Performance Analysis of Different Restoration Techniques for Degraded 3D Cervical Spine MRi image

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The Image processing takes an image as an input and provides uncorrupted output image or original image information. In the present scenario, digital image processing is used in various fields such as medical imaging processing for diagnosis of diseases, face recognition for security purposes and resource exploration 1 . There are several degradation sources such as noise and blur presented in the available literature which may corrupt the image 2,5,7,8,12 . The process of recovering an image that has been degraded by a son degradation process is known as Image Restoration. In the field of engineering, digital image processing introduced a different kind of image restoration methods to recover original scene from degraded observations. The noise removal method should be applied in accurate manner in order to obtain precise image in medical image processing 2 . Various restoration techniques Image restoration techniques exist both in spatial and frequency domain. In the proposed work, motion, out of focus and environmental turbulence blurs are considered in degradation of 3D cervical spine MRI Image. In the paper Salt and Pepper, Gaussian, Speckle and Poisson noises are added in order to corrupt image. The linear (Gaussian filter. Average filter, Poisson filter) and nonlinear (Median, Min and Max filter) restoration techniques both are used to obtain preciseimage so that uncorrupted image can be used to get correct observations for the given application in medical image process. In the paper, MSE, PSNR and CC performance analysis criterions are used for selection of best filter for a particular type of noise model to recover noiselessly and de blurred image and thus to enhance performance of restoration techniques.

Image Degradation Models
Image acquisition depends on the quality of sensing elements, transmission media and environmental conditions such as atmospheric disturbance, humidity, light, and temperature etc. In the proposed work, degradation of image is also done by motion blur, out-of-focus and environmental turbulence blurs. Motion blur is the visible line of a different colour of moving objects 3 . It is the most widely recognized corruption types found in the customer photography. In most cases, the out of focus blur caused by a system with a circular aperture. An Image formed by connecting the stage of optical system analogous to a lens, selected depth of the object is aimed by the lens, but the objects at different distances are corrupted by different level calculating on their distances. The parameters on which the camera focus depends on focal distance, wavelength of the incoming light object, object depth and aperture size 4 . This type of Long-term exposure to atmospheric distortions is commonly experienced in remote sensing and aerial imaging caused by optical turbulence and scattering and absorption by particulate results in a degraded image 3 . Salt and Pepper, Gaussian, Speckle and Poisson which are added in order to corrupt 3D cervical spinal MRI image and described as follows:

Salt & Pepper Noise Or Impulse Noise
This noise appears in images as black and/ or white impulse of the image. The noise is due to white and black spots which chaotically scattered gray scale images along image area. The Power Density Function for Salt & Pepper noise is given as 5,12 : The basic steps which are used to add salt and pepper noise into RGB and Gray Scale image are given as: 1. First color image is converted into monochrome image. 2. Random values will be generated by "randn" function for the given matrix size within the specified range. Consider an image matrix of size 4x3 image matrix as: The effect of the addition of this noise in RGB and Gray Scale Image is shown in Figure1.

Gaussian Noise
Gaussian noise is one of the most occurring noise and also called additive noise. In this noise certain distribution is added to each pixel in order to modify it 2,12 . Whenever this noise appears, then receiver interprets received sample value y(k) at the kth sample time as the sum of noise-free component y 0 (k), i.e., the sample value  It can be written as: The noise component w(k) is irregular, but assumed to be drawn at each sample time from a fixed Gaussian distribution for concreteness. And RGB and Gray Scale Image which is degraded by Gaussian Noise with noise variance 0.005 is presented in figure 2.

Speckle Noise
This noise is usually modeled by random element multiplication with pixel elements of the image 6 . The random settlement of the pixel in the image appears due to inherent characteristic of ultrasound imaging. This unknown settlement of the pixel in the image is known as speckle noise. Radical reduction in distinction resolution due to speckle noise produces a negative impact on medical imaging 7 . The speckle noise can be modelled as: The behavior of Speckle pattern depends on the number of disperse per resolution cell or disperse number density. In the figure3, speckle noise with noise density 0.04 is added to RGB and Gray Scale Image to degrade it.

Poisson Noise
When the electromagnetic waves of high energy are injected into patient's body from its source, this noise appears due to the statistical nature of electromagnetic waves on medical instrument of imaging systems. The noise is also called as quanta (photon) noise or shot noise. This noise obeys the Poisson distribution which is given as : Where l is the expected number of the particles i.e. photons per unit time interval, which is proportional to the occurrence of the scene radiance. A rate parameter 'lt' is known as the standard Poisson scattering or distribution which corresponds to the expected incident photon count. The uncertainty described by this diffusion is known as photon noise. Photon noise include random electron emission which consists of Poisson distribution with mean square value 8 . Because the occurrence of the light particle count follows a Poisson scattering, it has the property that its variance is equal to its expectation that is represented by equation 4.

[ ] =
[ ] = ...(4) This shows that its standard deviation grows with the square root of the signal and photon noise is information or signal dependent. Photon noise variance depends on the expected photon count and is often modelled using a Gaussian distribution as: This approximation in most cases is very accurate. According to the central limit theorem, for larger particles of light count or photon count Poisson distribution approaches to Gaussian distribution and for the small particles of light counts photon distribution is dominated by other signal independent sources of random signal. The effect of Poisson noise after its addition in RGB and Gray Scale Image is presented in figure 4.

Image restoration techniques Linear Restoration Method
In this method the original image is to be convolved with a mask. The mask represents a low-pass filter or smoothing operation which is used to restore certain type of noised images. The output of a linear operation due to the sum of two inputs is same as that of performing the operation on the inputs individually and then summing the results. Some of the linear restoration methods used to restore the captures 3D MRI image are given as:

Gaussian Filter
It works by using the 2D distribution as a point-spread function. This is achieved by convolving the 2D Gaussian distribution function with the image. And to implement it steps which are used are given as: 1. Design the kernel window 2. Use formula to design 2D Gaussian kernel For this consider the standard deviation, sigma =0.6 and the kernel size 3x3. i.e (1/ 2 ²) = 1/ 2.2619 3. The width of the kernel is X=3 and the height of the kernel is Y=3. On convolution of the local region and the Gaussian kernel gives the highest intensity value to the center part of the local region (38.4624) and the remaining pixels have less intensity as the distance from the center increases. The result obtained from the total sum is stored in the present pixel location (Intensity=94.9269) of the image.

Average Filter
The filter operates on a m x n mask by taking average of all pixel values within the window and replace the center pixel value in the final image with the result. It also causes a certain amount of blurring in the image 11 .   The weights (w) can depend on i and j for full generality and result in a filter which vary across the image. Also, all the filters will have windows composed of odd numbers of rows and columns. It is possible to have even-sized windows, but there will be half-pixel displacement between the input and output images.

Wiener Filter
It is a digital filter used to adjust variable parameters obtained due to mathematical programming. This filter is applied to the degraded image to adjust the local variance of the image. By adjusting its variance means calculating the distance between random number or noisy pixel and average of those pixels centered within the mask. Smoothing of the image is totally depending upon the variance of the image. Large value of the variance results in less smoothing and small value of the variance results in more smoothing. This type of linear filtering is more adaptive in the field of image processing as it produces better results. The following steps are used for its implementation: 1. Define a window of size m x n 2. Consider matrix B with Gaussian noise.

Nonlinear Restoration Method
In this method, it is necessary to impose constraints such as non-negativity i.e. either positive or zero to implement spatial adaptively and recover missing spatial or frequency components at the expense of economical implementation and native convergence. Non-linear filters preserve the details of the image. Non-linear filters have many applications, especially removal of noise that is not additive 10 . Some of the nonlinear restoration methods used in the proposed work are given as:

Median Filter
It is one of the order Statistic or Rank Filter due to its nature of edge preserving. In this middle pixel value from the ordered set of values within the mxn neighborhood(W) around the reference pixel is selected 2,4 ( , ) = { ( , ) |( , ) ∈ } ... (6) And an output value of pixel is determined by replacing the value of each corresponding pixel by the median of the neighboring pixels, rather than the mean. The mean of the extreme values of the pixels in the degraded image is more sensitive to its median. This filter has ability to preserve the edges of the image i.e contrast or sharpness of image. The image filtered with 3x3 windows still contains salt and pepper noise, but the edges are sharp. The image filtered with a larger window size contains less noise as compared to less window size. Now the implementation process used to restore the corrupted image is given as: Let the original image with the matrix   The middle pixel value A (2, 2) will be change after sorting   The pixel value of the output image matrix is replaced by median 0.Thevalueofthe output pixel is found using the median of the neighboring pixels. Repeat this process until the whole matrix is replaced by the median value safter that the final output matrix is

Minandmax filter
It works on a ranked set of pixel values. The min filter, also known as the zeroth percentile. The min filter replaces the reference pixel with the lowest value 11 . Similarly, the max filter, also known as the100th percentile filter, replaces the reference pixel within the window with the highest value. Now the following steps are used for the implementation of max filter to recover the original image: Consider matrix A :  Similarly the following steps can be used to implement min filter: 1. Find the darkest points in an image. 2. Also find the minimum value in the area encompassed by the filter. 3. Reduces the salt noise as a result of the min operation. 4. The 0th percentile filter is min filter.

ReSuLtS AND DIScuSSION
Image restoration techniques as discussed in section3 has been applied to degraded 3D cervical spine MRI image to improve de noising of the image. In the figures 5-10, input image is corrupted using Salt &Pepper Noise and restoration of the image using various restoration techniques to preserve the shape transitions has been shown.

Restoring Salt &Peppernoiseusing 5X5 Windows Filters Restoring Gaussian Noiseimageusing 5X5 Windows Filters
The figures 11-16 depicts restoration of input image crashed using Gaussian Noise using several 5x5 filter masks to improve clarity of image.

Restoring Speckle Noise Image using 5X5 Windows Filters
In the figures 17-22 restoration of input image degraded with the addition of speckle Noise using several 5x5 window filters to recover the original image have been presented.

Restoringpoisson Noiseimageusing 5X5 Windows Filters
The restoration of image corrupted using poisson noise using various restoration techniques has been achieved in the figures 23-28.

Filter performance Analysis MSe (Mean Square error)
It has been observed that for salt & pepper noise image of the cervical spine MRI as shown in figures 5-10, the MSE values of Gaussian filter window5x5 is much better than other filters as can been seen in table1. It can also be observed that wiener filter has provided better performance for degraded 3D cervical spine MRI image using Gaussian, speckle and Poisson noise as presented in table1.

PSNR(Peak Signal to Noise Ratio)
In table 2, it has been shown that for corrupted 3D cervical spine MRI images with the addition of salt and pepper, Gaussian, Speckle and Poisson, the wiener filter5x5window has provided a better peak signal to noise ratio. It can also be analyzed that performance of Gaussian filter with 5x5window is also good or stable for considered corrupted images.

cc(cross correlation)
For 3D cervical spine MRI image degraded with Salt & Pepper noise, cross correlation values of Gaussian filter are much better than other filters used to recover the original image as shown in table3. But cross correlation values of wiener filter5x5 window is much better than other filters cONcLuSION Image restoration techniques for medical images are not so much developed in the present scenario, but their use for proper application and performance measure is still a matter of ongoing research. In the proposed work, different linear and nonlinear restoration techniques have been applied to noisy images which are corrupted with the addition of Salt and Pepper, Gaussian, Speckle and Poisson noises to recover the image. The quantitative analysis using numerical parameters like MSE, PSNR and CC of linear and nonlinear filters for noisy images has been carried out in this proposed research work. It can be concluded that the Wiener Filter with5x5 window is the best filter for Gaussian, speckle and Poisson noise, according to the experimental results on 3D cervical spine MRI Image. Also, Gaussian filter with 5x5 window is the best filter in order to de noise and restores 3D cervical spine MRI image degraded by the addition of salt & pepper noise. The restoration techniques used in the proposed work can be used to retain the structural details of the medical image.

Conflict of Interest
Authors of the proposed research work declare that he/she has no conflict of interest.