MATLAB Implementation of 2D Wavelet Decomposition with Adaptive Thresholding

In the process of performing 2D wavelet decomposition, we can utilize Donoho's soft thresholding algorithm to process wavelet coefficients. This algorithm dynamically calculates distinct threshold values for each decomposition layer based on the statistical characteristics of the coefficients at that scale. The implementation typically involves using MATLAB's wavelet toolbox functions like wavedec2 for multilevel 2D decomposition, followed by threshold calculation using universal threshold rules (σ√(2logN)) where σ represents noise estimation and N is the coefficient count. The soft thresholding operation is then applied using wthresh function with 's' parameter, which shrinks coefficients toward zero by the threshold value while preserving significant features. Through this methodology, we can more precisely select and retain relevant wavelet coefficients by eliminating noise-dominated components, thereby achieving enhanced decomposition results for applications like image denoising and compression. The algorithm's adaptive nature allows optimal threshold selection across different resolution levels, maintaining important signal characteristics while effectively suppressing noise.