Moving Target Detection by Robust PCA in the Topological Space of Low-Rank Matrices

Moving targets in a heterogeneous environment can be extracted through traditional robust principal component analysis (RPCA). Competitive RPCA algorithms address a nonconvex constraint by relaxing it to a fixed rank. However, the solution does not necessarily reach a global optimum. To address this problem, a moving target detection method by RPCA in the topological space of low-rank matrices is proposed to obtain superior target detection performance. First, RPCA is considered in the topological space of low-rank matrices, which is the closure of the fixed-rank manifold. Then, combined with manifold optimization and the proximal gradient, the RPCA-proximal gradient in the topological space of low-rank (PGTSLr) algorithm is applied to solve the problem caused by a nondifferentiable sparsity term, so that the target can be precisely extracted. Experiments performed on measured data demonstrate that the proposed method exhibits advantages in detection performance over competitive methods in a heterogeneous environment.