Wavelet Transform Denoising with Enhanced 97 Lifting Scheme and Discrete Wavelet Transform MATLAB Implementation

This program implements denoising using wavelet transform techniques and presents enhanced MATLAB implementations of the 97 lifting scheme and discrete wavelet transform. Wavelet transform is a signal processing technique that decomposes signals into sub-signals at different frequency levels, enabling targeted processing of each frequency component. The denoising process involves thresholding wavelet coefficients where noise components typically reside in the high-frequency detail coefficients. Our improved implementations feature optimized decomposition algorithms using wavelet functions like 'db4' or 'sym8', with enhanced threshold selection methods including universal threshold and minimax threshold approaches. The 97 lifting scheme implementation includes customized prediction and update steps for better signal approximation, while the discrete wavelet transform module incorporates multi-level decomposition with improved boundary handling using symmetric padding. The program demonstrates practical denoising applications through coefficient thresholding techniques (hard and soft thresholding) and reconstruction algorithms that preserve signal characteristics while effectively removing noise components. We showcase performance improvements through reduced computational complexity and enhanced signal-to-noise ratio (SNR) metrics in the denoising results.