Chaoyi Zhang^{1}, Tanzil Mahmud Arefin^{2}, Ukash Nakarmi^{3}, Hongyu Li^{1}, Dong Liang^{4}, Jiangyang Zhang^{2}, and Leslie Ying^{1,5}

Diffusion MRI has showed great potential in probing tissue microstructure and brain structural connectivity. However, high-resolution diffusion MRI with multiple direction is limited by the lengthy scan time. In this abstract, we apply a kernel low rank model to accelerate diffusion imaging by undersampling the k-space. This method is validated using high-resolution mouse brain datasets. Compared with the conventional compressed sensing method, the proposed method demonstrate more accurate mean diffusivity, fractional anisotropy and fiber orientation distribution estimates with acceleration factors up to 8.

**Reconstruction: ** In conventional compressed sensing^{14}, know sparsity constraints (in spatial direction) are added to the original linear equation for reconstruction of each DWI, leading to an optimization problem which needs to be solved by nonlinear algorithms. In the KLR method used in this study, a kernel low rank constraint (in diffusion direction) is added to the set of original linear equations for joint reconstruction of all DWIs, where the mathematical representation for the constraint is learned from a number of low resolution images obtained from the fully sampled central k-space data. Kernel principal component analysis, a machine learning approach, is used to obtain the constraint from the training data, which is represented as very few nonlinear diffusion bases. After these diffusion bases are obtained (o.e., the constraint is learned), an optimization problem is solved using an iterative approach enforcing two constraints:(a) each voxel of the reconstructed DWIs along the diffusion direction should be represented by the learned diffusion bases; (b) the k-space data of the reconstructed DWIs should be consistent with acquired data at all locations. The details of the KLR method can be found in [15].

**Acquisition&Analysis:** KLR
method was validated using post-mortem mouse brain (adult C57BL, n=5) data
acquired by a horizontal 7T MRI system. The
data was acquired using a 3D GRASE sequence described in [16] (TE/TR = 30/600msec,
spectral width = 120kHz) with two non-diffusion weighted images and thirty DWIs
(b = 2000/mm2, resolution = 0.1 mm isotropic, matrix size = 128x104x180).
The fully sampled k-space data was retrospectively under-sampled with reduction
factors up to 8 using different 2D variable density under-sampling patterns
along ky-kz for different diffusion directions. The reconstructed images were analyzed using
Mrtrix3. Mean diffusivity (MD), fractional anisotropy (FA), and fiber
orientation distribution (FOD)^{17} were used as evaluation metrics.

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