Video background modeling is an important task in many video processing applications. Most existing algorithms assume a Gaussian noise model, but digital videos are, in practice, prone to be degraded by impulse noise, due to transmission errors in wireless or high data-rate wired channels. Principal Component Pursuit (PCP), which also assumes a Gaussian noise model, is currently considered the state of the art for video background modeling. We propose a new PCP-based algorithm that fully integrates the impulse noise model and has computational performance comparable with that of current PCP implementations.