Image Denoising by using Modified SGHP Algorithm

ABSTRACT


INTRODUCTION
Images affected by unwanted noise from different sources like traditional film cameras and digital cameras. These noise elements will create some serious issues for further processing of images in practical applications such as computer vision, artistic work or marketing and also in many fields. So, different classification of noises likes salt and pepper, Gaussian, shot and quantization. In salt and pepper noise, all the images are constructed with pixels in a two-dimensional array. In that pixel to pixel, the difference is observed when the image is affected by noise that is in terms of intensity of neighbouring pixels. So, it is identified pixels and neighbouring pixels only the small number of pixels is affected in an image. The salt and pepper noise is clearly identified in an image by it contains black and white speckles. When we viewed an image which is affected by salt and pepper noise, the image contains black and white dots, hence it terms as salt and pepper noise.
In Gaussian noise, noisy pixel value will be a small change of the original value of a pixel. A diagram consisting of rectangles whose area is proportional to the frequency of a variable or PSNR and whose width is equal to the different noise standard deviations is a histogram. Other Gaussian models are present mainly depends upon the central limit theorem shows that addition of different noises from different sources to associated with Gaussian distribution.
Denoising of an image involves the manipulation of the image data to produce a visually highquality image. There are numerous models that have been published so far which are used for denoising an image [1]. Sparse representation for image restoration [2], [3], Total variation model [4], Wavelet-based model [5], BM3D [6] model and histogram preservation algorithm [7] are some of them. Each method has its own characteristics, benefit and also demerit. Two major classes of denoising methods are (a) model based and (b) Learning-based method. In the model, based method, a statistical/mathematical model will be used for the denoising. Whereas in Learning based method, an algorithm will be trained by using sufficient parameters and then the model is allowed to work based on its weightage function [8].

PROPOSED METHOD
In the present work, the denoising is done in a more realistic way as in practical situations, only the noisy image will be available. A noisy image is taken as input to the algorithm is shown in Figure 1. We have adopted patch-based noise level estimation algorithm by Xinhao Liu et al [9]. Patches are generated from the single noisy image and its weak textured patches are identified. The Noise level is estimated from the Principal Component Analysis [10], [11]. In most of the denoising method, it is seen that, after its implementation, the image will be blurred than that of the original image. Also, the edge of the denoised image gets smoothened and will have lesser details than that of the original image. A study has been conducted to find the edge of the original and noisy image by using sample data. In this study, it is found that there fewer details of edges in the denoised image. To address this issue, we have employed fuzzy based edge detection and then the edge is enhanced in the denoised image that we have received by using our method. Now the denoising is performed based on the modified parameter S-GHP focus on smoothing of the image by implementing the gradient histogram preservation.

Noise estimation
Input image is decomposed into overlapping patches by y z n i i i  (1) Where z i has represented the original image patch with the ith pixel at its centre and y i is the observed vectorized patch corrupted by zero-mean Gaussian noise [12] vector n i . The objective of the noise level estimation is to compute the standard deviation σ n of the noisy image is given. In this method, the Horizontal and vertical derivative ( The Directional Derivative in both Horizontal Direction and Vertical Direction is calculated and trace of Gradient Matrix is calculated by Now the initial noise level is estimated by computing the First component of Eigenvalue of the covariant matrix. This is taken as the initial value for calculating noise level by using iterative noise estimation [13]   Now the noise level estimation form weak textured patch is performed [14]. For this Inverse gamma function with the shape parameter α and scale parameter β is used If the selected patch size is less than  then the patch is selected as a Weak Texture Patch.
Maximum eigenvalues of the gradient covariance are computed when the strength of image patches are to be estimated. Now the Noise Level of Weak Texture Patch is found by using the EigenValue of Covariance Matrix of the weak textured patch and its principal component [15], [16]. The iteration is continued until the difference between sigma in step n-1 and n is less than 10 -4 .

Image denoising frame work
The noisy image is defined by the Equation (6) that is Where the noisy image is represented with y, the Original image is represented with x, Additive white Gaussian noise (AWGN) with zero mean is represented with v and the standard deviation is denoted with  .
The main purpose of image denoising is to compute the clean image x from noisy image y. The vibrational method is the best denoising approach is obtained by Where regularization term is denoted with R(x) and positive constant is with λ. The R(x) relies on existing images. Image denoising methods have a general issue that image quality scale characteristics such as structures like texture will be over-smoothed. The original image has substantial gradients than the gradients of over smoothed image. Inherently, a structure like texture doesn't depend on over smoothing and the texture have an indistinguishable gradient distribution of x for good evaluation of x. For this reason, we propose a modified parameter in S-GHP method by taking different database images. The gradient histogram of the denoised image x very close to the reference histogram h r based on the compute of the gradient histogram of x, denote h r. The following proposed S-GHP denoising method is defined as x F x    F is updated by using modified parameter S-GHP specification operator.
Another case in the S-GHP method is what way to perceive the reference histogram h r of unspecified image x. Computation of h r depends on the noisy observation y. For finding h r, new methods are proposed first one is a regularized deconvolution method and the second one is an iterative deconvolution method from the noisy image [17] depends upon different noise levels [18]. After reference histogram is attained, then modified parameter in S-GHP method is applied for image denoising.

S-GRADIENT HISTOGRAM PRESERVATION DENOISING METHOD
S-GHP is a proposed method based on the patch method. Let ii Where concatenation belongs to α for all the values of i  .
Images are taken from databases are testing modified parameter S-GHP Method. So, the combination regarding identical priors refines the modified parameter S-GHP. For example, the estimation procedures in [19]- [23] merge image non-local NSS prior to image local sparsity prior and we have better denoising results. In the method modified parameter in S-GHP, the R(x), which is sparse non-local regularization term proposed in the non-locally centralized sparse representation (NCSR) model [24] is and coding vector of the qth nearest patch ( , where the predefined constant is h and normalization factor is W. The formula for modified parameter S-GHP method is defined as by using Equation (3) is Such that From the S-GHP method, using Equation (7), F (∇x) is approximate to ∇x when histogram parameter leads to larger and we can achieve required histogram parameter for S-GHP. When the histogram h F of |F (∇x)| is

Performance analysis
The proposed method is verified by using three different images like image-3, image-4 and image-5. Here, three images are grey-scale images having a range between 0 to 255. For image-3, image-4 and image-5 are taking five different noise levels are 20, 25, 30, 35 and 40 with respect to that different PSNR and SSIM values are obtained. In Figure 2, Figure 3 and Figure 4, there is original image and different enhanced images with different noise levels. In Figure 5, numbers of iterations are increased then PSNR value increases. When noise standard deviation is increased then the structural similarity index is decreased. From the Figure 5, image-3 having more structural similarity index. In Table 1, Table 2 and Table 3 give the structural similarity index and PSNR values of image-3, image-4 and image-5 by using a modified parameter in S-GHP method.

Comparative analysis
The existing methods and proposed method verified by using three different images like image-3, image-4 and image-5 with five different noise levels are 20, 25, 30, 35 and 40. Performance of these methods is mentioned in terms of Peak signal to noise ratio and structural similarity index [25], [26] as shown in Table 4.

CONCLUSION
In this paper, the proposed method modified Structure gradient histogram preservation used for enhancing the different images by taking different noise levels like 20, 25, 30 and 40. Based on the noise levels, the PSNR and SSIM values are improved compared to other methods like APBS and B-GHP. All the above-mentioned results proved that the modified parameter S-GHP is better compared to B-GHP and APBS.