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Many applications in data analysis rely on the decomposition of a data matrixinto a low-rank and a sparse component. Existing methods that tackle this taskuse the nuclear norm and L1-cost functions as convex relaxations of the rankconstraint and the sparsity measure, respectively, or employ thresholdingtechniques. We propose a method that allows for reconstructing and tracking asubspace of upper-bounded dimension from incomplete and corrupted observations.It does not require any a priori information about the number of outliers. Thecore of our algorithm is an intrinsic Conjugate Gradient method on the set oforthogonal projection matrices, the so-called Grassmannian. Non-convex sparsitymeasures are used for outlier detection, which leads to improved performance interms of robustly recovering and tracking the low-rank matrix. In particular,our approach can cope with more outliers and with an underlying matrix ofhigher rank than other state-of-the-art methods.

Robust PCA and subspace tracking from incomplete observations using L0-surrogates