays an important role because that the 3D MRA can provide plenty of details for more compact anatomic regions with various flow directions. However, the speed limitation of the 3D MRA reconstruction is still an unignorable problem due to the size of the dataset, especially when the dataset has multi channels. With our proposed method, the Multi-Channel Blind Deconvolution (MalBEC), the experiment demonstrate that this method can provide high quality reconstruction image with high acceleration factors using much less time.

**Purpose**

**Methods**

The MalBEC formulates the image reconstruction problem from multi-channel
undersampled data as to recover the unknown k-space
data in all channels using blind deconvolution. An important feature of MalBEC
is that it implicitly utilizes the coil sensitivity information but without the
need to estimate it a priori. Different from the existing methods where either
sparsity constraints are applied in image domain (e.g., [4-7]) or rank
deficiency is applied in k-space (e.g., [8]) to estimate the coil sensitivity
information indirectly, MalBEC assume the coil sensitivities are smooth such
that they have limited support in k-space. The assumption is generally valid
for most phased array coils. In addition, MalBEC is highly efficient in
computation and is requires much shorter CPU time than the existing methods for
3D reconstruction. Specifically, we solve the desired k-space data **s**
and channel responses **h _{c}** alternatively:

s step:$$$s=arg\min _{s}\sum_c||y_{c}-Ω(s\circledast h_{c})||^{2}$$$ (1)

h step:$$$h_{c} = arg\min_{h_{c}}||y_{c}-Ω(s\circledast h_{c}||^{2}$$$ (2)

where **y**_{c }is acquired data and
**Ω** as the undersampling operation. Those two steps
are performed alternately and iteratively. After convergence, Fourier transform
of the k-space data **s** provides the desired image.

We
applied MalBEC on 3D MRA datasets. A healthy volunteer was recruited for the
study and written consents approved by the local Institutional Review Board
were obtained from the volunteer prior to the scans. All scans were performed
on a Siemens 3T Verio system (Siemens Healthcare, Erlangen, Germany) with a
product 32-channel head coil. An interleaved
three-echo GRE sequence [9,10] was used for acquisition where three images were
acquired within a single scan. The scanning parameters of the interleaved
three-echo GRE sequence were: TE1/TE2(flow-rephased)/TE3(flow-dephased)/TR =
2.5/13/13/20 msec, flip angle (FA)= 12, bandwidth = 260 Hz/pixel, voxel size =
0.67 × 0.67 × 1.2 mm^{3}, matrix size = 384 x 288 x 104. The two flow-rephased and
flow-dephased images were subtracted to generate an MRAV. To evaluate the
performance of MalBEC under different acceleration factors of 4, 5, 6, and 8,
we retrospectively undersample the 3D data with 2D pseudo-random mask [11] (in
phase encoding and partition encoding directions).

**Results**

**Conclusion**

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Figure 1. Whole brain Maximum intensity
projections (MIP) for reference 3D MRAV and
the reconstructed 3D MRAV at different acceleration factors.

Figure 2. 20 slices MIP image in the middle of reference 3D MRAV and the
reconstructed 3D MRAV at different acceleration factors.

Figure 3. 20 slices MIP image at the end of
the reference 3D MRAV and the reconstructed 3D MRAV at different acceleration
factors.