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Alzheimer's disease (AD) is an irreversible brain disease that severely damages human thinking and memory. Early diagnosis plays an important part in the prevention and treatment of AD. Neuroimaging-based computer-aided diagnosis (CAD) has shown that deep learning methods using multimodal images are beneficial to guide AD detection. In recent years, many methods based on multimodal feature learning have been proposed to extract and fuse latent representation information from different neuroimaging modalities including magnetic resonance imaging (MRI) and 18-fluorodeoxyglucose positron emission tomography (FDG-PET). However, these methods lack the interpretability required to clearly explain the specific meaning of the extracted information. To make the multimodal fusion process more persuasive, we propose an image fusion method to aid AD diagnosis. Specifically, we fuse the gray matter (GM) tissue area of brain MRI and FDG-PET images by registration and mask coding to obtain a new fused modality called "GM-PET." The resulting single composite image emphasizes the GM area that is critical for AD diagnosis, while retaining both the contour and metabolic characteristics of the subject's brain tissue. In addition, we use the three-dimensional simple convolutional neural network (3D Simple CNN) and 3D Multi-Scale CNN to evaluate the effectiveness of our image fusion method in binary classification and multi-classification tasks. Experiments on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset indicate that the proposed image fusion method achieves better overall performance than unimodal and feature fusion methods, and that it outperforms state-of-the-art methods for AD diagnosis.