Wavelet Transform and Energy Distribution Characteristics of Noisy Signals for Image Denoising

Utilizing wavelet transform and the energy distribution characteristics of noisy signals, we have developed a novel approach for processing noisy images to achieve denoising. The implementation involves first performing multi-scale decomposition of the noisy image through wavelet transform, where we calculate both the noise variance and adaptive thresholds for the high-frequency coefficients at each decomposition level. These thresholds are then applied to process the high-frequency coefficients. The code implementation typically involves using functions like wavedec2 for 2D wavelet decomposition in MATLAB, where we can extract horizontal, vertical, and diagonal detail coefficients at each scale. Finally, we reconstruct the denoised image using the processed wavelet coefficients through inverse wavelet transform (waverec2 in MATLAB), effectively removing noise while preserving important image features. This method significantly enhances image quality by effectively eliminating noise components while maintaining structural integrity.