Technology-assisted clinical diagnosis has gained tremendous importance in modern day healthcare systems. To this end, multimodal medical image fusion has gained great attention from the research community. There are several fusion algorithms that merge Computed Tomography (CT) and Magnetic Resonance Images (MRI) to extract detailed information, which is used to enhance clinical diagnosis. However, these algorithms exhibit several limitations, such as blurred edges during decomposition, excessive information loss that gives rise to false structural artifacts, and high spatial distortion due to inadequate contrast. To resolve these issues, this paper proposes a novel algorithm, namely Convolutional Sparse Image Decomposition (CSID), that fuses CT and MR images. CSID uses contrast stretching and the spatial gradient method to identify edges in source images and employs cartoon-texture decomposition, which creates an overcomplete dictionary. Moreover, this work proposes a modified convolutional sparse coding method and employs improved decision maps and the fusion rule to obtain the final fused image. Simulation results using six datasets of multimodal images demonstrate that CSID achieves superior performance, in terms of visual quality and enriched information extraction, in comparison with eminent image fusion algorithms.