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

Abstract: The robust principal component analysis (RPCA), which aims to estimate underlying low-rank and sparse structures from the degraded observation data, has found wide applications in computer vision. It is usually replaced by the principal component pursuit (PCP) model in order to pursue the convex property, leading to the undesirable overshrink problem. In this paper, we propose a dual weighted lp-norm (DWLP) model with a more reasonable weighting rule and weaker powers, which greatly generalizes the previous work and provides a better approximation to the rank minimization problem for original matrix as well as the l0-norm minimization problem for sparse data. Moreover, an approximate closed-form solution is introduced to solve the lp-norm minimization, which has more stability in the nonconvex optimization and provides a more accurate estimation for the low-rank and sparse matrix recovery problem. We then apply the DWLP model to remove salt-and-pepper noise by exploiting the image nonlocal self-similarity. Both qualitative and quantitative experiments demonstrate that the proposed method outperforms other state-of-the-art methods. In terms of PSNR evaluation, our DWLP achieves about 7.188dB, 5.078dB, 3.854dB, 2.536dB and 0.158dB improvements over the current WSNM-RPCA under 10\% to 50\% salt-and-pepper noise with an interval 10\% respectively.