A Particle Swarm Optimization Technique-Based Parametric Wavelet Thresholding Function for Signal Denoising

The determination of threshold and the construction of thresholding function would directly affect the signal denoising quality in wavelet transform denoising techniques. However, some deficiencies exist in the conventional methods, such as fixed threshold value and the inflexible thresholding functions. To overcome the defects of the traditional wavelet thresholding techniques, a modified particle swarm optimization (MPSO) algorithm-based parametric wavelet thresholding approach is proposed for signal denoising. Firstly, a kind of parametric wavelet thresholding function construction method is proposed on the basis of conventional thresholding functions. With mathematical derivation, the properties of the constructed function are proved. Three dynamic adjustment strategies are then employed to modify the PSO algorithm. The mean square error (MSE) between the original signal and the reconstructed signal is minimized by the MPSO algorithm. Finally, the performances of the proposed approach and the existing methods are simulated by denoising four benchmark signals with different noise levels. The simulation results show that the proposed MPSO-based parametric wavelet thresholding can obtain lower MSE, higher signal-to-noise ratio, and noise suppression ratio compared to the other algorithms. Besides, the denoising visual results also indicate the superiority of the proposed approach in terms of the signal denoising capability.