Foreground Detection by Robust PCA Solved via a Linearized Alternating Direction Method

Robust Principal Components Analysis (RPCA) shows a nice framework to separate moving objects from the background. The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. RPCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the l1-norm. To solve this convex program, an Alternating Direction Method (ADM) is commonly used. However, the subproblems in ADM are easily solvable only when the linear mappings in the constraints are identities. This assumption is rarely veri ed in real application such as foreground detection. In this paper, we propose to use a Linearized Alternating Direction Method (LADM) with adaptive penalty to achieve RPCA for foreground detection. LADM alleviates the constraints of the original ADM with a faster convergence speed. Experimental results on di erent datasets show the pertinence of the proposed approach.