MATLAB Implementation of Wavelet Denoising with Local Adaptive Thresholding

Building upon the original foundation, we further elaborate on the principles and methodology of wavelet denoising. Wavelet denoising utilizes the correlation relationships of wavelet coefficients across adjacent scales to remove noise from images. Traditional wavelet coefficient estimation methods, including hard thresholding (which completely eliminates coefficients below threshold) and soft thresholding (which shrinks coefficients toward zero), suffer from limitations such as potential loss of image detail features during the denoising process. To address these issues, we propose a novel locally adaptive denoising algorithm in the wavelet domain. The algorithm implements a compromise approach by modifying the threshold obtained from a double shrinkage function through multiplication by an appropriate scaling coefficient. This approach involves calculating level-dependent thresholds, applying adaptive shrinkage to wavelet coefficients, and reconstructing the image from modified coefficients using inverse wavelet transform. Key implementation aspects include: - Multi-scale wavelet decomposition using functions like wavedec2() - Inter-scale correlation analysis for threshold determination - Adaptive threshold adjustment based on local coefficient statistics - Modified shrinkage function application to preserve edge information Experimental validation confirms that this method achieves excellent performance in both noise removal effectiveness and preservation of high-frequency detail features. The algorithm maintains image structural integrity while significantly reducing noise components, making it particularly suitable for medical imaging, remote sensing, and other detail-critical applications.