  Background subtraction is the primary task of the majority of video
inspection systems. The most important part of the background subtraction which
is common among different algorithms is background modeling. In this regard,
our paper addresses the problem of background modeling in a computationally
efficient way, which is important for current eruption of "big data" processing
coming from high resolution multi-channel videos. Our model is based on the
assumption that background in natural images lies on a low-dimensional
subspace. We formulated and solved this problem in a low-rank matrix completion
framework. In modeling the background, we benefited from the in-face extended
Frank-Wolfe algorithm for solving a defined convex optimization problem. We
evaluated our fast robust matrix completion (fRMC) method on both background
models challenge (BMC) and Stuttgart artificial background subtraction (SABS)
datasets. The results were compared with the robust principle component
analysis (RPCA) and low-rank robust matrix completion (RMC) methods, both
solved by inexact augmented Lagrangian multiplier (IALM). The results showed
faster computation, at least twice as when IALM solver is used, while having a
comparable accuracy even better in some challenges, in subtracting the
backgrounds in order to detect moving objects in the scene.
