Boosting RPCA by Prior Subspace

This paper introduces a novel method, boosting principal component analysis (BPCA), to address the challenge of extracting principal components in the presence of sparse outliers. Building on the traditional robust principal component analysis (RPCA) model, BPCA incorporates prior subspace information through a flexible weighting scheme, enhancing its robustness against the bias in prior subspaces. We develop a novel metric, based on QR decomposition, to assess the accuracy of a prior subspace, which facilitates the analysis of BPCA’s exact recovery feasibility. The exact recovery is achievable if the bias of the prior subspace meets a specific tolerance condition. We establish its recovery guarantee by introducing new incoherence conditions, which offer improved interpretability over existing conditions due to the boosting of prior subspaces. BPCA enjoys a more relaxed recovery bound than RPCA and traditional prior subspace-based methods, provided that the prior subspace is sufficiently accurate, though not necessarily perfect. The necessary level of accuracy for this relaxation is quantified, with an analysis using the convex geometry of the nuclear norm. Furthermore, the proposed BPCA model is scalable and successfully extended to three-dimensional scenes. Experimental results demonstrate the superior performance of BPCA over RPCA and traditional prior subspace-based methods in low-rank recovery. The code of the proposed methods is released at https://github.com/linchenee/BPCA-BTPCA.