Improvement of the wavelet transform filtering algorithm with threshold denoising method

In recent years, the wavelet transform filtering algorithm has attracted significant attention due to widespread applications in signal denoising.However, its fixed threshold method has limitations, such as constrained denoising performance and loss of signal details, which requires improvement to adapt to complex noise environments.To address this issue, a wavelet transforms filtering algorithm combining adaptive thresholding and an improved threshold function is proposed.The algorithm dynamically calculates thresholds based on the statistical properties of the signal and employs a continuously differentiable threshold function to balance denoising and signal fidelity.Experimental tests on simulated signals with varying noise levels and real-world signals show that the improved algorithm achieves an SSIM index of 0.942, the closest to the original image, preserving image details and textures to the greatest extent.In denoising house images, the GAPT-Wavelet method clearly preserves the contours and textures of the house, with a PSNR of 87.90 dB and an MSE of 0.021 dB.When the maximum data size n=800, the algorithm's runtime is 46 seconds, maintaining a fast response time.The study has shown that the improved algorithm outperforms traditional methods in terms of denoising performance, computational efficiency, and adaptability, demonstrating significant potential for practical applications in scenarios such as medical image denoising, engineering equipment fault diagnosis, and industrial signal monitoring, thereby highlighting its important practical significance in the fields of engineering and technical diagnostics.