Recently, the low-rank and sparse decomposition problem has attracted attention in several applications, especially surveillance videos. Due to the physical limitations in acquisition systems, measured frames are blurred by a low-pass filter. In this article, we aim to decompose blurred videos' frames into low-rank and sparse components, in order to extract the background. Unlike conventional methods, we simultaneously take into account the blurring effect, as well as the missing data. Our simulation results confirmed the advantage of this approach in extracting low-rank components in surveillance videos.