A robust version of Principal Component Analysis (PCA) can be constructed via a decomposition of a data matrix into low rank and sparse components, the former representing a low-dimensional linear model of the data, and the latter representing sparse deviations from the low-dimensional subspace. This decomposition has been shown to be highly effective, but the underlying model is not appropriate when the data are not modeled well by a single low-dimensional subspace. We construct a new decomposition corresponding to a more general underlying model consisting of a union of low-dimensional subspaces, and demonstrate the performance on a video background removal problem.