Medical image fusion technology integrates the contents of medical images of different modalities, thereby assisting users of medical images to better understand their meaning. However, the fusion of medical images corrupted by noise remains a challenge. To solve the existing problems in medical image fusion and denoising algorithms related to excessive blur, unclean denoising, gradient information loss, and color distortion, a novel medical image fusion and denoising algorithm is proposed. First, a new image layer decomposition model based on hybrid variation-sparse representation and weighted Schatten p-norm is proposed. The alternating direction method of multipliers is used to update the structure, detail layer dictionary, and detail layer coefficient map of the input image while denoising. Subsequently, appropriate fusion rules are employed for the structure layers and detail layer coefficient maps. Finally, the fused image is restored using the fused structure layer, detail layer dictionary, and detail layer coefficient maps. A large number of experiments confirm the superiority of the proposed algorithm over other algorithms. The proposed medical image fusion and denoising algorithm can effectively remove noise while retaining the gradient information without color distortion.