The original PCP problem considers the nuclear and l1 norms as penalties for the background (low-rank) and foreground or moving objects (sparse) with an equality constrain for the observed videos and low-rank and sparse components.

In this talk we propose to change constraints to penalties, obtaining a variant where the restoration error (observed video minus low-rank and sparse component) and l1 norm are penalties while imposing the rank of the low-rank component as a constraint. Interestingly, this particular variant can be effectively solved in an incremental fashion, allowing real-time implementation for live-feed HD videos; moreover, considering T(.), an unknown rigid transformation, applied to the low-rank component, we can also cope with translational and rotational jitter, allowing almost real-time processing.

Furthermore, in this talk we will also include a detailed analysis of the proposed PCP variant as well as incremental SVD, which is the key to solve the equivalent problem incrementally.

Host: Brendt Wholberg