Consider a matrix M, such that M = L0 + S0, where L0 is supposed to have low rank, and S0 is supposed to be sparse. An interesting question, also motivated by numerous applications described in the paper, is whether one can efficiently reconstruct L0 and S0 if only M is given.
The authors describe a procedure, called principal component pursuit (PCP), that recovers L0 and S0 exactly, under certain assumptions. One theorem clearly states the procedure, together with its necessary assumptions.
The paper contains not only a mathematical description of PCP, but also a section describing numerical experiments using real-life data.
