Video background modeling, used to detect moving objects in digital videos, is a ubiquitous pre-processing step in computer vision applications. Principal Component Pursuit (PCP) PCP is among the leading methods for this problem. In this paper we proposed a new convex formulation for PCP, substituting the standard ℓ₁ regularization with a projection onto the ℓ₁-ball. This formulation offers an advantage over the known incremental PCP methods in practical parameter selection and ghosting suppression, while retaining the ability to be implemented in a fully incremental fashion, keeping all the desired properties related to such PCP methods (low memory footprint, adaptation to changes in the background, computational complexity that allows online processing).