Robust Principal Component Analysis? [PDF], E. J. Candes, X. Li, Y. Ma, and J. Wright, Journal of ACM 58(1), 1-37.
Compressed Sensing and Matrix Completion with Constant Proportion of Corruptions [PDF], X. Li, to appear in Constructive Approximation.
Solving quadratic equations via PhaseLift when there are about as many equations as unknowns[PDF], E. J. Candes and X. Li, preprint
Sparse Signal Recovery from Quadratic Measurements via Convex Programming[PDF], X. Li and V. Voroninski, preprint.