## A novel robust principal component analysis method for image and video processing.(English)Zbl 1389.62096

Summary: 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.

### MSC:

 62H25 Factor analysis and principal components; correspondence analysis 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 68Q87 Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)

### Software:

Regularization tools; PRMLT; UTV; softImpute
Full Text:

### References:

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