Wavelet Soft-Thresholding Denoising Method with MATLAB Implementation

Wavelet soft-thresholding denoising is a widely-used signal processing technique that effectively reduces noise in signals. In MATLAB, this method can be implemented using specific source code that typically involves several key algorithmic steps. The implementation process generally begins with performing a wavelet transform on the input signal using functions like wavedec() to decompose the signal into different frequency components. The core of the method involves applying a soft-thresholding function to the wavelet coefficients, where coefficients below a specified threshold are set to zero while larger coefficients are shrunk toward zero by the threshold value. This thresholding operation can be implemented using the wthresh() function with the 's' parameter for soft thresholding. The threshold value can be determined using various methods such as the universal threshold (sqrt(2*log(length(signal))) or level-dependent thresholds. Finally, the denoised signal is reconstructed through inverse wavelet transformation using the waverec() function. This approach is extensively applied in signal processing domains and can be customized and optimized according to specific requirements through parameter adjustments like wavelet type selection (db4, sym8, etc.), decomposition level optimization, and threshold calculation methods.