Wavelet Threshold Denoising with Edge Detection

Wavelet threshold denoising with edge detection is an advanced signal processing technique that utilizes edge detection mechanisms to identify and preserve critical signal features during noise removal. This approach implements a dual-threshold strategy where wavelet coefficients corresponding to edge regions are processed with conservative thresholds to maintain sharp transitions, while non-edge coefficients undergo more aggressive thresholding for effective noise suppression. The algorithm typically involves three key steps: multi-scale wavelet decomposition to extract frequency components, edge detection using gradient-based operators or wavelet modulus maxima analysis, and adaptive threshold application based on edge classification. This method can be implemented in MATLAB using wavelet toolbox functions like wavedec for decomposition and wthresh for thresholding, combined with edge detection functions such as edge() for image processing applications. With applications spanning image processing, audio enhancement, and biomedical signal analysis, this technique provides superior denoising performance while maintaining critical structural information, making it particularly valuable for applications requiring precise feature preservation.