IMAGE DENOISING BY WAVELET TRANSFORM FOR MIXED NOISE.

*Kishan Shivhare 1 , and Gaurav Bhardwaj 2 . 1. M. Tech. Student, RJIT BSF Academy, Tekanpur (M.P.). 2. Asst. Prof., ECE Department, RJIT BSF Academy, Tekanpur (M.P.). ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

Image denoising is a very familiar technique which is used to remove the all unwanted noises from the original image. There are various methods to remove noise from digital images. In this paper we use Discrete Wavelet Transform for this purpose. In wavelet transform, there are two types of thresholding -Hard thresholding and Soft thresholding. We take a building image to describe the denoising process. First we add different types of noises in our image and then we apply the different thresholdings of DWT. We also use combination of both thresholdings in this paper to denoise the noisy image. To compare the denoised images with the noisy image, we take some performance parameters which are as follows; Signal to Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Root Mean Square Error (RMSE), and Structural Similarity Index (SSIM). We use MATLAB for simulation purpose.

…………………………………………………………………………………………………….... Introduction:-
Image denoising retains the details of an image by removing unwanted noise. Digital images become noisy when these are passed by a defective sensor or when these are transmitted through a faulty medium. To select a suitable denoising technique, we should have a good knowledge about the noise present in the image. The wavelet denoising technique is most suitable to speckle noise so it is generally used to denoise the speckle noise. But in this paper we use wavelet transform method to denoise mixed noise. To obtain mixed type of noise, we combine here three different types of noises. Only single thresholding is not enough capable to denoise the mixed noise, whether it is soft or hard thresholding. Therefore we use a combination of both of thresholdings, which is satisfactory to remove mixed noise.
Noise is a random variation of image Intensity and visible as grains in the image. It may arise in the image as effects of basic physics-like photon nature of light or thermal energy of heat inside the image sensors.
Here we are discussing three types of noise and their effects on the image signal. 1. Salt and pepper noise 2. Speckle noise 3. Gaussian noise Salt-and-pepper noise is also called impulsive noise or spike noise. Salt-and-pepper noised image has dark pixels in bright area and bright pixels in dark area of the image. It is similar to a binary system because it has only a high ISSN: 2320-5407 Int. J. Adv. Res. 4 (12), 1742-1750 1743 value and a low value. This noise strikes during analog-to-digital converter errors, bit errors in transmission. Saltand-pepper noise can damage the information or data embedded in the original image. One of the simplest ways to remove salt-and-pepper noise is by windowing the noisy image with a conventional median filter. The probability density function (pdf) for impulsive noise is given by: Speckle noise has an inherent nature of ultrasound images, which may have negative effects on image interpretation and diagnostic tasks. Speckle noise degrades the image quality and complicates diagnostic decisions for discriminating fine details in ultrasound images. Speckle noise is a kind of multiplicative noise. Speckle-noise is a granular noise which degrades the quality of the active radar, synthetic aperture radar (SAR), and medical ultrasound images. Speckle noise is seen in conventional radar due to random fluctuations while getting return signal from an object. Speckle noise follows a gamma distribution and is given as: - Gaussian noise model is additive in nature. Additive white Gaussian noise (AWGN) is generally caused by poor quality image acquisition, noisy environment or/and internal noise in communication channels. Gaussian noise is statistical noise. It has a probability density function (pdf) equal to that of the normal distribution, which is also known as the Gaussian distribution. Gaussian noise is uniformly distributed over the signal. It means that each pixel in the noisy image is the sum of the true pixel value and a random value of Gaussian distributed noise. The Gaussian distribution is given by: Where g = gray level, m = mean or average of the function, σ 2 = variance of the noise (a) Graphical representation (b) Example

Discrete Wavelet Transform (DWT):-
Denoising analysis of the images is performed by using Wavelet Transform. Simple denoising algorithms that used DWT consist of three steps; 1. It decomposes the noisy image and produces some coefficients which are called as wavelet coefficients. 2. These coefficients are modified with a particular threshold value. 3. At last Inverse Wavelet transform is applied to the modified coefficients to produce denoised image.
DWT of a noisy image consists two types of coefficients, a small number of coefficients having high SNR and a large number of coefficients having low SNR. These coefficients which are having low SNR are removed in DWT. Using inverse DWT, image is reconstructed after removing the coefficients of low SNR. Wavelet transform provides Time and frequency localization simultaneously. When DWT is applied to any noisy image, image is first divided into four sub bands as shown in Figure 4  and HH1 sub bands are detail images while coefficients of LL1 sub band is approximation image. The LL1 sub band is further decomposed in for sub bands to obtain the next level of wavelet coefficients as shown in Fig. 4(b).

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(a) One level Image Decomposition (b) One level Image Reconstruction Figure 5:-Wavelet Filter bank LL1 is called as the approximation sub band because it provides the image similar to original image. It comes by applying low pass filtering in both directions. The other bands are called as detail sub bands. The filters L and H as shown in Figure 5(a) are one dimensional low pass filter (LPF) and high pass filter (HPF) respectively for image decomposition. HL1 is horizontal fluctuation as it comes from low pass filtering in vertical direction and high pass filtering in horizontal direction. LH1 is vertical fluctuation as it is opposite toHL1. HH1 comes from high pass filtering in both the directions so it is called diagonal fluctuation. LL1 is further decomposed into 4 sub bands LL2, LH2, HL2 and HH2. The process is carried until the fifth decomposition level is reached. After L decompositions a total of D(L) =3*L+1 sub bands are obtained. Therefore for 5 level decompositions D(5) = 3*5+1 = 16 sub bands will be obtained. The decomposed image can be reconstructed by inverse discrete wavelet transform as shown in Figure 5(b). In figure 5(b) the filters L and H represent low pass and high pass reconstruction filters respectively.

Wavelet Thresholding:-
Thresholding technique operates on wavelet coefficients. It uses one of the wavelet coefficients at a time. In this process the coefficient which is smaller than the threshold value is set to zero otherwise the coefficient is kept or may be modified.
If the coefficient has small value then it carries more noise than a large valued coefficient. While if it has large value then coefficient carries more signal information than small valued coefficients. Therefore noise coefficients or small valued coefficients below a certain threshold value are replaced by zero and for remaining coefficients, an inverse wavelet transform is taken for reconstruction that has lesser noise.
Firstly wavelet analysis of a noisy image up to level N is done with thresholding of the each detail coefficients from level 1 to N and then signal is synthesized by using the altered detail coefficients from level 1 to N and approximation coefficients of level N. There are two types of thresholding; 1. Hard thresholding technique, 2. Soft thresholding technique.

Hybrid Thresholding:-
Hybrid thresholding is a combination of two thresholdings i.e. Soft and Hard thresholding. The performance of the Soft thresholding is better for noise removal than Hard thresholding but the image get blurred after performing Soft thresholding. The performance of Hard thresholding is not very good for noise removal but the image also does not get blurred. So, there is a need of such technique that can remove mixed noise and produce a good quality image with removal of as possible as value of information of the image during denoising process. Therefore we use hybrid thresholding to combine the properties of both thresholdings.
Steps for designing hybrid thresholding model:

Performance parameters:-
For comparing original building image with different denoised images, we calculate following parameters: 1) Mean Square Error (MSE): The MSE is the cumulative square error between the synthesized image and the original image defined by: Where 'f' is the original image and 'g' is the synthesized image. MSE should be as low as possible.
2) Peak signal to noise ratio (PSNR): PSNR is the ratio between maximum possible power of a signal and the power of distorting noise which affects the quality of the original signal. It is defined by: PSNR = 20 log 10 (MAX F )

MSE
Where MAX F is the maximum signal value that exists in our original image. PSNR should be as high as possible.
3) Root mean square error (RMSE): It measures of the differences between value predicted by a model or an estimator and the values actually observed. It is the square root of mean square error. RMSE should be as low as possible.

4) Structural Similarity Index (SSIM):
It is a method for measuring the similarity between two images. The SSIM measure the image quality based on an initial distortion-free image as reference.
Where: μ x is average of x; μ y is average of y; σ X 2 is variance of x; σ Y 2 is variance of y; σ XY is covariance of x and y; C 1 = (k 1 L) 2 and C 2 = (k 2 L) 2 are two variables to stabilize the division with weak denominator. L is the dynamic range of the pixel-values k 1 = 0.01 and k 2 = 0.03 by default.