In order to address the potential deviation in rank function approximation caused by the kernel function used in the latent low-rank representation(LatLRR) method, an approach based on Schatten-p norm and latent low-rank decomposition was proposed. Theoretical analysis and experimental validation were conducted using this method. The images were first denoised using a median filtering method. The images were decomposed into low-rank and salient parts using the Schatten-p norm-based latent low-rank decomposition method combined with LatLRR. Then, an arithmetic mean strategy was employed to fuse the low-rank parts of the infrared and visible light images, while a summation strategy was used to fuse their salient parts. Finally, a summation strategy was applied to fuse the already merged low-rank and salient parts, resulting in fused infrared and visible light images with clear texture information and prominent thermal fault information. Through qualitative and quantitative experimental analysis, a p-value of 0.6 was determined to achieve the optimal fusion effect, and the proposed method outperformed seven other algorithms in fusion performance comparison. Through this approach, rich structural information at both global and local levels in infrared and visible light source images of power systems can be effectively captured.