Wavelet Threshold Denoising: Soft and Hard Threshold Algorithms

Wavelet threshold denoising using soft and hard threshold algorithms is a widely adopted signal processing technique that effectively reduces noise in signals while enhancing signal quality. These two thresholding approaches produce different denoising effects - soft thresholding provides smoother results by shrinking coefficients continuously toward zero, while hard thresholding preserves more signal details through abrupt coefficient truncation. The choice between them depends on specific application requirements. When implementing these algorithms, key functions include calculating wavelet coefficients at multiple decomposition levels, determining optimal thresholds using methods like universal threshold (VisuShrink) or minimax threshold, and applying the selected thresholding function to process coefficients before reconstruction. Through studying the principles and applications of these algorithms, we can better understand how to handle real-world signal processing challenges, such as selecting appropriate wavelet bases, optimizing threshold parameters, and balancing noise removal with signal preservation in practical implementations.