## 1 Introduction  
Heart disease is currently one of the most critical problems that greatly influence human health [1]. Previous studies have shown that the myocardial fiber structure is closely related to the systolic, diastolic, and electromechanical functions of the heart [2, 3]. Cardiac fiber disarray usually appears in the early stage of many cardiomyopathies [4]. Therefore, investigating the myocardial fiber structure is of great significance for understanding the causes of various cardiovascular diseases and potentially promoting their early diagnosis. At present, diffusion tensor imaging (DTI) is usually used for mapping the structure of fibrous tissues, which is currently the most promising method to elucidate in vivo myocardium structures non-invasively. However, due to the long acquisition time and the sensitivity of diffusion-weighted (DW) image signals to cardiac or breath motion, the acquired DW images are usually disrupted by the noise, which greatly influences the estimation accuracy of the cardiac fiber structure. To deal with the effects of noise on DW images, numerous post-processing methods have been proposed. The early DW image denoising methods are based on spatial filters [5, 6], edge regularizations [7, 8], sparse regularizations [9, 10], or prior information [11, 12, 13], such as adaptive smoothing methods, sparse dictionary-based methods, non-local means, Bayesian methods, etc. These traditional methods require manually setting many hyperparameters; in addition, they need to be optimized for each DW image individually, which is time-consuming and not stable. Accordingly, they are prone to introducingerrors in the subsequent analysis regarding diffusion metrics. To address these problems, according to the nature of DW image volumes, noise removing methods based on four-dimensional (4D) DW images have been proposed. For instance, [PERSON] et al. proposed an adaptive optimized non-local means (AONLM) [14], which fully considered the spatially or directionally varied noise level in DW images, and designed an adaptive noise filter according to the similarity of the local blocks. Subsequently, the authors presented another local principal component analysis (LPCA) method [15], which fully exploited the multidirectional redundancy of DW images, and used the thresholded principal component decompositions of each 4D local block to remove the noise in DW images. Recently, [PERSON] et al. proposed a novel method, Patch2 Self [16], which approximated the clean signal of a single DW image voxel from the noisy DW signals of several small local patches around this voxel along different directions through linear regression. Since the random noise cannot be linearly fitted, Patch2 Self can achieve better noise reduction performance on a variety of diffusion datasets. Even though the above-mentioned methods can deal with the spatially or directionally varying non-Gaussian noise in DW images, many of them are sensitive to the number of diffusion directions. When the number of diffusion directions is not sufficient, the performance of these methods decreases dramatically. Recently, emerging convolutional neural networks (CNNs) have provided another promising alternative for medical image denoising. Using the supervised CNN models can easily restore the noise-free images from the noisy observations by fully exploring the redundancy embedded in large image datasets. For instance, [PERSON] et al. proposed a denoising convolutional neural network (DnCNN) [17] which can achieve a better performance than traditional block matching and 3D collaborative filtering (BM3D) denoising methods [18] with an extremely simple architecture. Currently, CNN-based denoising methods have been widely used in X-ray [19], PET [20; 21], CT [22; 23], and MRI images [24]. Regarding DW images, [PERSON] et al. first proposed a joint denoising CNN (JD-CNN) model which can effectively reduce noise by taking multiple b-value DW images as the multichannel input of the network [25].