We propose a simple alternating minimization algorithm for solving a minor variation on the original Principal Component Pursuit (PCP) functional. In computational experiments in the video background modeling problem, the proposed algorithm is able to deliver a consistent sparse approximation even after the first outer loop, (taking approximately 12 seconds for a 640 × 480 × 400 color test video) which is approximately an order of magnitude faster than Inexact ALM to construct a sparse component of the same quality.