To address the low signal-to-noise ratio of infrared images and their vulnerability to the impact of the background environment, this study proposes an image enhancement algorithm based on non-separable wavelet based multiscale directional analysis (NSWMDA) and linking synaptic computation network (LSCN). Firstly, the original image is subjected to non-separable wavelet transform (NSWT) with redundant lifting, which yields a high-frequency detail subband and a low-frequency approximation subband. Then, the high-frequency detail subband is filtered in multi-direction before its enhancement by the LSCN algorithm, while the low-frequency approximation subband is directly enhanced by the LSCN algorithm. Finally, the processed sub-images are fused and reconstructed to constitute the enhanced infrared image. In the infrared image of a power transformer, the edge strength, information entropy, peak signal-to-noise ratio, structural similarity and average gradient of the proposed algorithm are at least 10.86%, 14.39%, 19.95%, 7.06%, and 6.70% higher than those of other algorithms. The experimental results show that the algorithm not only improves the overall clarity of the infrared image but also strengthens the detail texture and contrast of the image. It has a good infrared image enhancement effect and thus a bright application prospect for power equipment detection.