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The robust principal component analysis (RPCA), which aims to estimateunderlying low-rank and sparse structures from the degraded observation data,has found wide applications in computer vision. It is usually replaced by theprincipal component pursuit (PCP) model in order to pursue the convex property,leading to the undesirable overshrink problem. In this paper, we propose a dualweighted lp-norm (DWLP) model with a more reasonable weighting rule and weakerpowers, which greatly generalizes the previous work and provides a betterapproximation to the rank minimization problem for original matrix as well asthe l0-norm minimization problem for sparse data. Moreover, an approximateclosed-form solution is introduced to solve the lp-norm minimization, which hasmore stability in the nonconvex optimization and provides a more accurateestimation for the low-rank and sparse matrix recovery problem. We then applythe DWLP model to remove salt-and-pepper noise by exploiting the image nonlocalself-similarity. Both qualitative and quantitative experiments demonstrate thatthe proposed method outperforms other state-of-the-art methods. In terms ofPSNR evaluation, our DWLP achieves about 7.188dB, 5.078dB, 3.854dB, 2.536dB and0.158dB improvements over the current WSNM-RPCA under 10\% to 50\%salt-and-pepper noise with an interval 10\% respectively.

Dual Reweighted Lp-Norm Minimization for Salt-and-pepper Noise Removal