Online Decomposition of Compressive Streaming Data Using $n$-$\ell_1$ Cluster-Weighted Minimization.

We consider a decomposition method for compressive streaming data in thecontext of online compressive Robust Principle Component Analysis (RPCA). Theproposed decomposition solves an $n$-$\ell_1$ cluster-weighted minimization todecompose a sequence of frames (or vectors), into sparse and low-rankcomponents, from compressive measurements. Our method processes a data vectorof the stream per time instance from a small number of measurements in contrastto conventional batch RPCA, which needs to access full data. The $n$-$\ell_1$cluster-weighted minimization leverages the sparse components along with theircorrelations with multiple previously-recovered sparse vectors. Moreover, theproposed minimization can exploit the structures of sparse components viaclustering and re-weighting iteratively. The method outperforms the existingmethods for both numerical data and actual video data.