Multifocus Image Fusion With Complex Sparse Representation

Multifocus image fusion aims to merge source images with distinct focused areas into a single, fully focused fused image. Sparse representation (SR) stands out as a robust signal modeling technique that has achieved remarkable success in multifocus image fusion. Numerous SR-based fusion methods have been proposed over the years, underscoring the importance of SR in enhancing fusion quality. However, a fundamental problem appearing in most existing SR models is the absence of directionality. This deficiency restricts their capacity to extract intricate details. To address this issue, we propose the complex SR ( $\mathbb {C}$ SR) model for image fusion. This model utilizes the properties of hypercomplex signals to extract directional information from real-valued signals through complex extension. Subsequently, the directional components of the input signal are decomposed into sparse coefficients over corresponding directional dictionaries. The key advantage of our design over conventional SR models is the ability to capture the geometrical image structures effectively, since $\mathbb {C}$ SR coefficients can provide precise measurements of detailed information along specific directions. Experimental results conducted on three widely used multifocus image fusion datasets substantiate the superiority of our method over 17 representative multifocus image fusion methods in terms of both visual quality and objective evaluation.