*(A) White noise*

Noise is usually described by its probabilistic characteristics. Idealized noise called white noise. White noise is frequently applied as the worst approximation of degradation. A white noise process is a random process of random variable that are uncorrelated, have mean zero, and a finite variance. Its advantage being that its use its simplifies calculations.

*(B) Discrete Wavelet Transform (DWT)*

De-noising of natural images corrupted by Gaussian noise using wavelet techniques is very effective. The wavelet coefficients calculated by a wavelet transform represent change in the image at a particular resolution. In numerical analysis and functional analysis a Discrete Wavelet Transform is any wavelet transform for which the wavelets are discretely sampled.

The discrete wavelet transform is

x= Row,

y= Column,

n= Number of pixels,

ff (i) = Location of the matrix

The Discrete wavelet transform is obtained by the sum of the location of the matrix from the range of zero to number of pixel n. An image can be decomposed into a sequence of different spatial resolution images using DWT. In case of a 2D image, an N level decomposition can be performed resulting in 3N+1 different frequency bands namely, LL, LH, HL and HH.

**Figure 2:** *2-D Data preparation of the image*

LLn,i= Noisy coefficients of approximation.

LHn,i= Noisy coefficients of vertical detail.

HLn,i = Noisy coefficients of horizontal detail.

HHn,i = Noisy coefficients of diagonal detail

*(c) Wavelet Noise Thresholding*

The wavelet coefficients calculated by a wavelet transform represent change in the image at a particular resolution. By looking at the image in various resolutions it should be possible to filter out noise.

**Figure 3 :** *Two dimensional DWT*