Comparison of Hard Thresholding and Soft Thresholding Methods for Image Denoising

This study conducts a comprehensive comparison between hard thresholding and soft thresholding methods for image denoising, and introduces a novel compromise thresholding approach. The implementation typically involves calculating wavelet coefficients using discrete wavelet transform (DWT), applying thresholding functions, and reconstructing the image through inverse DWT. Hard thresholding completely eliminates coefficients below a threshold (implemented as coeffs.*(abs(coeffs)>threshold)), while soft thresholding shrinks coefficients toward zero (using sign(coeffs).*max(abs(coeffs)-threshold,0)). Based on the comparative analysis, we developed a compromise thresholding method that combines advantages of both techniques - effectively removing image noise while preserving critical image information through adaptive threshold selection algorithms. This compromise thresholding approach shows significant potential for practical applications and could be widely implemented in image processing domains, particularly in medical imaging and photographic enhancement where edge preservation is crucial. The method can be implemented using weighted combinations of hard and soft thresholding functions or through continuous thresholding functions with adjustable parameters.