Here are two presentation of the Compressive Principal Component Pursuit and Modeling High-dimensional (Visual) Data by Yi Ma which feature in part some theoretical work that provides some grounding to PCP ( for instance SpaRCS: Recovering Low-rank and Sparse matrices from Compressive Measurements is based on CoSAMP competes with CPCP yet has little theoretical grounding)
The supporting papers which provide the theoretical grounding are:
Principal Component
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