Fast ℓ1-minimization algorithm for robust background subtraction

Huaxin Xiao, Yu Liu, Maojun Zhang

Abstract: This paper proposes an approximative ℓ 1-minimization algorithm with computationally efficient strategies to achieve real-time performance of sparse model-based background subtraction. We use the conventional solutions of the ℓ 1-minimization as a pre-processing step and convert the iterative optimization into simple linear addition and multiplication operations. We then implement a novel background subtraction method that compares the distribution of sparse coefficients between the current frame and the background model. The background model is formulated as a linear and sparse combination of atoms in a pre-learned dictionary. The influence of dynamic background diminishes after the process of sparse projection, which enhances the robustness of the implementation. The results of qualitative and quantitative evaluations demonstrate the higher efficiency and effectiveness of the proposed approach compared with those of other competing methods.