Threshold Selection in Wavelet Transform

Threshold selection through wavelet transform enables effective noise reduction processing, clearly demonstrating that soft thresholding outperforms hard thresholding in denoising applications. In wavelet transform implementations, we can employ various threshold selection methods such as absolute value-based thresholds and percentage-based thresholds for noise reduction processing. By performing wavelet decomposition on signals and applying appropriate soft thresholding (implemented through functions like wthresh() in MATLAB with 's' parameter), we can better preserve important signal characteristics while effectively reducing noise interference, thereby enhancing denoising performance. Soft thresholding algorithms typically apply continuous shrinkage to wavelet coefficients using mathematical operations like sign(c).*max(0,abs(c)-threshold), providing smoother signal reconstruction. In contrast, hard thresholding (using 'h' parameter in wthresh()) simply sets coefficients below the threshold to zero through binary operations, lacking the flexibility to adapt to different signal characteristics and noise levels. Consequently, soft thresholding has gained widespread adoption in noise reduction applications and has been empirically proven more effective than hard thresholding through both theoretical analysis and practical implementations involving wavelet decomposition and reconstruction processes.