Stripe non-uniformity severely affects the quality of infrared images. It is challenging to remove stripe noise in low-texture images without blurring the details. We propose a single-frame image stripe correction algorithm that removes infrared noise while preserving image details. Firstly, wavelet transform is used for multi-scale analysis of the image. At the same time, Total variation model is used for small window to smooth the original image. The small-scale total variation model can well preserve the edge information of the image, but it will leave stripe noise. Therefore, according to the prior knowledge of the vertical component of the stripe noise, the spatial filtering is finally performed: the smoothed image is used as the guide image for the stripe noise denoising. It is possible to prevent the lead filter from mistaking the strong stripe noise as edge detail, resulting in corrected image residual streak noise. The algorithm is systematically evaluated by experiments on simulated images and original infrared images, as well as compared with the current advanced infrared stripe non-uniformity correction algorithms. It is proved that our algorithm can better eliminate stripe noise and preserve edge details.