Wavelet Denoising with Multiple Methods (Soft/Hard Thresholding, Adaptive Thresholding, etc.)

This document presents MATLAB implementations of wavelet denoising using multiple thresholding approaches. The discussed methods include soft thresholding, hard thresholding, and adaptive thresholding techniques. While all these methods effectively remove noise from signals, they employ distinct implementation strategies through MATLAB's wavelet toolbox functions. For instance, hard thresholding (implemented using 'wthresh' with 'h' parameter) completely eliminates wavelet coefficients below a specified threshold, while soft thresholding (using 'wthresh' with 's' parameter) shrinks coefficients toward zero by the threshold value. Adaptive thresholding methods, such as those utilizing 'wthbmpen' for Birgé-Massart penalty or 'wthrmngr' for threshold selection management, dynamically adjust thresholds based on local signal characteristics through scale-dependent calculations. When applying these wavelet denoising techniques in MATLAB, practitioners should select the appropriate method (using functions like 'wden' or 'wdencmp') based on specific signal properties and noise characteristics to achieve optimal denoising performance through proper threshold selection and wavelet decomposition parameters.