## 5 Discussion and Conclusions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Method** & **RMSE** & **PSNR** & **SSIM** & **AAE** \\ \hline \multirow{4}{*}{W/O edge} & DW images & 99.24 & 33.30 & 0.97 & – \\  & FA maps & 0.033 & 28.44 & 0.83 & – \\  & MD maps & \(3.25\times 10^{-5}\) & 39.68 & 0.99 & – \\  & Fiber orientations & – & – & – & 2.68 \\ \hline \multirow{4}{*}{Edge-weighted} & DW images & 86.29 & 34.51 & 0.97 & – \\  & FA maps & 0.029 & 29.38 & 0.85 & – \\ \cline{1-1}  & MD maps & \(2.95\times 10^{-5}\) & 4 0.52 & 0.99 & – \\ \cline{1-1}  & Fiber orientations & – & – & – & 2.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative comparisons between using and not using edge-weighted loss. the redundancy of the local signals is not sufficient; as a result, the performance of LPCA is not good, as expected. This can be observed in the denoising results of the synthetic dataset, where only six diffusion directions are used. DIP, NB2 NB, Patch2 Self, and SSECNN are recently proposed unsupervised or self-supervised learning-based image denoising methods. Of these, DIP and Neighbor2 Neighbor are used to deal with natural image noise, while Patch2 Self and SSECNN are designed for diffusion-weighted images. DIP assumes that the deep network can learn the image priors, meaning that using the random noise as the input and a noisy image as the target, the network can first learn the clean version of the noisy image and then learn the disrupted information. Based on this assumption, DIP uses an early stop strategy to denoise. Even though the DIP can remove the noise and use only one noisy image to train the network, this on-line learning process is not suitable to deal with a series of images since the iteration number of early stop for each individual image may be totally different. It is not practical to denoise DW image volumes by training a DIP network several times. In this work, all the denoised DW images along different diffusion directions are derived with the same early stop setting, which cannot guarantee that all the denoised DW images have already achieved their optimum status; accordingly, it performs worse on all the datasets. The methodologies of Neighbor2 Neighbor and SSECNN are essentially different from that of DIP; they use the self-similarity of different noisy image pairs to denoise rather than the deep network prior. The Neighbor2 Neighbor uses a downsampling operation to generate similar image pairs and then uses them to train the denoising network based on the Noise2 Noise method, while SSECNN leverages the SSIM between the DW images along different directions to obtain these image pairs. Since the spatial resolution of all the datasets used in this work is not high enough (128 \(\times\) 128 for the real dataset and 55 \(\times\) 55 for the synthetic dataset), the image pairs obtained with the nearest-neighbor downsampling may be not similar enough to meet the assumptions of Noise2 Noise; therefore, the performance of Neighbor2 Neighbor is not satisfactory. SSECNN searches the DW image pairs by maximizing the SSIM between the noisy DW images along different directions. For the synthetic dataset, SSECNN can achieve the better results, while for both ex vivo porcine and in vivo human cardiac DTI datasets, its performance decreases dramatically. This may be caused by the differences in noise distribution among the different datasets. In the synthetic dataset, the noise conforms to the Gaussian distribution, while in the real dataset, the noise usually conforms to the Rician distribution (as illustrated in Figure 10). Rather than using the image pairs to train the network to denoise, Patch2 Self uses a linear regression method to denoise. Specifically, for a given voxel along a certain diffusion direction, its clean DW signal is obtained by linearly fitting the DW signals of its surrounding neighbors along the other directions.