The non-uniformity correction is crucial for the successful application of infrared images, as it directly impacts the visual quality and the accuracy of sea surface temperature. However, this method often results in residual stripe noise and flash pixels within the infrared remote images, which fails to meet the requirements for high-sensitivity infrared images. To improve the relative radiation correction precision for high-sensitivity infrared images, we propose a high-precision non-uniformity correction algorithm in this paper. Firstly, infrared marine images are corrected based on on-board calibration data. Secondly, an improved statistical algorithm based on small samples of infrared images is proposed to remove residual stripe noise. Finally, flash pixels are detected and removed based on the images in real-time. The accuracy of the relative radiation correction was better than 1%, and the algorithm's validity was verified through experiments.