  We analyze the decomposition of a data matrix, assumed to be a superposition
of a low-rank component and a component which is sparse in a known dictionary,
using a convex demixing method. We provide a unified analysis, encompassing
both undercomplete and overcomplete dictionary cases, and show that the
constituent components can be successfully recovered under some relatively mild
assumptions up to a certain $\textit{global}$ sparsity level. Further, we
corroborate our theoretical results by presenting empirical evaluations in
terms of phase transitions in rank and sparsity for various dictionary sizes.
