## 1 Introduction
Subsequently, the DeepDTI model was proposed [26], which leverages a 3D CNN to denoise DW image volumes along six optimally selected diffusion directions. For providing a target to train the network in a supervised manner, numerous noise-free DW images are synthesized from the given tensors. DeepDTI can not only be used to denoise but also to accelerate DTI reconstruction since it uses only six directions. Despite the superior performance of these supervised learning-based methods, their requirement for additional noise-free images or large amounts of SNR data makes them difficult to use in clinical applications. In one aspect, large amount of noise-free images or large amounts of SNR data are almost unavailable; in the other aspect, well-trained CNNs are usually not generalized, so they cannot adapt well to new data with different image contrasts, noise levels, spatial resolutions, etc. Accordingly, this prohibits the real clinical applications of a supervised model. To address these challenges, unsupervised or self-supervised learning-based denoising methods have emerged. For instance, [PERSON] et al. used a deep image prior (DIP) model to denoise multiple b-value DW images [27]. It assumes that with some given network parameters, the output of the network can represent noise-free images. This is considered to be the prior of the deep network. Due to this assumption, the denoising performance of DIP is dependent on the iteration times. In other words, for DW images with different b-values or different diffusion gradient directions, the optimal iteration times will change since the optimal parameters for different DW images are totally different. This increases the difficulty in optimization; in addition, stability in the denoising performance cannot be guaranteed. Based on DeepDTI, the authors present another DTI denoising model, SDnDTI [28]. Instead of using synthesized clean data as the learning targets, SDnDTI uses the average of multiple repetitions of the synthesized noisy DW images as the target. This operation allows the model to train using its self-information rather than the additional ground-truth. Besides the models focused on DW images, there are numerous models that use self-information to denoise the natural images, such as Noise2 Noise [29], Neighbor2 Neighbor [30], Noise2 Void [31], Noise2 Self [32], Self2 Self [33],etc. The key of these methods is to generate similar image or block pairs from the noisy image-self, and to take them as the input and target of a learning network, respectively, to denoise. For instance, Noise2 Noise uses two noisy observations of the same scene obtained at different times as the input and target; in Neighbor2 Neighbor, the adjacent image patches in one noisy image are taken as the input and target; and Self2 Self it uses Bernoulli dropout sampling to form the input and target image pairs. These self-supervised learning-based denoising methods cannot directly be used on DW images since they do not consider the relationships among the DW images along different directions, which may cause problems for the subsequent diffusion tensor reconstruction. To solve this problem, recently, a structural-similarity-based convolutional neural network with edge-weighted loss (SSECNN) was proposed by [PERSON] et al. [34]. It explores the self-similarity in DW images along different directions to denoise, achieving promising results. However, the similarity between the noisy directional DW images in SSECNN was calculated with a structural similarity index (SSIM), which is very sensitive to noise and may introduce bias in similar image pair matching, therefore influencing its denoising performance. To address this issue, we propose a novel self-supervised cardiac DW image denoising network, Node2 Node, which uses graph framelet transform (GFT) [35] to divide the DW signals into different sub-bands, allowing it to more accurately search the similar DW image pairs in a band-to-band manner.