In view of poor denoising performance and unideal speed of the current median filter, a fast and Adaptive Four-dot Midpoint Filter (AFMF) was proposed. Firstly, noise pixels and non-noise pixels of an image were identified using a simple extreme method to reduce the computational complexity. Then, the traditional full-point window was discarded, instead of median filtering, but on the basis of switch filtering and clipping filtering, a new nonlinear filtering method named midpoint filtering was adopted to simplify the algorithm flow, improve the calculation efficiency, improve the denoising effect. Finally, starting from a 3×3 window from inside to outside, the window was gradually enlarged to form adaptive filtering, until all the noise pixels were processed, the setting of window size parameters was avoided. The experimental results show that compared with AMF, SAMF, MDBUTMF and DBCWMF, AFMF not only has better denoising performance but also faster operation speed (about 0.18 s), but also does not need to set parameters, which is easy to operate and has strong practicability.

In order to solve the problems of the Social Learning Particle Swarm Optimization (SLPSO) algorithm, such as slow convergence speed and low search efficiency, a Cross opposition learning and Particle-based social learning Particle Swarm Optimization (CPPSO) algorithm was proposed. Firstly, a cross opposition learning mechanism was formulated based on combining general opposition learning, random opposition learning and vertical random cross on the optimal solution. Secondly, the cross opposition learning was adopted for the optimal particle to improve the population diversity, exploration ability and avoid the disadvantage of SLPSO's slow convergence and low search efficiency. Finally, a novel social learning mechanism was adopted for the non-optimal particles in the particle swarm, and the new social learning method used particle-based approach, instead of the dimension-based one of SLPSO, not only improved the exploration capacity, but also improved exploitation and the optimization efficiency. The simulation results on a set of benchmark functions with different dimensions show that the optimization performance, search efficiency and generalizability of the CPPSO algorithm are much better than those of the SLPSO and the advanced PSO algorithms such as Crisscross Search PSO (CSPSO), Self-Regulating PSO (SRPSO), Heterogeneous Comprehensive Learning PSO (HCLPSO) and Reverse learning and Local learning PSO (RLPSO).

Aiming at the deficiencies of the current filters in removing salt-and-pepper noise from images, such as low denoising performance and slow running speed, an image denosing method based on Iterative Adaptive Weighted-mean Filter (IAWF) was proposed. Firstly, a new method was used to construct the neighborhood weight by using the similarity between the neighborhood pixels and the processed point. Then a new weighted-mean filter algorithm was formed by combing the neighborhood weight with switching trimmed mean filter, making full use of the correlation of the image pixels and the advantages of switching trimmed filter, effectively improving the denoising effect. At the same time, the window size of the filter was automatically adjusted to protect the details as much as possible. Finally, the iterative filter was applied to continue until the noisy points were processed completely in order to process automatically and reduce manual intervention. The simulation results show that compared with several state-of-the-art denoising algorithms, the proposed algorithm is better in Peak Signal-to-Noise Ratio (PSNR), collateral distortion and subjective denoising effect under various noise densities, with higher denoising speed, more suitable for practical applications.