1. A method for processing a video acquired of a scene, wherein the video includes a sequence of images, comprising the steps of: solving for a low rank component of the video; solving for a sparse component of the video; following a Newton root finding step to traverse separately Pareto curves of each low rank component and sparse component; repeating alternately the solving for the low rank component and the sparse component until a termination condition is reached; and outputting the low rank component and the sparse component when the termination condition is reached, wherein the low rank component represents a background in the video, and the sparse component represents moving objects in the video, and wherein the steps are performed in a processor.