Sparse and low rank decomposition using l0 penalty

High dimensional data is often modeled as a linear combination of a sparse component, a low-rank component, and noise. An example is a video sequence of a busy scene where the background is the low-rank part and the foreground, e.g. moving pedestrians, is the sparse part. Sparse and low rank (SLR) matrix decomposition is a recent method that estimates those components. In this paper we develop an l₀ based SLR method and an associated tuning parameter selection method based on the extended Bayesian information criterion (EBIC) method. In simulations the new algorithm is compared with state of the art algorithms from the literature.