MATLAB Implementation of Wavelet Soft Threshold Denoising with Performance Analysis

This article presents a MATLAB implementation of wavelet soft threshold denoising algorithm. The code accepts a noise mean value as input and generates both noisy and denoised images while calculating the peak signal-to-noise ratio (PSNR) for quantitative evaluation. The algorithm's core functionality involves wavelet decomposition using functions like wavedec2 for 2D signals, followed by threshold application to detail coefficients. The soft thresholding operation is implemented using element-wise operations that shrink coefficients toward zero: coefficients below the threshold are set to zero, while others are reduced by the threshold value. Key parameters like threshold selection (often using universal threshold or level-dependent thresholds) and wavelet type (Daubechies, Symlets, etc.) can be configured through the code. This denoising method effectively removes image noise while preserving important edge information, significantly improving image quality. Practical applications include medical imaging processing, image recognition systems, and security surveillance. The implementation allows comparison with related algorithms such as wavelet hard threshold denoising (which uses discontinuous thresholding) and wavelet packet denoising (employing more flexible decomposition structures) to better understand the trade-offs between noise removal and feature preservation. The MATLAB code typically includes functions for: - Adding simulated Gaussian noise using imnoise function - Multi-level wavelet decomposition with wavedec2 - Threshold calculation based on noise estimation - Coefficient processing with soft thresholding operation - Wavelet reconstruction using waverec2 - PSNR computation for quality assessment This algorithm serves as a valuable tool for enhancing image quality and processing accuracy in various computer vision and image processing applications.