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Multi-modal medical image fusion (MMIF) is crucial for disease diagnosis and treatment because the images reconstructed from signals collected by different sensors can provide complementary information. In recent years, deep learning (DL) based methods have been widely used in MMIF. However, these methods often adopt a serial fusion strategy without feature decomposition, causing error accumulation and confusion of characteristics across different scales. To address these issues, we have proposed the Coupled Image Reconstruction and Fusion (CIRF) strategy. Our method parallels the image fusion and reconstruction branches which are linked by a common encoder. Firstly, CIRF uses the lightweight encoder to extract base and detail features, respectively, through the Vision Transformer (ViT) and the Convolutional Neural Network (CNN) branches, where the two branches interact to supplement information. Then, two types of features are fused separately via different blocks and finally decoded into fusion results. In the loss function, both the supervised loss from the reconstruction branch and the unsupervised loss from the fusion branch are included. As a whole, CIRF increases its expressivity by adding multi-task learning and feature decomposition. Additionally, we have also explored the impact of image masking on the network's feature extraction ability and validated the generalization capability of the model. Through experiments on three datasets, it has been demonstrated both subjectively and objectively, that the images fused by CIRF exhibit appropriate brightness and smooth edge transition with more competitive evaluation metrics than those fused by several other traditional and DL-based methods. [ABSTRACT FROM AUTHOR]