## 2 Methods  
### Network Architecture  
Figure 1 illustrates the network architecture under the extended many-to-one framework. The aim of the intensity standardization generator \(G_{forward}\) is to transform every T2-FLAIR MR image slice \(x_{n,m}\), where \(n\in\{1,\ 2,\cdots,\ N\}\) represents the group which the slice is from and \(m\in\{1,\ 2,\cdots,M_{n}\}\) is the slice number in the \(n_{th}\) group, ensuring \(G_{forward}\left(x_{n,m}\right)\) \"seems to be\" from the \(N_{th}\) group, which is treated as the reference, while keeping its own structure/tissue properties. \(N\) reverse transformations \(G_{backward\ n}\) are established, ensuring that \(G_{backward\ n}\left(G_{forward}\left(x_{n,m}\right)\right)\approx x_{n,m}\), which could indicate the preservation of image-specific structure/tissue properties. A forward discriminator \(D_{forward}\) and \(N\) backward discriminators \(D_{backward\ n}\) are also applied to form the GAN structures. Each \(G\) is optimized in turn with the corresponding \(D\) during the training process to form the adversarial scheme so that the intensity distribution of the generated images is gradually close to that of the corresponding reference ones.  
Figure 1: The network architecture of the proposed method. Different groups of MR images acquired from different machines or using different acquisition parameters are standardized with a same forward generator \(G_{forward}\) while the standardized images are transformed back using \(G_{backward\ n}\) to evaluate the information consistency.  
Each generator shown in Figure 2, in particular, consists of a convolutional concentration path, a low-dimensional feature extraction residual convolution path, a convolutional dispersion path, and jump connection paths. The convolutional concentration path contains a preprocessing convolution layer and two strided convolution layers. The dispersion path contains two strided transposed convolution layers and a synthetical transposed convolution layer. Two jump connections feed the feature maps before and during the concentration process into the corresponding position in the dispersion path to provide more details of input images [23].  
The low-dimensional feature extraction residual convolution path employs cascading residual network (CARN) blocks in order to provide more \"fast propagate\" jump connections and acquire multi-level representations by integrating features between layers [24]. This may significantly increase the information richness of the generated images, thus be conducive to image resolution. Such residual  
Figure 2: The structure of the proposed generative networks. The orange arrow indicates the cascading block in the dotted box at the bottom right of the figure. The plum arrow within the cascading block indicates the residual block in the dotted box at the bottom left of the figure. All submodules in the same parent module share a same set of parameters.  
convolution path consists of three cascading blocks. The \(1\times 1\) convolutional layers are instantiated after each cascading block to synthesize feature maps with fixed output channel number from all previous cascading blocks along with the original result of the concentration path. The cascading block consists of three residual blocks. Inside the cascading block, \(1\times 1\) convolutional layers are also instantiated after each residual block to build a fixed-channel intermediate feature map. A residual block contains two \(3\times 3\) convolutional layers, and the filter number is fixed to 256.  
The discriminators are classical PatchGAN with three successive \(4\times 4\) strided convolutions and two synthetical convolutions. Each convolution process applies leaky rectified linear unit (LeakyReLU) as the activation function. The discriminative feature map is \(30\times 30\) with a single layer, which is then used to create the final discriminative result.