Wavelet Threshold Denoising: Performance Comparison of Soft, Hard, and Modern Thresholding Methods

In this research, we conduct an in-depth investigation of wavelet threshold denoising. Our study compares not only the two common threshold calculation methods - soft thresholding and hard thresholding - but also evaluates the performance of various contemporary threshold determination approaches and threshold function processing techniques. Through systematic comparisons using signal-to-noise ratio (SNR) and mean square error (MSE) metrics, we determine the relative advantages and disadvantages of different algorithms. The research findings provide valuable references for further studies in the wavelet threshold denoising domain. Additionally, we perform detailed analyses of threshold calculation methods and threshold function processing techniques to better understand their working principles and application scenarios. Key implementation aspects include threshold calculation using universal threshold rules (like VisuShrink), minimax threshold selection, and Stein's unbiased risk estimate (SURE) method, along with threshold function implementations that handle wavelet coefficients differently based on chosen strategies. From a code implementation perspective, soft thresholding typically applies a continuous shrinkage function (e.g., sign(x)*max(0, |x|-threshold)), while hard thresholding uses a binary approach (preserving coefficients above threshold, zeroing others). Modern methods may incorporate adaptive thresholds or hybrid approaches that optimize denoising performance for specific signal characteristics. Overall, our research aims to deeply explore various methods in wavelet threshold denoising and contribute to both academic research and practical applications in this field, providing guidance for algorithm selection and parameter tuning in real-world signal processing implementations.