A variational approach to stable principal component pursuit
  We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthetic and real data experiments, that our approach offers advantages over the classical SPCP formulations in scalability and practical parameter selection. 
Aleksandr Aravkin, Stephen Becker, Volkan Cevher, Peder Olsen
math.OC stat.ML