Wavelet Denoising: Implementation and Comparison of Soft and Hard Thresholding Techniques

This article discusses the implementation of soft and hard thresholding methods along with a comparative analysis of their denoising performance. Soft and hard thresholding are widely used signal processing techniques that reduce noise by setting signal components below a certain threshold (soft thresholding) to zero, while maintaining components above another threshold (hard thresholding) at their original values or other predetermined values. We will examine the implementation approaches for both methods, including key algorithmic steps such as threshold calculation using universal threshold rules (e.g., Donoho-Johnstone threshold) and wavelet coefficient processing. The implementation typically involves wavelet decomposition using functions like wavedec() in MATLAB, followed by threshold application using element-wise operations comparing coefficients against calculated thresholds. We will compare their denoising effectiveness through performance metrics like Signal-to-Noise Ratio (SNR) and Mean Squared Error (MSE). Additionally, we explore the application scope and limitations of these methods, and discuss optimization strategies such as adaptive threshold selection and level-dependent thresholding to enhance denoising performance.