Wavelet Transform Denoising: Soft Threshold, Hard Threshold, and Custom Threshold Functions

Wavelet transform denoising is a commonly used signal processing method that effectively removes noise from signals. This graduation project introduces the principles and methodologies of wavelet transform denoising, with detailed discussion on the application of both soft thresholding and hard thresholding techniques. The implementation typically involves decomposing signals using wavelet transforms (like Daubechies or Symlets wavelets), applying threshold rules to wavelet coefficients, and reconstructing the denoised signal. Additionally, the project presents a custom-designed threshold function that demonstrates enhanced performance in the denoising process. The custom threshold function can be implemented in code with adjustable parameters to optimize noise removal while preserving signal features. Key implementation aspects include wavelet decomposition levels selection, threshold calculation methods (universal threshold, SURE threshold), and reconstruction algorithms. This comprehensive graduation project material covers all essential aspects, including mathematical foundations, practical code examples (featuring wavelet toolbox functions in MATLAB or PyWavelets in Python), and performance evaluation metrics. The complete documentation ensures deep understanding and practical knowledge acquisition for signal processing applications.