Grey wolf optimizer (GWO) is a global search algorithm based on grey wolf hunting activity. However, the traditional GWO is prone to fall into local optimum, affecting the performance of the algorithm. Therefore, to solve this problem, an equalized grey wolf optimizer with refraction opposite learning (REGWO) is proposed in this study. In REGWO, the issue about the low swarm population variety of GWO in the late iteration is well overcome by the opposing learning of refraction. In addition, the equilibrium pool strategy reduces the likelihood of wolves going to the local extremum. To investigate the effectiveness of REGWO, it is evaluated on 21 widely used benchmark functions and IEEE CEC 2019 test functions. Experimental results show/ that REGWO performs better than the other competitors on most benchmarks.

In real-world scenarios, images may be affected by additional noise during compression and transmission, which interferes with postprocessing such as image segmentation and feature extraction. Image noise can also be induced by environmental variables and imperfections in the imaging equipment. Robust principal component analysis (RPCA), one of the traditional approaches for denoising images, suffers from a failure to efficiently use the background’s low-rank prior information, which lowers its effectiveness under complex noise backgrounds. In this paper, we propose a robust PCA method based on a nonconvex low-rank approximation and total variational regularization (TV) to model the image denoising problem in order to improve the denoising performance. Firstly, we use a nonconvex $\gamma$-norm to address the issue that the traditional nuclear norm penalizes large singular values excessively. The rank approximation is more accurate than the nuclear norm thanks to the elimination of matrix elements with substantial approximation errors to reduce the sparsity error. The method’s robustness is improved by utilizing the low sensitivity of the $\gamma$-norm to outliers. Secondly, we use the $l_1$-norm to increase the sparsity of the foreground noise. The TV norm is used to improve the smoothness of the graph structure in accordance with the sparsity of the image in the gradient domain. The denoising effectiveness of the model is increased by employing the alternating direction multiplier strategy to locate the global optimal solution. It is important to note that our method does not require any labeled images, and its unsupervised denoising principle enables the generalization of the method to different scenarios for application. Our method can perform denoising experiments on images with different types of noise. Extensive experiments show that our method can fully preserve the edge structure information of the image, preserve important features of the image, and maintain excellent visual effects in terms of brightness smoothing.