Wavelet Transform Scale Correlation Denoising Algorithm

In this article, we present a scale correlation denoising algorithm based on wavelet transform and validate its denoising performance through practical examples. The implementation typically involves wavelet decomposition using functions like wavedec() in MATLAB or pywt.wavedec() in Python, followed by cross-scale correlation analysis to identify noise components. First, we explain the fundamental principles and concepts of wavelet transform, including multi-resolution analysis and wavelet coefficient thresholding techniques. Next, we detail the working mechanism of the scale correlation denoising algorithm, providing complete algorithmic steps and mathematical formulations for correlation coefficient calculation between adjacent scales. The core algorithm implementation involves calculating correlation thresholds and applying soft/hard thresholding to wavelet coefficients using functions such as wthresh(). We then demonstrate practical applications through several example signals (e.g., ECG data, vibration signals), showing signal-to-noise ratio improvement metrics and visualization comparisons between original and denoised signals. Finally, we discuss the algorithm's advantages in preserving signal edges while removing noise, address limitations in handling non-stationary signals, and suggest potential improvements like adaptive threshold selection or hybrid wavelet packet approaches. Through comprehensive analysis of this wavelet-based scale correlation denoising algorithm, we aim to enhance understanding and application of this method for improved signal processing outcomes.