Wavelet Transform Scale Correlation Denoising Algorithm

This project implements a denoising algorithm based on wavelet transform scale correlation and validates its noise reduction performance through concrete examples. The algorithm performs wavelet decomposition on input signals and leverages inter-scale correlations to effectively separate noise from useful signal components. Key implementation aspects include: - Wavelet decomposition using functions like wavedec() to obtain coefficients at multiple scales - Calculation of correlation coefficients between adjacent scales to identify noise-dominated regions - Application of adaptive thresholding based on scale correlation analysis - Signal reconstruction using waverec() with modified coefficients To validate the algorithm's denoising performance, we conduct tests using noisy signal examples. For instance, we can select a signal contaminated with Gaussian or impulse noise and apply the algorithm for noise removal. The performance evaluation involves comparing signal quality metrics such as Signal-to-Noise Ratio (SNR) and Peak Signal-to-Noise Ratio (PSNR) before and after processing. Visual comparison of waveform plots and statistical analysis of residual noise further demonstrate the algorithm's effectiveness. Experimental results show that by analyzing correlation patterns across different wavelet scales, the algorithm can accurately distinguish noise components from meaningful signal features, significantly enhancing signal quality while preserving important characteristics. This validation process confirms the algorithm's feasibility and effectiveness for practical denoising applications in signal processing.