MANAGEMENT IMAGE DENOISING USING WAVELET THRESHOLDING METHODS

This paper presents a comparative analysis of vario us image denoising techniques using wavelet transfo rms. A lot of combinations have been applied in order to f ind the best method that can be followed for denois i g intensity images. In this paper, we analyzed severa l methods of noise removal from degraded images wit h Gaussian noise by using adaptive wavelet threshold (Bayes Shrink, Neigh Shrink, Sure Shrink, Bivariate Shrink and Block Shrink) and compare the results in term o f PSNR and MSE. Keywords— wavelet thresholding, Bayes Shrink, Neigh Shrink, SureShrink, Bivariate Shrink and Block Shr ink Introduction An image is often corrupted by noise in its acquisition and transmission. The goal of image denoising is to produce good estimates of the original image from noisy observations. Wavelet denoising attempts to remove the noise present in the signal while preserving the signal characteristics, regardless of its frequency conten t. In the recent years there has been a fair amount o f research on wavelet thresholding and threshold selection for signal de-noising [3], [5]-[6], [4], because wavelet provides an appropriate basis for separating noisy signal from the image signal. Wavelet thresholding is a signal estimation technique that exploits the capabilities of wavelet transform for signal denoising. It removes noise by killing coefficients that are insignificant relativ e to some threshold, and turns out to be simple and effective, depends heavily on the choice of a thresholding parameter and the choice of this threshold determines, to a great extent the efficac y of denoising. * Corresponding Author E. mail: manisha771@gmail.com Wavelet Thresholding Let f = { fij, i, j = 1, 2.M} denote the M×M matrix of the original image to be recovered and M is some integer power of 2. During transmission the signal f is corrupted by independent and identically distributed (i.i.d) zero mean, white Gaussian Noise nij with standard deviation σ i.e. nij ~ N (0, σ ) and at the receiver end, the noisy observations gij= f ij + σ nij is obtained. The goal is to estimate the signal f from noisy observations gij such that Mean Squared error (MSE) is minimum. Let W and W -1 denote the two dimensional orthogonal discrete wavelet transform (DWT) matrix and its inverse respectively. Then Y = Wg represents the matrix of wavelet coefficients of g having four sub bands (LL, LH, HL and HH) [6], [7]. The sub-bands HH k, HLk, LHk are called details, where k is the scale varying from 1, 2 . J and J is the total number of decompositions. The size of the sub band at scale k is N/2 × N/2. The sub band LL J is the lowresolution residue. The wavelet thresholding denoising method processes each coefficient of Y from the detail sub bands with a soft threshold function to obtain . The denoised estimate is inverse transformed to = . In the experiments, soft thresholding has been used over hard thresholding because it gives more visually pleasant images as compared to hard thresholding; reason being the latter is discontinuous and yields abrupt artifacts in the recovered images especially when the noise energy is significant. A. Bayes Shrink (BS) The Bayes Shrink method is effective for images including Gaussian noise. The observation model is expressed as follows: [Dewangan, 2(2): April-June, 2012] ISSN: 2277-5528 Int. J. of Engg. Sci. & Mgmt. (IJESM), Vol. 2, Issue 2: April-June: 2012, 271 -275 Y = X + V