Exact or noisy matrix completion under incoherence

Near-Optimal Matrix Completion, Candes & Tao, 2009

Incoherence-Optimal Matrix Completion, Chen, 2013

Recovering Low-Rank Matrices From Few Coef´Čücients In Any Basis. Gross, 2010

Using low-rank factorization instead of nuclear norm: Matrix Completion from Noisy Entries. Keshavan et al, 2010.

Noisy matrix completion w/o incoherence

Restricted strong convexity and weighted matrix completion: Optimal bounds with noise. Negahban & Wainwright, 2010.

Noisy low-rank matrix completion with general sampling distribution. Klopp, 2012.

Sparse + low-rank & variants

Robust Principal Component Analysis? Candes et al, 2009.

Robust PCA via Outlier Pursuit. Xu et al, 2010.

Nuclear norm as a surrogate for rank

Rank, Trace-Norm and Max-Norm. Srebro & Shraibman, 2005.

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization. Recht, Fazel, Parrilo, 2007.