Unmanned aerial vehicles (UAVs) are equipped with optical systems including an infrared (IR) camera such as electro-optical IR (EO/IR), target acquisition and designation sights (TADS), or forward looking IR (FLIR). However, images obtained from IR cameras are subject to noise such as dead pixels, lines, and fixed pattern noise. Nonuniformity correction (NUC) is a widely employed method to reduce noise in IR images, but it has limitations in removing noise that occurs during operation. Methods have been proposed to overcome the limitations of the NUC method, such as two-point correction (TPC) and scene-based NUC (SBNUC). However, these methods still suffer from unfixed pattern noise. In this paper, a background registration-based adaptive noise filtering (BRANF) method is proposed to overcome the limitations of conventional methods. The proposed BRANF method utilizes background registration processing and robust principle component analysis (RPCA). In addition, image quality verification methods are proposed that can measure the noise filtering performance quantitatively without ground truth images. Experiments were performed for performance verification with middle wave infrared (MWIR) and long wave infrared (LWIR) images obtained from practical military optical systems. As a result, it is found that the image quality improvement rate of BRANF is 30% higher than that of conventional NUC.