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As a popular signal modeling technique, sparse representation (SR) has achieved great success in image fusion during the last decade. However, due to the patch-based manner adopted in standard SR models, most existing SR-based image fusion methods suffer from two drawbacks, namely, limited ability in detail preservation and high sensitivity to mis-registration, while these two issues are of great concern in image fusion. We introduce a recently emerged signal decomposition model known as convolutional sparse representation (CSR) into image fusion to address this problem, which is motivated by the observation that the CSR model can effectively overcome the above two drawbacks. A CSR-based image fusion framework is proposed for multi-focus image fusion and multi-modal image fusion. In addition, we also extend the CSR model from single-component to multi-component for image fusion via the morphological component analysis (MCA) technique. Experimental results demonstrate that the proposed CSR-based fusion methods clearly outperform conventional SR-based methods in terms of both objective assessment and visual quality.