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Image Denoising with 2-D FIR Filter by Using

Artificial Bee Colony Algorithm

Serdar Kockanat

Cumhuriyet University

Sivas Vocational School

Electronic Communication

Technology

58140, Sivas, Turkey

[email protected]

Nurhan Karaboga

Erciyes University

Faculty of Engineering

Department of Electrical-Electronic

Engineering

38039, Kayseri, Turkey

[email protected]

Turker Koza

Bozok University

Vocational School

Electronic Technology

66200, Yozgat, Turkey

[email protected]

Abstract In this paper, a new design approach that has

employed the artificial bee colony algorithm for image denoising

using two dimensional finite impulse response digital filter, is

discussed. Four different images have been used for testing. The

white Gaussian noise has been added to each of the images and

the two dimensional finite impulse response digital filter removesthe noise from the noisy images. The original images have been

compared with the restored images.

Keywords-2D digital filter; noise elimination; artificial bee

colony algorithm; image denoising

I. INTRODUCTION

In todays, image processing area has attracted muchattention for scientific as well as its applications anddevelopments. This research field has been used in many areasfrom medical imaging to geographical application [1].Moreover, the communication technologies that are based on

the sending and receiving the collected images from one pointto another point are developed in every day.

In the area of communication, biomedical imaging, spaceapplication, image acquisition and etc., one of the mostimportant and common research topics is to eliminate differentnoises such as impulse or gaussian [2]. Different methods andapproaches have been proposed to the elimination of thevarious noises from the images. For example, a simple neuro-fuzzy method has been suggested to eliminate the impulsivenoise by Yuksel [3]. Abadi et. al. has been used two-dimensional adaptive filter algorithms for image denoising [4].

Recently, two dimensional (2D) digital filters have found awide range application in the image denoising application,

image enhancement, space image processing, etc. [5-7]. Inaddition to these developments, the evolutionary and swarmintelligence based 2D digital filter design approaches have

been introduced by Mastorakis et al., Das et al. and Kumar etal. [8-10].

In 2005, Karaboga has proposed the artificial bee colony(ABC) algorithm for numerical optimization problems [11]. Inaddition, ABC algorithm was competed by Basturk andKaraboga with the other population-based optimizationalgorithms [12, 13] and they concluded that ABC is simple toimplement and also quite robust compared to that of the other

algorithms. Moreover ABC has been used to solve variousproblems from different areas such as noise elimination usingFIR and IIR digital filter and the parameter extraction of theSchottky (SBD) diode [14-15].

This study is presented that a design method based on theABC algorithm is proposed for the elimination of the noisefrom digital image using 2D digital filter. The content of this

paper has been presented as following order. Section 2 explainsnoise elimination method using 2D FIR digital filter. Section 3describes ABC algorithm. The results of the proposed methodare presented in Section 4 and the last section presents theconclusions.

II. NOISE ELIMINATION

Noise elimination is the process of removing noise from theimage. The scheme of the 2D noise cancellation is shown inFigure 1. The 2D digital filter eliminates the noise from the

noisy image.

Figure 1. The scheme of noise elimination

As shown in Figure 1, the image d(i,j) is the contaminatedimage containing both the desired image, s(i,j), and the noisen

(i,j), assumed uncorrelated with each other. The signal, n(i,j),

is a measure of the contaminating signal which is correlated insole way with n

(i,j), n(i,j) is processed by the digital filter to

produce an estimate y(i,j), ofn(i,j). An estimate of the desired

image, e(i,j) is then obtained by subtracting the digital filteroutput,y(i,j), from the contaminated image.

The relationship between the input and output image of the2D FIR filter in Figure 1 is given as

2D FIR

FILTER

ABC

ALGORITHM

( , )y i j( , )n i j

'( , ) ( , ) ( , )d i j s i j n i j ( , )e i j

,(((


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1 21 1

0 0

( , ) ( , ) ( , )N N

t l

y i j w t l u i t j l

(1)

where u(i,j) is the input image, y(i,j) is the output image,w(t,l) is the model coefficients, andN1 andN2 specify the orderof the 2D FIR filter.

The coefficients of the 2D FIR filter are successively

adjusted by ABC algorithm until the error between the outputof the filter and system is minimized. The goal of thisapplication is to minimize the mean square error (mse)

produced by the objective function:

1 21 1

2

0 01 2

1( ( , ) ( , ))

M M

i j

mse d i j y i j M M

(2)

whereM1 andM2 are the size of input images.

III. ARTIFICIAL BEE COLONY ALGORITHM

ABC algorithm has been applied to design the 2D FIR filter

for noise elimination problem. The pseudo-code of the ABC

algorithm for the proposed problem is given below:Step 1: Initialize the population of solutions ijx ,

1,...,i SN , 1,...,j D (SN: number of solutions in the

colony), (D: the number of optimization parameters of 2Dfilter)

Step 2: Evaluate the population by using equation (2)

Step 3: cycle=1

Step 4: repeat

Step 5: Produce a new solution for each employed bee

using ( )ij ij ij ij kj v x x xI and evaluate it by using equation

(2). Here, (1,..., )k SN

, k iz

and (1,2, ..., )j D

arerandomly chosen indexes. ijI is random number in the range [-

1, 1].

Step 6: Apply the greedy selection process for theemployed bees

Step 7: Calculate the probability values for the solutions by

1

ii SN

nn

fitp

fit

Step 8: Produce the new solutions iv for the onlookers

from the solutionsi

x selected depending on ip values and

evaluate by equation (2) themStep 9: Apply the greedy selection process for the

onlookers

Step 10: Determine the abandoned solution for the scout, ifexists, and replace it with a new randomly produced solution

ix by min max min[0,1]( )j j j j

ix x rand x x

Step 11: Memorize the best solution achieved so far

Step 12: cycle = cycle + 1

Step 13: until cycle = Maximum Cycle Number

IV. R ESULTS AND DISCUSSION

In this study, four standard images have been used. Thewhite Gaussian noise with zero mean and 0.025 variance isadded to the images to produce the noisy images. Figure 2 and3 show the original and noisy images.

(a) (b)

(c) (d)

Figure 2. Original images (a) Lena (b) Cameraman (c) Coins (d) Mri

(a) (b)

(c) (d)

Figure 3. Noisy images with Gaussian noise of mean=0, variance=0.025

(a) Lena (b) Cameraman (c) Coins (d) Mri


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The size of each original image is 256x256, 256x256,246x300 and 128x128 pixels, respectively and they are 8-bitgray level image. Also, the order of the 2D FIR filter is set to

N1=N2=3.

The control parameter settings of the ABC algorithm aregiven in Table 1. The selection of the control parameters of theABC is important and has a significant effect on its

performance [16].

TABLE I. PARAMETER SETTINGS FORTHE ABC ALGORITHM

The algorithm was simulated 30 times with different

random seed. The initial values of the parameters have been

selected randomly from the interval (-1, 1).

The simulation was processed in a PC with the following

features: Intel Pentium Core2 Duo T7500 2.2 G CPU, 2048MB RAM and a Windows Vista OS.

Figure 4 shows the restored images obtained by the ABC

algorithm based approach.

(a) (b)

(c) (d)

Figure 4. Restored images (a) Lena (b) Cameraman (c) Coins (d) Mri

Figure 5.a, 5.b, 5.c and 5.d show the convergence

characteristics of ABC for Lena, Cameraman, Coins and Mri

images.

0 100 200 300 400 5000.27

0.28

0.29

0.3

0.31

0.32

Cycles

MeanSquare

Error(MSE)

Lena

(a)

0 100 200 300 400 500

0.27

0.28

0.29

0.3

0.31

0.32

Cycles

MeanSquareError(MSE)

Cameraman

(b)

0 100 200 300 400 5000.2

0.21

0.22

0.23

0.24

0.25

0.26

Cycles

Mean

SquareError(MSE)

Coins

(c)

Colony Size 20

limit value 90

Iteration 500


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0 100 200 300 400 5000.02

0.025

0.03

0.035

0.04

0.045

0.05

Cycles

MeanSquare

Error(MSE)

Mri

(d)

Figure 5. Convergence characteristics of ABC

The algorithm for the 2D FIR filters was simulated 30 timesand the mean, standard deviation and PSNR values of thedigital filters are tabulated in Table 2. Table 3 shows therunning time of the ABC algorithm

TABLE II. MEAN VALUE, STANDARD DEVIATIONS AND PSNROF THEFINAL RESULTS AFTER30 INDEPENDENT RUNS BY ABC

Image Mean ValuesStandard

DeviationsPSNR (dB)

Lena 0.2728 1.0614e-015 44.4928

Cameraman 0.2765 1.2600e-015 48.1714

Coins 0.2108 7.6120e-016 35.7006

Mri 0.0247 1.1074e-016 34.1392

TABLE III. RUNNING TIME VALUE OF THE ABC

Image Running Time (s)

Lena 34.0440

Cameraman 23.18

Coins 20.02

Mri 7.9780

V. CONCLUSION

In this paper, the artificial bee colony algorithm has beenapplied to design 2D FIR digital filters for the noiseelimination on the noisy images. The designed filters have beenused to remove the low level white Gaussian noise from theimages. The results show that the 2D FIR filters are able tosuccessively remove noises from the images and ABC can beused as an alternative algorithm for designing optimal 2D FIR

filter to the classical method such as wiener filter for imagedenoising.

REFERENCES

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[3] M. E. Yksel, A simple neuro-fuzzy method for improving theperformances of impulse noise filters fo digital images, Int. J. Electron.Commun., vol. 59, pp. 463-472, 2005.

[4] M. Abadi and S. Nikbakht, Image Denoising with Two-dimensionaladaptive Filter Algorithms, Iranian Journal of Electrical&ElectronicEngineering, vol. 7, pp. 84-105, 2011.

[5] T. Kaczorek, Two Dimensional Linear Systems. Berlin, Springer, 1985.

[6] S. W. Lu and A. Antoniou, Two-Dimensional Digital Filters. New York,Marcel Dekker Inc., 1992.

[7] S. G. Tzafestas, Multidimensioanl Systems, Techniques andApplications. New York, Marcel Dekker Inc., 1986.

[8] N. Mastorakis, F. I. Gonos, and M. N. S. Swamy, Design of two-dimensional recurisve filters using genetic algorithms, IEEETransactions on Circuits and Systems, vol. 50, pp. 634-639, 2001.

[9] S. Das and A. Konar, A swarm intelligence approach to the synthesis oftwo-dimensional IIR filters, Engineering Applications of ArtificialIntelligence, vol. 20, pp. 1086-1096, 2007.

[10] R. Kumar and A. Kumar, Design of two dimensional infinite impulserespose recursive filters using hybrid multiagent particle swarmoptimization, Applied Artificial Intelligence, vol. 24, pp. 295-312,2010.

[11] D. Karaboga, An idea based on honey bee swarm for numericaloptimization, Technical Report-TR06, Erciyes University, EngineeringFaculty, Computer Engineering Department, 2005.

[12] D. Karaboga, Artificial Bee Colony Algorithm. Scholarpedia 5(3) 6915,www.scholarpedia.org/article/Artificial_bee_colony_algorithm, 2010.

[13] D. Karaboga and B. Basturk, A powerful and efficient algorithm fornumerical function optimization: artificial bee colony (ABC) algorithm,Journal of Global Optimization, vol. 39, pp. 459471, 2007.

[14] N. Karaboga, S. Kockanat, and H. Dogan, Parameter Determination ofthe Schottky Barrier Diode Using by Artificial Bee Colony Algorithm,International Symposium on Innovations in Intelligent Systems andApplications, pp. 6-10, 2011.

[15] S. Kockanat, T. Koza, and N. Karaboga, Cancellation of noise on mitralvalve Doppler signal using IIR filters designed with artificial bee colonyalgorithm, Current Opinion in Biotechnology, vol. 22, pp. 57, 2011.

[16] D. Karaboga and B. Basturk, On the performance of artificial beecolony (ABC) algorithm, Appl. Soft Computing, vol 8, pp. 687697,2008.

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