RPCA Model and Application Based on Half Threshold Operator

CHEN Wensong; DING Yongmei; WU Shiqian

doi:10.3969/j.issn.1672-9722.2025.04.019

Abstract：Foreground-background separation in video is one of the important tasks of video surveillance system.Its purpose is to separate moving objects in the foreground from the video background.The robust principal component analysis(RPCA)algo-rithm based on principal component tracking(PCP)can not approach the rank function well because its nuclear norm is a biased es-timate of the rank function,and the sum of singular values is easily affected by individual values,resulting in sharp degradation of its separation performance and low accuracy in some complex scenarios.Therefore,this paper proposes a robust principal compo-nent analysis(NCRPCA)algorithm based on nonconvex function and half threshold operator.The nuclear norm of PCP algorithm is replaced by nonconvex function.Compared with the nuclear norm,nonconvex function is a more rigorous approximation of rank func-tion,and the approximation effect is better.In addition,in order to obtain more sparse and accurate solutions,the sparse terms are constrained by l1/2 norm.Finally,the proposed algorithm is applied to the experiments of foreground-background separation in stat-ic and dynamic video respectively,and the effectiveness and superiority of this algorithm are verified from the visual effect and quan-titative aspects.