<p>Traditional low-rank sparse decomposition (LRSD) methods have difficulty in detecting moving objects quickly and accurately in noisy videos due to the high-dimensional singular value decomposition (SVD) of the video data and noise. Noise contaminates both the video background and the moving object. Therefore, there is an urgent need to remove the noise from both the background and the moving object, as well as to improve the efficiency of the traditional methods for detecting moving objects. To tackle these challenges, we propose a novel low-rank sparse decomposition method for processing noisy videos. Our approach integrates representative coefficient total variation (RCTV) regularization and spatio-temporal total variation (STTV) regularization to reconstruct the video background and detect moving objects. Specifically, RCTV regularization is applied to constrain the low-rank video background, effectively eliminating background noise and reducing the computational complexity of traditional model optimization. Additionally, STTV regularization enforces the smooth sparsity of moving objects, significantly mitigating false detections caused by dynamic background variations and noise. Experimental results demonstrate that the proposed method successfully recovers a clean background while accurately detecting moving objects in noisy videos.</p>