A Study on Wavelet-based Image Denoising Using a Modified Adaptive Thresholding Method

The denoising of a natural image corrupted by additive white Gaussian noise (AWGN) is a classical problem in the signal processing community. The corruption of an image by noise is common during its acquisition or transmission. The aim of denoising is to remove the noise while keeping the signal featuresas much as possible. Traditional algorithms, such as the standard median (SM) filter and mean filter (MF) perform image denoising in the spatial domain [1-4,11]. In recent years, wavelet transform-based image denoising algorithms have shown remarkable success. In 1992, Donoho and Johnstone [5] presented a method named wavelet shrinkage, and showed its obvious efficiency for signal denoising and inverse problem solving. In this method, a discrete wavelet transform (DWT) is performed on the noisy signal first. Then with a preset threshold, coefficients with a magnitude smaller than the threshold are set to zero while those with a larger magnitude are kept and used to estimate the noiseless coefficients. Finally, an inverse discrete wavelet transform (IDWT) reconstructs the signal from the estimated coefficients. Later, Donoho [7] proposed a sample thresholding rule that sets all the coefficients smaller than the universal threshold to zero and shrinks the rest of the coefficientsby the threshold (soft thresholding) or leaves them with out change (hard thresholding). Donoho and Johnstone [6] also presented a thresholding method using Stein's risk estimator called Sure Shrink. Sendur and Selesnick [8, 9] proposed BiShrink for denoising. The BiShrinkage function indicates that the estimated wavelet coefficients dependon the parent coefficients. In this paper, a modified wavelet based image denoising thresholding method is proposed. A modified thresholding function considering the inter scale dependency between the parent coefficient and child coefficient and conventional soft thresholding function are adaptively J. lnf. Commun. Converg. Eng. 10(1): 45-52, Mar. 2012 Regular Paper