Introduction

Diffusion-weighted MRI (DWI) provides valuable information for neuroscience study and disease diagnosis¹. However, the decreased SNR caused by the diffusion weighting gradients hinders the acquisition of high-resolution DWI images. Many efforts have been made to develop denoising methods by exploiting the intrinsic redundancy of DWI signals^2-4. Among these works, redundancy for local patches has been studied for denoising and is widely used^5-7. Denoising methods on complex-valued data have also been proposed⁸ . Currently MPPCA based on local low-rank is widely used for DWI denoising⁷. With that, also inspired by another non-local low-rank denoising work⁹, we propose a 2-step non-local low-rank denoising method to process complex-valued DWI images.

Theory

Two-step non-local low-rank denoising method
DWI images share structural similarities among different directions. Non-local methods can further improve the low-rankness by searching similar spatial patches with patch size 4. We implement a 2-step denoising method. The first step is to extract 3D patches across diffusion directions and then search non-local patches that are similar to each other. For this search, the noisy images are denoised using MPPCA first. Based on the Euclidian distance calculated from corresponding MPPCA-denoised patches, K=140 nearest patches are selected for each noisy patch. The second step is to denoise the noisy images based on the Casorati matrix formed by the selected non-local patches. For this, the singular value shrinkage is used to estimate the low-rank components.

Methods

Simulation dataset
Data from Fiberfox¹⁰ and HCP¹¹ were used for simulation. For Fiberfox dataset, the noise-free and artifact-free images were created by simulating diffusion signals across a 3D brain-like phantom using Fiberfox. Single-shell b1k noise-free data with 34 diffusion directions were used and the matrix size was 108×90×90. For the HCP dataset, the reference images were generated using a DTI model¹². Then we extracted 6 b0 and 30 b1k images from the generated reference images. The matrix size was 145×174×145. For both datasets, constant phase (=0) was added to generate complex images. 3D spatially variant noise with the characteristic of fast variations in x, and slow in y and z was added to the reference images¹³. Different noise levels were applied to test the performance.

In vivo dataset
We collected human brain images on a 7T MR scanner (Siemens, Erlangen, Germany), equipped with a body gradient (70 mT/m maximum strength and 200 T/m/s maximum slew rate). A healthy subject who signed a consent form approved by the local Institutional Review Board was scanned using the commercially available Nova 32-channel receive coil (Nova Medical Inc., MA).
We acquired slice-accelerated whole-brain DWI at 0.7-mm isotropic resolutions and with double-shell q-space sampling (b = 1k and 2k s/mm2). Relevant imaging parameters were: 2-fold slice acceleration and 3-fold in-plane acceleration, 6/8 partial Fourier, and TR/TE = 13370/91 ms. The data consisted of a total of 53 image volumes each obtained twice with opposed phase encoding. FLEET ACS ¹⁴ was utilized to minimize residual aliasing in final reconstructed images. Diffusion images of individual receive channels were reconstructed using the split-slice-GRAPPA algorithm ¹⁵ and were combined to form the final image via the SENSE combination method ¹⁶.
Using each dataset, we compared our method to existing methods including MPPCA and conventional non-local low-rank approach in which the patch searching was based on noisy images.

Result

For Fiberfox simulation data, the use of our method substantially improved the image quality (Fig. 1), outperforming MPPCA or conventional non-local low-rank approach, especially for higher noise levels. Quantitatively, it increased PSNR by up to 34.9% relative to the noisy images, by 3.7% relative to MPPCA and by 2.1% relative to the conventional non-local approach at noise level 10. The proposed method also provides higher SSIM.

Likewise, the use of our method largely improved image quality (Fig. 2) for the HCP simulation data, increasing PSNR by 16.8% relative to the noisy images, by 1.1% relative to MPPCA and by 0.6% relative to the conventional non-local approach at a moderate noise level 4. SSIM is also increased by the proposed method.

Correspondingly, the improvement in image quality translated into improvement in the color-coded fractional anisotropy (cFA) (Fig. 3) as obtained from FMRIB Software Library(fsl)¹⁷.

In agreement with the simulation, the use of our method substantially improved the image quality for the 0.7 mm in-vivo data (Fig. 4), outperforming both MPPCA and conventional non-local approach in terms of restoring gray white matter contrast. Accordingly, the use of our method led to a cFA map (Fig. 5) that best delineated brain structure with least noise levels.

Conclusion

We proposed a 2-step non-local low-rank denoising method to jointly denoise complex-valued DWI images. Using both simulation and in-vivo data, we demonstrated that the proposed method can suppress noise while preserving the fine structures and provide better denoising performances than existing methods though the computation time for patch selection is relatively long. Part of our future research is to investigate how our method may improve DWI at even higher resolutions.

Acknowledgements

This work was supported in part by the NIH grants NIBIB P41 EB027061 and NIH U01 EB025144.

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