In the context of non-uniformity correction (NUC) within infrared imaging systems, current methods frequently concentrate solely on high-frequency stripe non-uniformity noise, neglecting the impact of global low-frequency non-uniformity on image quality, and are susceptible to ghosting artifacts from neighboring frames. In response to such challenges, we propose a method for the correction of non-uniformity in single-frame infrared images based on noise separation in the wavelet domain. More specifically, we commence by decomposing the noisy image into distinct frequency components through wavelet transformation. Subsequently, we employ a clustering algorithm to extract high-frequency noise from the vertical components within the wavelet domain, concurrently employing a method of surface fitting to capture low-frequency noise from the approximate components within the wavelet domain. Ultimately, the restored image is obtained by subtracting the combined noise components. The experimental results demonstrate that the proposed method, when applied to simulated noisy images, achieves the optimal levels among seven compared methods in terms of MSE, PSNR, and SSIM metrics. After correction on three sets of real-world test image sequences, the average non-uniformity index is reduced by 75.54%. Moreover, our method does not impose significant computational overhead in the elimination of superimposed noise, which is particularly suitable for applications necessitating stringent requirements in both image quality and processing speed.