Introduction

Diffusion MRI is a crucial tool for investigating microstructural tissue properties, particularly when high b values are used. However, the inherent low SNR in high b-value diffusion MR can present challenges in precisely characterizing these properties. Conventional MR averaging is limited in its ability to efficiently boost SNR, as it results in only a $$$\sqrt{N}$$$ increase in SNR for an N-fold increase in acquisition time. Alternatively, an increase in magnetic field strength can linearly improve SNR, but it often comes at the cost of high-field artifacts and substantial hardware expense.

To address the SNR limitations, denoising algorithms have been developed as post-acquisition processing techniques. These algorithms^1-3 leverage the inherent redundancy within medical images, offering a promising avenue to enhance SNR without the need for extensive hardware upgrades and longer acquisition times. Low-rank Tensor Dictionary Learning (LTDL)^4,5 exploits non-local spatial redundancies and image correlations across different b-values with learned dictionaries and low-rank tensor approximation, providing a promising denoising performance.

Method

Simulation: The simulation datasets used in this study were downloaded from online. Specifically, one dataset had an image size of 108$$$\times $$$90$$$\times$$$7 and a b-value = 1000 s/mm². The second dataset, with the same image size, was simulated at b-value = 2000 s/mm² . In both datasets, the third dimension included a b-value = 0 s/mm² and six distinct diffusion directions. (source: https://github.com/joey024/DWIdenoising)

Acquisition: TE/TR = 190/3000 $$$ms$$$ ; FOV = 220$$$\times $$$220 $$$mm^{2}$$$ ; Matrix size = 192$$$\times $$$192; Partial Fourier = 6/8; Slice thickness = 4 $$$mm$$$ ; Data at two b-values = 1000/2000 s/mm² with seven diffusion directions per b-value was acquired using a single shot EPI readout and a 32-channel head coil.

Denoising: the framework of denoising using the LTDL method is illustrated in Fig.1. The mathematic expression of LTDL is formulated as follows:$$ \min_{D_{_s},D_{_q}} \sum \left ( \left\| \chi ^{(k)} - Z^{(k)}\times _{_1} D_s \times _{_2}D_{_q} \right\|_F^2 + \lambda _s\left\| Z^{(k)}\right\|_1 + \lambda _{L}\left\| Z^{(k)}\times _{_1} D_s \times _{_2} D{_q} - G^{(k)}\times _{_1} U_2^{(k)} \times _2 U_3^{(k)}\right\|_F^{2} \right )$$
$$s.t. \left\| D_{s}(:,r)\right\|_{2}^{2} = 1 $$
$$s.t. \left\| D_{q}(:,r)\right\|_{2}^{2} = 1 $$
$$s.t. U_{i}^{(k)}U_{i}^{(k)} = I $$
where the denoised tensor group $$$\chi ^{(k)} $$$ is a sparse representation of two dictionaries, spatial domain dictionary $$$D_{s} $$$ and q space domain dictionary $$$D_{q} $$$ . These two dictionaries are learned from all tensor groups.$$$Z^{(k)}$$$ is the coefficient tensor of the tensor group. $$$\lambda _{S}$$$ and $$$\lambda _{L}$$$ are the weights for sparsity and low-rankness. In the last term, the tensor group is enforced to a low-rank tensor, where $$$G^{(k)}$$$ is a core tensor for tensor decomposition.

The commonly-used MPPCA¹, the recently developed WNNM-based denoising method³ and a pre-trained complex-valued DnCNN method⁶ were used for comparison.

Results

In the simulation, the proposed LTDL method exhibited superior denoising capabilities when compared to MPPCA and WNNM. Specifically, at a b-value of 1000 s/mm², LTDL achieved the lowest RMSE of 1.6/0.01 for diffusion-weighted images and mean diffusion coefficient, as compared to 1.54/0.016 for MPPCA and 2.59/0.013 for the WNNM method. These results were consistent when the b-value increased to 2000 s/mm².

For the in-vivo data, the proposed LTDL method demonstrated a promising ability of denoising while better preserving the image structure. This preservation is evident in areas whit low SNR, as indicated by the yellow arrow. Conversely, the WNNM method exhibited blurring in these low SNR areas. Furthermore, LTDL successfully identified and retained details represented by the black line, as indicated by the red arrow, which were missed by the DL-based method, although the DL-based method achieves higher denoising performance.

Conclusion

The LTDL method show promising results on denoising while keeping image structures when high b-values are given. However, a larger dataset is required to further demonstrate the effectiveness of the LTDL method.

Acknowledgements

No acknowledgement found.