Removal of Gaussian Impulsive Noise from Computed Tomography

Removal of Gaussian Impulsive Noise from Computed Tomography

Sanjay M N1, Nidhi V Aradhya2, Thejaswini M B 3, Meghana G R4,,Prof.Harish Kundar5 1,2,3,4 Student, Dept of CSE, AIET

5 Associate Professor, Dept of CSE, AIET

Abstract– Computed tomography images can be corrupted by noises like Gaussian and impulsive noise during which causes reduction of quality. So removing the noise from the image is very important in medical image processing. Mean and median filters which are present now are not very efficient in removing impulse and Gaussian noise. Thus, in this paper, a new filter is

image transmission. Impulsive noise is always independent. With impulsive noise, only certain pixels of CT image will be affected. There are different types of impulsive noises such as Salt and pepper impulsive noise and Random Valued Noise.

proposed which removes mixed noise such

as Gaussian and

The salt and pepper noise take either salt value or the

impulse noise. Based on existence of noises in their small neighbourhood, pixels of image are separated into non-corrupted pixels and corrupted pixels. For non-corrupted pixels, greyscale value is taken as output and for corrupted pixels removing noises are done base on their characteristics. The proposed filter eliminates these noises of varying density.

Keywords Noise; Gaussian Noise; Impulsive Noise; mixed noise

1. INTRODUCTION

   Noise is a unwanted disturbance that is produced in a CT scan image. Denoising means removal of noise from a image and hence it increases image quality. Different noise has its own attribute and it affects the method of image denoising. There are different types of noises. Some CT scan image contain Gaussian noise or some contain impulsive noise or some may contain its combination.

   Gaussian Noise damage CT scan image which complicates further image analysis. It is statistical type of noise. The probability density function is same as normal distribution which is also called Gaussian distribution. Poor illumination, high temperature, transmission can be the sources of Gaussian noise in CT scan images. This noise is created while film exposure and image development. There is Gaussian random noise, in case of thermal motion, when electrical variation meet Gaussian distribution. The probability density function p is given by:

   (1.1)

   Where z represents the grey level, represents the mean value and represents the standard deviation.

   Gaussian noise has random and normal distribution of instantaneous amplitudes over time. Impulsive noise is

   pepper value whose grey level can be either -225 or -0. It also contains black and white spots. If the total density of image is p then the salt and pepper noise density will be p/2.

   (1.2)

   Where represents the noisy image pixels, is the total noise density of the impulsive noise and is the uncorrupted image pixels. At any point of time the image densities of salt and pepper type of impulsive noise are different i.e. p1and p2. Hence the total noise density of the salt and pepper noise is calculated as:

   = 1 + 2……….(1.3)

   The random valued impulsive noise can take grey value between 0 and 255. The noise is randomly distributed over the entire image and the probability of its occurrence is same as noise. The random valued impulsive noise can be mathematically represented as follows:

   (1.4) Where is the grey level of the noisy pixel.

   As different noise has its own features and properties, its removal too need special filters. Filters are tool which can be used to remove noise from unprocessed image. CT scan can be done by giving high dose or low dose CT radiations. By high dose radiation, patients body will be exposed to large amount of radiation and image obtained will be of no or minimum noise. Even though noise will be absent, high radiation may affect patients health which is not advisable. Wherein low dose scan, patient will not be affected but image quality is low which contain noise. For this removal of noise is important. This paper tells about removal of those noises induced by low

   autonomous and uncorrelated to image pixels. It is randomly

   dose CT radiations. Presence

   of noise make image grainy,

   dispersed over CT image and it is short duration noise. It is

   snowy in appearance. Generally, quality of CT scan image

   immersed during image acquisition because of switching or atmospheric disturbances or interference of channel while

   depends on many factors.

   One such important factor is

   radiation dose. Noise will hide minor details and hence its removal is essential to analyse image.

   Noise in an image may be due to transmission and acquisition or due to some hardware issues. Amount of noise present in an image can be calculated by checking number of pixels corrupted. Noises in CT image can be divided as

   amplifiers or Gaussian noise, salt and pepper noise, shot noise

   planar cutters cannot be removed as their volumes look similar to the lobar fissures.

   1. PROPOSED METHODOLOGY

      As noise is unavoidable in image, main objective of this paper is to remove noise. Since high dose is not advisable as it is harmful, low dose is recommended. And to remove that noise

      or Poisson noise and Speckle Noise.

      produced by low dose, noise removal algorithm has been

      designed. As CT scan image contain both Gaussian and

2. LITERATURE SURVEY

Impulsive noise, removal of

both types of noise can be

Many literature reviews has proposed different procedures for removing noise from the CT scan image. Ehsan Lotfi [1] proposed a novel approach for removing Gaussian noise using adaptive Fuzzy filter and Image histograms. Major drawback of this is it takes longer time for execution.

Gnanambal Ilango et. Al. [2] have proposed a hybrid filtering technique for the removal of Gaussian noise using topological approach. In this, three filters are used. Drawback

of this will be it requires longer processing time due to

difficult. The algorithm proposed here can remove both Gaussian and impulsive noise spread across various regions of the image. The Hybrid filter proposed can remove mixed noise of Gaussian and impulsive noise. Initially image generated by low dose will contain noise. Then, before removing the noise, parameters like image density should be pre-processed. Based on type of noise, image is categorized into different regions and each region of the image is processed separately. The Gaussian distribution is calculated and using that Gaussian

presence of three filters.

Dmitri Van De Ville et. Al [3] has proposed a new fuzzy filter for images affected by additive noise. Drawback of this will be, for low noise levels which contain fine textures, this will not give satisfactory results.

Stephen M. Schmitt et. Al [4] have proposed a method to predict the noise properties of iteratively reconstructed CT image. But the drawback is its noise removal prediction was not satisfying from the edges.

Zhiqian Chang et. Al [5] have proposed Local Linear

Smoothing is done along with the median filter which considers the Gaussian distribution and the median is calculated and the noise is removed. Then, each region of the image is reconstructed using the pre-processed image details and the final step is to enhance the image quality for further diagnosis and processing.

Algorithm1: Hybrid Algorithm for removing Gaussian and Impulsive Noise.

Minimum Mean Squared Error (LLMME) Filter and Point

wise Bayesian Restoration for extracting the image details for

Model Based Iterative Reconstruction (MBIR) method based images. Drawback of this will be it does not give satisfactory results as image noise reconstruction was done on negative territory.

Input: The low dose CT scan image containing noise.

Output: The denoised high quality CT scan image.

Xue Ying Cui et. Al. [6] Have proposed learning based artifact removal by fragmenting the image into low frequency and high frequency parts. Based on the dictionary learning, the image is strengthened by removing noise and artifacts. Drawback of this is it will not remove the noise in the tissue structures.

Jun Feng Zhang et. Al. [7] have proposed improved non local means (INLM) method by calculating weight map from the pre-processed one for removing streak artifact and noise. But this is not efficient and simple as neighbour patches can contain other types of noise and the low dose protocol below 50mA has not been tested for succession.

L.L Chen et. Al [8]. Have proposed improved block matching and 3D filtering which is based on the context to

Step 1: The input image is partitioned into different

regions based on the image density.

Step 2: The Gaussian distribution is calculated by

..(3.1)

Step 3: The median of the image pixels are calculated by

. (3.2)

Step 4: Using the Gaussian distribution and the median of the pixel, the neighbour pixels are analysed and the noisy and corrupted pixels are removed

Step 5: Using the pre-processed image details, the denoised image fragments are reconstructed for obtaining CT scan image containing no noise and outliers.

reducenoise from low dose CT image. Drawback is it will not

preserve minute details such as the tissue and features at the edges.

Changyan Xiao et. Al. [9] have proposed a novel filter

for removing pulmonary fissure called as the Derivative of

Stick Filter which can be used for denoising and post processing of CT image. Drawback of this is, accessory and

Input Image containing noise

Partitioning image into different regions

based on pixels

Partitioning image into different regions

based on pixels

Calculating Gaussian Distribution

Calculating Gaussian Distribution

The median of the image pixels are calculated

The median of the image pixels are calculated

Using the Gaussian distribution and median corrupted neighbouring pixels are removed

Using the Gaussian distribution and median corrupted neighbouring pixels are removed

Output denoised image

Output denoised image

Fig 1: Proposed Algorithm

Algorithm2: Mixed noise removal by WESNR

Input : Dictionary ø, noise image y; Initialize e and W; Initialize µto 0.

Output : Denoised image x.

Loop : Iterate on k=1,2. K;

1. Compute (k)

2. Compute x(k) = øa(k) and update the non-localcoding vector µ;

3. Comute the residual e(k) = y-x(k);

4: Calculate the weights W by e(k)

Image 1(a): Original image

Image 1(b): Denoised image

Image 2(a): Original image

END

Output the denoised image x = ø(k)

Algorithm 2 depicts when dictionary ø is noted for a patch, problem can be solved by iteratively updating W and which depends on coding residual e. e can be initialized as:

e(0) = y-x(0) .(3.3)

1. RESULTS AND DISCUSSION

   Obtained images were denoised and smoothed. The algorithm removed noise from the CT image. The regions which had noise were smoothed and hence image details were enhanced. The denoised image shows that the edges are being preserved. The Peak Signal to Noise Ratio (PSNR) was improved with proposed algorithm.And Higher this ratio, image will be more denoised, and hence quality of the image will be high. The following images shows the denoising methodology where Image 1(a) contains noise in the image and Image. 1(b) do not contain noise and has been smoothed. Ten CT scan images are considered for denoising and the PSNR values have been provided in the Table 1 and Table 2.

   Image 2(b): Denoised image

   Image 3(a): Original image

   Image 3(b): Denoised image

   Image 4(a): Original image

   Image 4(b): Denoised image

   Image 5(a): Original image

   Image 5(b): Denoised image

   Image 6(a): Original image

   Image 6(b): Denoised image

   Image 7(a): Original image

   Image 7(b): Denoised image

   Image 8(a): Original image

   Image 8(a): Denoised image

   Image 9(a): Original image

   Image 9(b): Denoised image

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   PSNR after denoising

   PSNR

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   PSNR after denoising

   Image 10(a): Original image

   Im Im Im Im Im Im Im Im Im Im ag ag ag ag ag ag ag ag ag ag e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e

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   Im Im Im Im Im Im Im Im Im Im ag ag ag ag ag ag ag ag ag ag e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e

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   Image 10(b): Denoised image

   Table 1: COMPARISON BETWEEN THE PSNR VALUES OF

   ORIGINAL IMAGE AND THE DENOISED IMAGE

   Sl.no.	Image for analysis	PSNR (Original)	PSNR after denoising
   1	Image 1(a)	21.867	30.609
   2	Image 2(a)	21.5	33.16
   3	Image 3(a)	21.62	35.44
   4	Image 4(a)	21.66	42.044
   5	Image 5(a)	21.59	37.62
   6	Image 6(a)	20.91	34.63
   7	Image 7(a)	20.24	36.036
   8	Image 8(a)	15.36	34.448
   9	Image 9(a)	21.0619	35.327
   10	Image 10(a)	21.353	30.9

   Im Im Im Im Im Im Im Im Im Im ag ag ag ag ag ag ag ag ag ag

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   A graph has been plotted based on the table 1 in which the PSNR values of the images implemented through the Proposed algorithm is calculated

   GRAPH FOR COMPARING PSNR VALUES OF GAUSSIAN AND MEDIAN FILTER

   TABLE:2:COMPARING PSNR VALUES BETWEEN PROPOSED ALGORITHM AND EXISTING ALGORITHM

   Sl.n o.	Image for analysis	Gaussian Filter	Median filter	Denoising algorithm 30.609
   1	Image 1(a)	18.168	19.554
   2	Image 2(a)	21.522	27.677	33.16
   3	Image 3(a)	26.571	23.16	35.44
   4	Image 4(a)	29.028	27.231	42.044
   5	Image 5(a)	24.786	36.239	37.62
   6	Image 6(a)	20.058	25.019	34.63
   7	Image 7(a)	23.608	33.405	36.036
   8	Image 8(a)	1.898	26.118	34.448
   9	Image 9(a)	24.031	27.822	35.327
   10	Image 10(a)	17.653	20.861	30.9

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   Gaussian Filter Median filter

   denosing algorithm

   1. Zhiqian Chang, Ruoqiao Zhang, Jean-Baptist Thibault, Debashish Pal, Lin Fu, Ken Sauer, Charles Bouman, Modeling and Pre-Treatment of Photon-Starved CT Data for Iterative Reconstruction, IEEE Transactions on Medical Imaging, Vol 36, No. 1, January 2017, pages 277- 287.

   2. Xue-Ying Cui, Zhi-Guo Gui, Quan Zhang, Hong Shangguan, and An-Hong Wang, Learning-Based Artifact Removal via Image Decomposition for Low-Dose CT Image Processing, IEEE transactions on nuclear science, vol. 63, no. 3, June 2016, pages 1860-1873.

   3. MJungfeng Zhang, Yang Chen, Limin Luo, Improved Non Local Means for Low dose X-Ray CT Image , 3rd

   Internationational Conference on Information Science and

   GRAPH FOR COMPARING PSNR VALUES OF GAUSSIAN FILTER,MEDIAN FILTER AND THE PROPOSED ALGORITHM

   From the graphs shown above, the proposed denoising algorithm has higher PSNR values. Hence, images are more denoised and the quality of the image increases. This shows that the proposed algorithm works well and produces good quality images.

2. CONCLUSION

A new filter is proposed in this paper. The algorithm proposed can be used to remove mixed noise such as Gaussian and impulse noises. The image obtained after removing mixed noises has higher PSNR values. By comparing the value of PSNR with different experiments,it can be said that the proposed filter has better performance for mixed noise than any other existing. The proposed filter can eliminate different mixed noises and preserve every single detail of the image. But, the filter needs more running time than other existing filters. Therefore, the future work can be on reducing the computational cost and thus improving the efficiency of the algorithm.

REFERENCES

1. Ehsan Lotfi, An Adaptive Fuzzy Filter for Gaussian Noise Reduction using Image Histogram Estimation, Advances in Digital Multimedia (ADMM), Vol 1, No. $, Pages 190-193, 2013.

2. Gnanambal Ilango, R Marudhachalam, New Hybrid Filtering Technique for Removal of Gaussian Noise from Medical Images, APRN Journal of Engineering and Applied Sciences, Vol 6, No. 2, February 2011

3. Dmitri Van De Ville, Mike Nachteguel, Dietrich Van der weken, Etienne E Kerre, Wilfred Phillips, Noise Reduction by Fuzzy Image Filtering, IEEE Transactions on Fuzzy System, Vol 11, No. 4, August 2003

4. Stephen M.Schmitt, Mitchell M Goodsitt, Jeffrey F Fessler, Fast Variance Prediction for Iteratively Reconstructed CT Image, with Locally Quadratic Regularization, IEEE transactions on medical imaging, vol. 36, no. 1, January 2017, pages 17-26.

Control Engineering, 2016.

[8]L.L.Chen, S.P.Gou, Yao Yao, Jing Bai, Licheng Jiao, Ke Sheng, Denoising of Low Dose CT Image with Context-

Based BM3D, IEEE

[9] Changyan Xiao*, Berend C. Stoel, M. Els Bakker, Yuanyuan Peng, Jan Stolk, and Marius Staring, Pulmonary Fissure Detection in CT Images Using a Derivative of Stick Filter IEEE Transactions on Medical Imaging , Vol 35, No. 6, June 2016, pages 1488-1500