## 2 Related Anomaly Detection Works  
For better observation of the changes in the brain caused by AD, there has been a tremendous effort in the medical imaging field. Multiple machine learning applications have been proposed to classify different stages of AD using brain images [34; 35; 36]. Different imaging techniques such as PET [37; 38], structural magnetic resonance imaging (sMRI) [39; 40], functional magnetic resonance imaging (fMRI) [18; 41; 42] have been used in AD diagnosis. It has also been shown that multi-modal use may increase the performance compared to a single modal [43]. For example, using the ADNI dataset, [PERSON] et al. [44] propose a multi-modality CNN model for binary classification of AD vs. NC with a classification score of 93.26%. [PERSON] et al. [45] achieved a remarkable 97.37% F1 score with their proposed method. Various implementations of GANs in medical imaging have also opened new possibilities from image segmentation [46] to image translation [47]. GANs are a type of generative machine learning framework that includes a generator that creates realistic images, usually from random noise, and a discriminator that identifies if the input image is real or fake. The generator is usually a decoder that learns the input data distribution from the latent vector, and the discriminator generally has a classic architecture that reads the input image and discriminates fake images from real images. The comparison between the novel GAN framework and the proposed model can be seen in Figure 1.  
Due to their potential uses, GANs have been examined in great depth [48] and many approaches have been proposed to improve their stability [49]. A well-known work, called Deep Convolutional GAN (DCGAN) [50], removes fully-connected layers and makes use of convolutional layers and batch normalization [51]. With the use of Wasserstein loss, the performance is improved even further [52]. Figure 1: The comparison between the novel generative adversarial network (GAN) and the proposed model architecture. (**a**) GAN takes a random noise as an input, reconstructs the image using a decoder and the discriminator distinguishes between the normal input image and the reconstructed image. (**b**) The proposed model takes a real input image, obtains the latent vector using the embedded parallel network that is comprised of a conventional convolutional neural network (CNN) pipeline, and a dilated convolutional neural network (DCN) pipeline, and reconstructs the image. The discriminator then distinguishes between the normal input image and the reconstructed image. More detailed information about the proposed model can be found in Section 3 and the details of the proposed architecture can be seen in Figure 2. (**a**) The novel GAN architecture. The input is a random noise vector that is built into an image with the generator. The constructed image and a real image from the dataset are then fed to the discriminator where they can be classified as real or fake. (**b**) The proposed model architecture. The input is an actual image that is sent through the parallel network to generate a latent vector which will then be used to reconstruct the image. This reconstructed image and the corresponding real image are fed to the discriminator where the discrimination between the real and the fake image can be made. shows the anomaly score during the inference by pinpointing an anomaly. Furthering this study, [PERSON] et al. [32] (EGBAD) uses BiGAN [55], examining joint training to map the data distribution end from the image and latent space, respectively. [PERSON] et al. [29] propose the use of a conventional autoencoder (GANomaly) with the addition of another encoder the decoder to jointly train the model and the discriminator with the additional latent space loss. Furthering their work, [PERSON] et al. [56] propose a U-Net-like [57] autoencoder model (Skip-GANomaly) with skip-connections trained jointly with a discriminator. The human brain has a structure with many unique features that can be extracted by different CNN models.