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标题中的“Ani.pdf.zip_PSNR_de-noising_ief_impulse noise_median filter”揭示了这个压缩包文件涉及的主要内容，即图像处理领域中的噪声去除技术，特别是针对高密度盐和胡椒噪声（salt and pepper noise）的处理。其中关键词包括PSNR（峰值信噪比）、de-noising（去噪）、ief（理想边缘滤波器）和median filter（中值滤波器）。接下来我们将详细探讨这些知识点。 1. **PSNR（峰值信噪比）**：峰值信噪比是衡量图像质量的一个重要指标，通常用来评估经过处理后的图像与原始图像之间的相似度。它是通过计算两幅图像的均方误差然后取其倒数的对数得到的，单位通常是dB（分贝）。PSNR值越高，表示处理后的图像质量越好，噪声更少。 2. **De-noising（去噪）**：去噪是图像处理中的核心任务，目的是从含有噪声的图像中恢复或提取清晰的图像信息。去噪算法有很多，如基于统计的滤波器、小波分析、稀疏表示以及深度学习方法等。在这个案例中，我们关注的是针对高密度盐和胡椒噪声的去噪技术。 3. **Impulse Noise（脉冲噪声）**：脉冲噪声，也称为盐和胡椒噪声，是一种常见的图像噪声类型，表现为图像像素值突然变为最大或最小值。这种噪声通常由传感器故障、传输错误或电子干扰引起。在MRI（磁共振成像）中，由于设备的不稳定或外部磁场的影响，可能会引入此类噪声。 4. **Ideal Edge Filter（理想边缘滤波器）**：理想边缘滤波器是一种理想的低通滤波器，用于保留图像边缘而去除高频噪声。然而，由于其数学上的理想性，它在实际应用中无法实现，因为会导致图像边缘模糊。在去噪过程中，通常会采用其他滤波器来尽可能地平衡噪声去除和边缘保持。 5. **Median Filter（中值滤波器）**：中值滤波器是一种非线性的滤波方法，特别适用于去除脉冲噪声。它的工作原理是用窗口内像素的中值替换中心像素的值，有效地将噪声点替换为周围像素的平均值，而不会显著改变图像的边缘。对于高密度盐和胡椒噪声，中值滤波器通常表现出较好的效果。综合以上知识点，该压缩包可能包含一篇关于如何使用理想边缘滤波器和中值滤波器来提升MRI图像在高密度盐和胡椒噪声环境下的PSNR的论文。"Ani.pdf"很可能是这篇论文的PDF版本，详细阐述了这一算法的设计、实施和性能评估。通过阅读这份文档，我们可以深入理解如何利用这些技术改善医疗图像的质量，从而提高诊断的准确性。

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344 | P a g e

A NEW ALGORITHM FOR REMOVAL OF HIGH

DENSITY SALT AND PEPPER NOISE IN MR IMAGES

Sumanta Saha

, Anindita Mohanta

, Sharmistha Bhattacharya (Halder)

Department of IT, Tripura University, Agartala, (India)

Department of Mathematics, Tripura University, Agartala, (India)

ABSTRACT

Magnetic Resonance Images (MRI) are corrupted by impulsive noise mainly due to sensor faults of image

acquisition devices. This impulsive noise is most commonly referred to as “salt and pepper” noise. In this

article, a new approach has been introduced for removal of “salt and pepper” noise while preserving the image

details. This proposed method is basically a two-step method, wherein the first step; detect the corrupted pixel

since the impulse noise affects only certain pixels in the corrupted image and the remaining pixel values are

unchanged. In the second step, the corrupted pixel is replaced by the median value or by itsneighborhood

uncorrupted pixelvalueof the considering window. This proposed algorithm (PA) has shown encouraging

results, the Peak Signal to Noise Ratio (PSNR), Structured Similarity Index (SSIM) and Image Enhancement

Factor (IEF) of the filtered image using the PA are much higher values than the Wiener Filter (WF), Mean

Filter (MF), Standard Median Filter (SMF), Adaptive Median Filter (AMF)and other existing algorithms.

ThePA is also effective for other types of highly corrupted gray-scale and color images to remove salt-and-

pepper noise.

Keywords- De-noising, IEF, Impulse noise, Median filter, PSNR, Salt-and-Pepper noise, SSIM.

I. INTRODUCTION

Magnetic Resonance Images (MRI) are one of the most widely used medical imaging tools in both clinical and

research applications [1]. The pixels in MR image, mainly gets corrupted due to the acquisition, bit errors in

transmission and transformation process from analog to digital domain. In addition, images corrupted by these

processes are mostly by the impulse noise. Also, impulse noise can be of two types namely, fixed valued

impulse noise and random valued impulse noise [2]. Fixed valued impulse noise is also called as Salt and Pepper

noise, which takes only two values either 0(Pepper) or 255(Salt), whereas random valued impulse noise can take

any value between 0 and 255.

The process of removing noisy pixels is called as image de-noising [2]. Before performing any examination on

corrupted MR image, it is necessary to eliminate the noisy pixels first. However, to remove Salt and Pepper

noise from MR images many algorithms have been used, but one of the simplest and effective methods is the

Standard Median filter (SMF). An SMF is basically a non-linear filter. In addition, linear filtering techniques are

not effective in removing impulse noise, so non-linear filtering techniques are widely used in the restoration

process [3]. The SMF is one of the most popular non-linear filters used to remove salt-and-pepper noise in a

corrupted MR image. However, the major drawback of the SMF is that the filter is effective only for low noise

345 | P a g e

densities. Also it exhibits blurring if the window size is large and leads to insufficient noise suppression if the

Window size is small [3]. In the case of the highly corrupted image, the edge details of the original image will

not be preserved and blurring effect in the filtered image is one of the major drawbacks of SMF. During the

filtering process of the corrupted image, it is importantthat the edge details have to be preserved. The perfect

approach is to apply the filtering technique only to noisy pixels.

To remove SMF problems, Median filters such as Adaptive Median Filter (AMF), Decision–based median

filters can be used for selecting the corrupted pixels first, and then apply the filtering technique on the corrupted

pixel. As a result, only noisy pixels will be replaced by the median value and uncorrupted pixels will be left

unchanged. AMF gives satisfactory performance at low noise densities since the corrupted pixels which are

replaced by the median values are very few. Also, at higher noise densities, window size has to be increased to

get better noise removal which will lead to less correlation between corrupted pixel values and replaced median

pixel values. In the decision-based median filters, the decision is based on a pre-defined threshold value.

However, the major drawback of Decision–based median filters is that defining a robust decision measure is

difficult [3].

To overcome existing filtering problems, we proposed a new algorithm in this paper.This is consists of two

stages. In the first stage, each pixel values are checked if a windows center pixel is corrupted and classify the

corrupted and uncorrupted pixels. In the second stage, corrupted pixels are replaced by either the median pixel

or neighborhood uncorrupted pixel. This proposed algorithm (PA) has used a fixed window size of 3×3 resulting

in lower processing time compared with AMF and a smooth transition between the image pixels. Edge

preservation, remove all noisy pixels and better visual quality have been observed from the results. Also, it gives

better PSNR, SSIM and IEF values compared to the other filtering techniques like Mean Filter, Wiener Filter,

Standard Median Filter [1], Adaptive Median Filter [4], [5], Decision Based Algorithm (DBA) [3], Modify

Standard Median Filter (MMF) [1],and other existing algorithms[7], [8], [9], [10].

II.LITERATURE REVIEW

Chan et al., [6] proposed an algorithm to overcome AMF problem, which consists of two stages. The first stage

is to classify the corrupted and uncorrupted pixels by using AMF and in the second stage, regularization method

is applied to the corrupted pixels to preserve edges and correct noisy pixels. Also, the drawback of this method

is that for high impulse noise, it requires large window size of 39×39, so processing time is very high.

Additionally, it requirescomplex circuitry for the implementation.

There are several approaches for identification and replacement of corrupted pixels butthe simplest approach is

HanafyM.Ali [1] proposed algorithm. This algorithm consists of two stages. The first stage is to classify the

corrupted and uncorrupted pixels and in the second stage, corrupted pixel is replaced by the median of its

neighbors. However, the drawback of this method is that for high noise density, some noisy pixel values are left

unchanged.

Madhu S. Nair et al.[3] proposed a New Decision-Based Algorithm (DBA) can be applied for high noise

density. At the start, it makes a difference between the corrupted and the uncorrupted pixels. Then the filter is

applied only to the corrupted pixels. The advantage of the DBA lies in removing only the noisy pixel either by

the median value or by the mean of the previously processed neighboring pixel values.

346 | P a g e

Esakkirajanet al. [7] proposed a Modified Decision Based Unsymmetrical Trimmed Median Filter

(MDBUTMF) for the restoration of highly corrupted salt and pepper noise. In this algorithm, the noisy pixels is

replaced by trimmed median value when other pixel values are 0’s and 255’s. When all pixel values are 0’s and

255’s, then the corrupted pixel is replaced by the mean value of all the elements present in the selected window.

A.K. Samantarayet al. [8] proposed First Order Neighborhood DecisionBased Median Filter (FONDBMF)

motivated by MDBUTMF filter. In this algorithm, the noisy pixels is replaced by the first order neighborhood

pixels trimmed median value when other first order neighborhood pixel values are 0’s and 255’s. When all first

order neighborhood pixel values are 0’s and 255’s, then the corrupted pixel is replaced by the mean value of the

first order neighborhood pixels in the selected window.

Biswal, Satyabrata, and NilamaniBhoi[9]proposed a new method (NMF) for removal of high density salt and

pepper noise. In this technique when the processing pixel is corrupted then its neighbors are checked. When all

theneighbors are corruptedthen the processing pixel isreplaced with the mean value of the window. When some

of the neighbors arecorrupted then processing pixel is replaced by the unsymmetric trimmed mean value.

Aswini K Samantarayet al. [10] proposed a Decision Based Adaptive Neighborhood Median Filter

(DBANMF).That is consists of three stages. In the first stage, it considers only the first order neighborhood

(FON) pixels. In that if it finds one un-corrupted pixel, then that un-corrupted pixel replaces the corrupted center

pixel. If it finds more than one un-corrupted pixel among the FON pixels, then the median value of those un-

corrupted pixels replaces the corrupted center pixel. The second stage is followed by the first phase if and only

if it does not find at least one un-corrupted pixel in the FON pixels. In the second stage, it considers only the

diagonal neighborhood (DN) pixels. In DN if it finds only one un-corrupted pixel, then that un-corrupted pixel

replaces the corrupted center pixel.And if it finds more than one un-corrupted pixel, then the median value of

those un-corrupted pixels replaces the corrupted center pixel. If the method fails in above two phases i.e. if it

does not find at least one un-corrupted pixel in its neighborhood, then it goes to the third phase. In this stage it

calculates the mean of all the neighborhood pixels and replaces the corrupted center pixel by the calculated

mean value.

III. SALT-AND-PEPPER NOISE

An image containing salt-and-pepper noise will have dark pixels in bright areas and bright pixels in dark areas.

Also, the negative impulse appears as black point (pepper noise) and the positive impulse appears as white point

(salt noise) [1]. This type of noise can be caused by dead pixels, analog-to-digital converter errors, bit errors in

transmission, fault memory locations in hardware or transmission in a noisy channel etc. This noise can be

dark/bright pixels [11]. However, all pixels are not corrupted by salt and pepper noise in an image instead of

some pixel values are changed and remaining pixels are unchanged. It is also known as fixed valued impulse

noise and it is restricted to the minimum (0) or the maximum (255) intensity value [1]. The minimum intensity 0

appears as black pixels on the MR images. On the other hand, the maximum intensity 255 appears as white

pixels on the MR images.

The Salt and Pepper noise model, the distribution P (N) of noise intensity N is defined in the equation as

follows:

347 | P a g e

(1)

IV. PRELIMINARY STUDY

Image de-noising is avery important task in image processing for the analysis of images. MR image de-noising

methods can be linear as well as non-linear. Linear methods do not preserved the details of the images, whereas

the non-linear methods preserved the details of the images. The non-linear filters like Median filter, provides

good restoration from the noisy image [12]. It move filtering window over the noisy image and replace each

center pixel by the median of the filtering window. The Median filter arecommonly used for removing impulse

noise in MRI due to its good de-noisy property.

The standard median filter (SMF) is derived from the median filter.It attempts to remove noise by changing the

center pixel value of the filtering window with the median of the neighbor’s pixel values. The median value is

calculated by arranging all the neighbor’s pixel values in ascending order and select the middle pixel. SMF is

very useful in salt -and-pepper noise filtering because they do not depend on values which are significantly

different from the typical values in the neighborhood. The basic principal behind SMF is that the original pixel

value, which is replaced by a newer one, that is closer to or the same as the median value eliminates isolated

noise points [1]. However, the drawback of SMF is that itremoves thin lines and blurs image details even at

medium noise densities. Also, the major drawback of SMF method is that it changed middle pixels value of

selected 3x3 window without checking whether, it is corrupted or not.

There are several MRI image de-noising methods based on median filter like SMF, MMF [1] DBA [3],

MDBUTMF [7], FONBDMF [8], NMF [9] and DBANMF [10], but they have the disadvantage of blurring

edges. So, the aim of the new algorithm is to remove all corrupted pixel and maintaining reasonably edge of the

MRI images even at the high noise density.

V. THE PROPOSED ALGORITHM

Median filters have chosen for removing salt-and-pepper noise because of their simplicity and less

computational complexity. This paper describesa new decision based non-linear filteringtechnique for tackling

the problem of median filters with minimal increase in computational load.Also, it preserved edges and restored

all the noisy pixels. In most of the existing algorithms including SMF and AMF, only median values are used

for the replacement of the corrupted pixels. The proposed de-noising algorithm (PA) is based on non-linear

filtering technique. The PA first detects the salt and pepper noise in the image. The corrupted pixels in the image

are detected by checking the pixel element value against the 0 and 255 values in the selected 3x3 window.

Afterwards, inthe case of impulse noise corrupted pixel value is 0 or 255 and other values remain unchanged. In

addition, this proposed algorithm (PA) consists of two stages. In the first stage, each pixel values are checked if

a windows center pixel is corrupted and classify the corrupted and uncorrupted pixels. In the second stage,

corrupted pixels are replaced by either the median pixel or neighborhood uncorrupted pixel. If the pixel have a

value between 0 and 255 values in the 3x3 window of processing, then it is an uncorrupted pixel and any kind of

changes are not required.

The steps of the proposed algorithm as follows:

Step 1. Select a 2-D Window W of size 3x3. Assume that the center pixel is A

2, 2

348 | P a g e

Step 2.If 0< A

2, 2

<255, then A

2, 2

is an uncorrupted pixel.Its value is left unchanged and go to Step 7.

Otherwise, A

2, 2

is a noisy pixel.

Step 3.Find Wmin, Wmed and Wmax - the minimum, median and maximum pixel values respectively of W by

arranging the pixel values in ascending order.

Step 4.If A

2, 2

is a noisy pixel, it will be replaced by Wmed, the median value of the W.

Step 5.If Wmin=0 or Wmax =255, then read each pixel values of the W row wise.

Else go to Step 7.

Step 6.For each pixel Ax, yin the W do

If 0< Ax, y <255, then Ax, y is an uncorrupted pixel and its value is left unchanged.

Otherwise Ax, y is a noisy pixel.

Case (i) If Ax, y is a noisy pixel and x=y=1 then Ax, y will be replaced by the right neighbor (A

1, 2

) pixel value,

if the right neighbor pixel value is also noisy pixel then Ax, y will be replaced by the down neighbor (A

2, 1

) pixel

value, if the down neighbor pixel value is also noisy then Ax, y will be replaced by A

2, 2.

Case (ii)If Ax, y is a noisy pixel, where x ≠ y and y=2, then Ax, y will be replaced by the right neighbor pixel

value, if the right neighbor pixel value is also noisy pixel then Ax, y will be replaced by the left neighbor pixel

value.

Case (iii) If Ax, y is a noisy pixel, x ≠ y and x=2 then Ax, y will be replaced by the down neighbor pixel value,

if the down neighbor pixel value is also noisy pixel then Ax, y will be replaced by the right/left neighbor (A

2, 2

)

pixel value.

Case (iv)If Ax, y is a noisy pixel, where x =1 and y= 3 then Ax, y will be replaced by the down neighbor (A

2, 3

)

pixel value, if the down neighbor pixel value is also noisy then Ax, y will be replaced by the left neighbor (A

1, 2

)

pixel value.

Case (v)If Ax, y is a noisy pixel, where x =3 and y= 1 then Ax,y will be replaced by the right neighbor (A

3, 2

)

pixel value, if the right neighbor pixel value is also noisy pixel then Ax, y will be replaced by the upper

neighbor (A

2, 1

) pixel value.

Step 7. Repeat Steps 1 to 6 until all the pixels in the entire image are processed.

In the PA, the nature of the pixel being processed first, that is, it is corrupted or not, is checked. The value of the

pixel being processed is then replaced with the corresponding value as in Step 4 and cases (i), (ii), (iii), (iv), (v)

of Step 6. The window is then subsequently moved to form a new set of values. This process is repeated until

the last image pixel is processed.

VI. METHODOLOGY OF THE PROPOSED ALGORITHM

Consider a 3x3 window:

P1 P2 P3

P4 P5 P6

P7 P8 P9

For each selected 3x3 window first checked pixel value P5 is corrupted or not.

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