Authors: A. Aravkin (IBM TJ Watson Research Center, USA), S. Becker (University of Colorado,USA)
Chapter Description
This chapter reviews some recent techniques in convex optimization and contributes several novel results. We apply these techniques to the robust principal component analysis (RPCA) problem. A distinguishing feature of this chapter, in the context of this handbook, is the emphasis on a range of optimization formulations of the RPCA problem.
Linear superposition is a useful model for many applications, including nonlinear mixing problems. Surprisingly, we can perfectly distinguish multiple elements in a given signal using convex optimization as long as they are concise and look sufficiently different from one another. RPCA is a key example, where we decompose a signal into low rank and sparse components and stable principal component pursuit (SPCP), where we also seek an explicit noise component within the RPCA decomposition. Applications include alignment of occluded images, scene triangulation, model selection, face recognition, and document indexing.