Display Omitted Highly promising and applied noisy multispectral image fusion.Adopting the matrix of structure tensor to fuse the gradient information.Gradient entropy metric-based weighted gradient to extract image features, avoiding noise interference.Local adaptive p-Laplace diffusion constraint is constructed while rebuilding the fused gradient field rebuilding the fused image from the fused gradient field. Noise is easily mistaken as useful features of input images, and therefore, significantly reducing image fusion quality. In this paper, we propose a novel gradient entropy metric and p-Laplace diffusion constraint-based method. Specifically, the method is based on the matrix of structure tensor to fuse the gradient information. To minimize the negative effects of noise on the selections of image features, the gradient entropy metric is proposed to construct the weight for each gradient of input images. Particularly, the local adaptive p-Laplace diffusion constraint is constructed to further suppress noise when rebuilding the fused image from the fused gradient field. Experimental results show that the proposed method effectively preserves edge detail features of multispectral images while suppressing noise, achieving an optimal visual effect and more comprehensive quantitative assessments compared to other existing methods.