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MSC: 60J20, 62H25, 68Q87
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robust principal component analysis; sparse Bayesian learning; Markov random fields; matrix factorization; contiguity prior
The research on the robust principal component analysis has been attracting much attention recently. Generally, the model assumes sparse noise and characterizes the error term by the $\ell _1$-norm. However, the sparse noise has clustering effect in practice so using a certain $\ell _p$-norm simply is not appropriate for modeling. In this paper, we propose a novel method based on sparse Bayesian learning principles and Markov random fields. The method is proved to be very effective for low-rank matrix recovery and contiguous outliers detection, by enforcing the low-rank constraint in a matrix factorization formulation and incorporating the contiguity prior as a sparsity constraint. The experiments on both synthetic data and some practical computer vision applications show that the novel method proposed in this paper is competitive when compared with other state-of-the-art methods.
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