Impulse Noise Removal Based on Hybrid Genetic Algorithm

Impulse Noise Removal Based on Hybrid Genetic Algorithm

Nail AlaouiArwa Mashat Amel Baha Houda Adamou-Mitiche Lahcène Mitiche Aicha Djalab Sara Daoudi Lakhdar Bouhamla 

Laboratoire de Recherche Modélisation, Simulation et Optimisation des Systèmes Complexes Réels, Université ZIANE Achour de Djelfa, Ain Chih, Djelfa 17000, Algeria

Faculty of Computing & Information Technology, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia

Department of Electrical Engineering, Faculty of Technology, University of Djelfa, P. O. B. 3117, Djelfa, Algeria

RCAM Laboratory Dept of Electronics, Djillali Liabès University Sidi Bel Abbes, Sidi Bel Abbes 22000, Algeria

Corresponding Author Email: 
n.alaoui@univ-djelfa.dz
Page: 
1245-1251
|
DOI: 
https://doi.org/10.18280/ts.380436
Received: 
21 November 2020
|
Revised: 
2 July 2021
|
Accepted: 
12 July 2021
|
Available online: 
31 August 2021
| Citation

© 2021 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).

OPEN ACCESS

Abstract: 

In this paper, we introduce a new method, impulse noise removal based on hybrid genetic algorithm (INRHGA) to remove impulse noise at different noise densities of noise while preserving the main features of the image. The proposed approach merges the genetic algorithm and methods for filtering images that are combined into the population as essential solutions to create a developed and improved population. A set of individuals is developed into a number of iterations using factors of crossover and mutation. Our method develops a group of images instead of a set of parameters from the filters. We then introduced some of the concepts and steps of it. The proposed algorithm is compared with some image denoising algorithm. By using Peak Signal to Noise Ratio (PSNR), structural similarity (SSIM). For example, for Lenna image with 60% salt and pepper noise density, PSNR, SSIM results of AMF, MDBUTMFG and NAFSM methods are 20,39/ 28.74/ 29.85 and 0.5679/ 0.8312/ 0.8818 respectively, while PSNR, SSIM results of the proposed algorithm are 29.92 and 0.8838, respectively. Experimental results indicate that INRHGA is very effective and visually comparable with the above-mentioned methods at different levels of noise.

Keywords: 

image denosing, noise removal, impulse noise, salt and pepper noise, genetic algorithm

1. Introduction

Impulse noise removal is one of the essential issues in image processing, many approaches have been proposed to suppression of noise in digital images from the literature, and however, eliminate noise from digital images is still a difficult problem [1-7].

Different sensors, for example, laser scanners, medical scanners, cameras, and weather satellites, can obtain digital images, but these images might inherently be polluted by noise during acquisition compression processes, transmission [8-11]. It is essential to remove the noise while retaining the basic features of the image, such as edges and corners.

Some nonlinear filters have been suggested for the recuperation of images corrupted by impulse noise. The average filter, as well as its derivatives, are most common in image filtering.

The Median Filter (MF) method utilizes a fixed Window Size and is used to all pixels [12].

There are many common noise filters. For instance, the Adaptive Media Filter (AMF), which uses an adaptive window size, unlike MF which uses a fixed window size. However, although AMF is very effective at removing high-density Impulse noise in images compared to MF, but if the window size is large, it prevents us from finding pixels that match the pixels of the original image [13].

In high-density Impulse noise, a Modified Decision-Based Unsymmetrical Trimmed Median Filter (MDBUTMF) is used, where an adaptive window is used to identify and remove noisy pixels. Then, the MF is utilized to them [14]. Whereas Noise adaptive fuzzy switching median filter (NAFSM) applies the histogram to detect noise pixels in the noisy image, then these pixels are changed by applying MF or estimated according to their neighbors' values [15].

Other methods study the problem of removing noise from images as an optimization problem. Hence, genetic methods have been successfully applied. Some of the most modern papers involving genetic algorithms are [16-25].

Despite this interest, do not exist GAs intended to remove impulse noise in gray images by evolving images.

In this work, we describe a new genetic algorithm called INRHGA that removes impulse noise in gray images.

Our work is inspired by the approaches [19-21], but we address the problem from a different perspective. The fundamental idea is to merge the output images of two of the best methods found in the literature into the initial population of the Genetic Algorithm as essential solutions. Evolution happens for a certain number of epochs aiming to find the best image. During this process, a specific crossover and mutation are applied. Our method develops a group of images instead than a group of parameters from the filters. Our experimental results show that the proposed algorithm improves, in general, the performance for both image denoising and preservation of images details.

2. Methodologies

This section describes our proposed genetic algorithm that suppresses noise in an image. The input of this proposed method is an image gray-scale N(x,y) perturbed through impulse noise. Enhanced image of N(x,y) is the output each individual in the proposed algorithm of the initial population is represented a denoised image of N(x,y).

In this paper, we employ the following two models for impulse noise in gray images:

  1. Noise Model 1: Salt-and-pepper Impulse noise. For this model, the image is corrupted value by noise can only be 0 or 255 with the same probability.

The probability distribution function is given by:

$f(x)=\left\{\begin{array}{c}

\frac{p}{2} \text { for } N=0 \\

1-p \text { for } N=O(i, j) \\

\frac{p}{2} \text { for } N=255

\end{array}\right.$      (1)

where, p is the noise density in the image.

For each original image pixel at location (i; j) the intensity value is $O(i, j)$  , the corresponding pixel of the noisy image is given by $N(i, j)$ .

  1. Noise Model 2: For this model, Here corrupted image have fixed value for salt (i.e. 255) and pepper (i.e. 0) noise with unequal probability.

The probability distribution function is given by:

$f(x)=\left\{\begin{array}{c}

P_{1} \text { for } N=0 \\

1-p \text { for } N=O(i, j) \\

P_{1} \text { for } N=255

\end{array}\right.$       (2)

where, p = p1 + p2 is the noise density in the image and p1 ± p2.

Hybrid genetic algorithm is guided by the objective function expressed in Eq. (3).

$\begin{gathered}

\text { ObjectFitness }(F)=\lambda|I-N|+ \\\quad\quad\quad\quad\quad

\left(\sum_{\Omega} \sqrt{1+\beta^{2}|\nabla I|^{2}}\right)

\end{gathered}$       (3)

which is an edge aware feature preserving diffusion flow function stems from the studies [26, 27]. The term I(x,y) is the image being recovered, N(x,y) the noisy image, β and λ are balancing parameters and Ω is the set of all points in the image.

where, λ > 0 and 1≤ β ≤ 2 from [26].

By minimizing Eq. (1), we are basically trying to reduce the total variation of the image while preserving fidelity in relation to the original image.

The general execution for the proposed algorithm consists of the following steps:

INRHGA Algorithm Steps

Step 1. (Input image) Read a noisy image N(i,j) is represented by an array of pixels N(i,j) where i and j range from 0 to 255 and 255, respectively.

Step 2.(Initialization) Execute filters MDBUTMFG and NAFSM over noisy image N(i, j) to create two new images. NMDBUTMFG and NNAFSM, respectively.

The first two individuals (images) of the population, denoted as NMDBUTMFG, NNAFSM, are the resulting images after applying the following filters: MDBUTMFG and NAFSM to noisy images (Input image)

Then, execute a pixel recombination procedure that randomly exchanges pixels between NMDBUTMFG and NNAFSM to create an initial population of size Ps.

Step 3.(Evaluation) Use Eq. (1) to evaluate the fitness of the initial population.

Step 4.(Selection) Select a pair of the initial population by a Roulette Wheel selection.

Step 5.(Crossover) crossing pairs of selected parents to create offspring. We have applied the same crossover factors proposed by Ahmed and Das [4].

Step 6.(Mutation) Mutate each offspring with probability Pm through the execution of one of the filters MDBUTMFG or NAFSM selected randomly.

Step 7.(Update population) Choose the best Ps individuals of previous generation and their offspring according to their fitness, then retain these individuals for the next iteration as an initial population.

Step 8.Steps 3 to 7 are repeated until $\text { itermax }$ is reached.

The best individual according to the fitness value in the last generation is considered as the denoised image I(i,j).

This configuration was based on some empirical tests that took into account the computational time spent by executing the INRHGA combined with the other denoising methods. For example, it is not possible to set a large-sized population since it makes initialization and mutation processes very time-consuming.

Table 1. Configuration set for the impulse noise removal based on hybrid genetic algorithm

Size of the population (Ps)

30

Mutation rate (Pm)

0.02

Completion-criteria ($\text { itermax }$

) number of iterations

when the algorithm reaches = 20 generations

β

1

l

0.08

Selection criteria

Roulette Wheel selection

Table 1 shows the parameter settings for the proposed algorithm. We selected the values of these parameters by performing initial experiments taking into account the trade-off between time and efficiency.

3. Experimental Results

In this section, we first presented six test images exposed. The first four of these images are among the most popular images. The second two of them are from TEST IMAGES [5, 28], as Figure 1 and Figure 2 shown, respectively.

Figure 3 and Figure 4 give the results of AMF, MDBUTMF, NAFSMF, and INRHGA for Girl face and Chair image with 80% and 90 % densities by model 1 and model 2 of impulse noise, respectively. INRHGA preserved better the details of the image compared to other methods.

Moreover, Figure 5 and Figure 6 illustrates the results of INRHGA considering the input image Lenna and Billiard-Ball with noise densities (20%, 40%, 60%, 80% and 90%) by model 1 and 2 of impulse noise, respectively

Afterwards, in Tables 2 and 3, we give results PSNR and SSIM of the methods of model 1, for Bridge, Couple, Girl face, and Lenna images ranging in noise densities from 10% to 90%. Moreover, in Tables 4 and 5, we give the results PSNR and SSIM of the methods of model 2 for the same as test images. The results show that INRHGA performs better than the others at all noise densities in model 1 above 10% and all noise densities in model 2 above 30%.

Peak signal to noise ratio (PSNR) is defined as:

$P S N R=10 \cdot \log \left(\frac{255^{2}}{M S E}\right)$       (4)

where, MSE (Mean Square Error) is defined as:

$M S E=\frac{1}{M \times N} \sum_{i=0}^{M-1} \sum_{j=0}^{N-1}[O(i, j)-I(i, j)]^{2}$       (5)

where, O(i,j) and I(i,j) are the original image and the recovered image, respectively. Where M and N are the image dimensions.

Structural similarity index metric (SSIM), which can be mathematically formulated [6, 29], is defined as:

$\operatorname{SSIM}(x, y)=\frac{\left(2 \mu_{x} \mu_{y}+c_{1}\right)\left(2 \sigma_{x y}+c_{2}\right)}{\left(\mu_{x}^{2}+\mu_{y}^{2}+c_{1}\right)\left(\sigma_{x}^{2}+\sigma_{y}^{2}+c_{2}\right)}$       (6)

where, $\mu_{x}, \mu_{y}, \sigma_{x}^{2}, \sigma_{y}^{2}, \text { and } \sigma_{x y}$ are the mean intensities, standard deviations and covariance for images x and y, respectively. $c_{1}=\left(k_{1} L\right)^{2} \text { and } c_{2}=\left(k_{2} L\right)^{2}$  that L = 255 for 8-bit grayscale images and $k_{1}$ =0.01 and $k_{2}$ =0.03 are constant.

Figure 1. Classic test images

Figure 2. TESTIMAGES Database

Figure 3. Restoration results of Girlface image perturbed by model 1 impulse noise with 80% densities

Figure 4. Restoration results of chair image perturbed by model 2 impulse noise with 90% densities

Figure 5. Lenna perturbed by impulse noise of model 1, and Lenna images after INRHGA

Figure 6. Billiard-Ball perturbed by impulse noise of model 2, and Billiard-Ball images after INRHGA

Table 2. PSNR results in the methods of model 1 for some images

Image

Filter

10%

20%

30%

40%

50%

60%

70%

80%

90%

Bridge

AMF

20,1999

20,1086

19,9944

19,849

19,373

17,8678

15,0618

11,577

8,1826

 

MDBUTMF

34,1312

31,0621

28,6614

26,9952

25,454

23,5619

21,1819

18,1645

14,6439

 

NAFSM

31,4271

28,6628

26,8445

25,5179

24,4377

23,4427

22,582

21,472

19,5182

 

INRHGA

33,9909

30,8605

28,8919

27,0549

25,4826

23,6082

22,6709

21,7622

20,3202

Couple

AMF

22,4939

22,4284

22,332

22,1433

21,5342

19,5363

15,9518

12,0989

8,578

 

MDBUTMF

38,5303

35,1063

32,6023

30,7843

27,2103

26,2491

23,5481

19,8943

16,0675

 

NAFSM

34,3544

31,5208

29,5767

28,3064

27,1942

26,2143

25,2502

24,1182

21,5846

 

INRHGA

38,5815

35,1237

32,6975

30,8103

28,9488

26,6344

25,3306

24,3105

22,873

Girlface

AMF

25,8914

25,8499

25,7482

25,4966

24,0687

20,5702

15,9459

11,7346

7,973

 

MDBUTMF

38,8938

34,7307

32,9888

30,2575

27,9465

25,098

21,529

17,6643

13,7966

 

NAFSM

37,7447

35,0151

33,3937

31,9485

30,985

29,7196

27,9988

26,031

21,8677

 

INRHGA

38,9201

35,399

33,6443

32,2003

31,0969

30,1319

28,0003

27,4157

24,7181

Lenna

AMF

24,4338

24,3768

24,2976

24,0807

22,9636

20,3858

16,4434

12,1157

8,4666

 

MDBUTMF

42,9759

39,0355

36,6427

34,6372

31,0664

28,7388

24,7712

20,1186

15,8785

 

NAFSM

38,8213

35,6225

33,7468

32,323

31,0581

29,8547

28,639

27,0991

23,5366

 

INRHGA

42,9204

39,2671

36,7048

34,6952

32,1341

29,9186

28,7633

27,4698

23,4983

Mean

AMF

23,2548

23,1910

23,0931

22,8924

21,9849

19,5900

15,8507

11,8816

08,3000

 

MDBUTMF

38,6328

34,9837

32,7238

30,6686

27,9193

25,9120

22,7576

18,9604

15,0966

 

NAFSM

35,5869

32,7053

30,8904

29,5240

28,4188

27,3079

26,1175

24,6801

21,6268

 

INRHGA

38,6032

35,1626

32,9846

31,1902

29,4156

27,5733

26,1913

25,2396

22,8524

Table 3. SSIM results in the methods of model 1 for some images

Image

Filter

10%

20%

30%

40%

50%

60%

70%

80%

90%

Bridge

AMF

0,4901

0,4823

0,4765

0,4698

0,4477

0,3857

0,2663

0,1242

0,0386

 

MDBUTMF

0,9789

0,9535

0,9208

0,8839

0,8348

0,7194

0,6147

0,4207

0,2037

 

NAFSM

0,9622

0,9225

0,8774

0,8311

0,778

0,7185

0,6483

0,5678

0,4337

 

INRHGA

0,978

0,9528

0,9224

0,8857

0,8354

0,7536

0,6523

0,5731

0,4556

Couple

AMF

0,6086

0,6028

0,5974

0,5881

0,5614

0,4694

0,291

0,1146

0,0353

 

MDBUTMF

0,9865

0,9682

0,9446

0,9164

0,8514

0,7889

0,6556

0,4283

0,2031

 

NAFSM

0,9715

0,941

0,9065

0,8712

0,8318

0,7872

0,735

0,6642

0,5328

 

INRHGA

0,9868

0,9684

0,9456

0,9173

0,8754

0,7978

0,7372

0,674

0,5785

Girlface

AMF

0,8117

0,8068

0,8015

0,7926

0,7425

0,6065

0,3393

0,1197

0,0307

 

MDBUTMF

0,9788

0,9643

0,9481

0,9295

0,8888

0,7925

0,5933

0,3292

0,1289

 

NAFSM

0,9808

0,9636

0,9488

0,9305

0,9133

0,8919

0,8642

0,8258

0,7048

 

INRHGA

0,9797

0,9651

0,9499

0,9308

0,9128

0,8925

0,8643

0,8398

0,7655

Lenna

AMF

0,7606

0,7544

0,7501

0,739

0,6941

0,5679

0,3325

0,116

0,0308

 

MDBUTMF

0,9923

0,9805

0,9671

0,9486

0,9081

0,8312

0,6622

0,3982

0,17

 

NAFSM

0,9859

0,9684

0,9504

0,9304

0,9078

0,8818

0,8511

0,8017

0,6819

 

INRHGA

0,9922

0,9806

0,9671

0,9486

0,9141

0,8838

0,8546

0,8145

0,6843

Mean

AMF

0,6678

0,6616

0,6564

0,6474

0,6114

0,5074

0,3073

0,1186

0,0339

 

MDBUTMF

0,9841

0,9666

0,9452

0,9196

0,8708

0,7830

0,6315

0,3941

0,1764

 

NAFSM

0,9751

0,9489

0,9208

0,8908

0,8577

0,8199

0,7747

0,7149

0,5883

 

INRHGA

0,9842

0,9667

0,9463

0,9206

0,8844

0,8319

0,7771

0,7254

0,6210

Table 4. PSNR results in the methods of model 2 for some images

Image

Filter

10%

20%

30%

40%

50%

60%

70%

80%

90%

Bridge

AMF

20,2292

20,1175

19,7925

19,7336

15,5264

12,2532

8,3407

8,1846

8,2234

 

MDBUTMF

34,2978

30,9631

28,4768

27,2498

24,7438

23,3324

19,1457

17,194

14,686

 

NAFSM

31,6324

28,6236

27,1551

25,668

24,6961

23,3968

21,3106

20,4548

19,576

 

INRHGA

34,2485

31,1783

29,1414

27,4299

25,6565

23,4906

22,6891

21,9699

20,2707

Couple

AMF

22,4913

22,3805

21,6792

21,4383

21,5016

9,7861

14,3058

6,4795

7,7111

 

MDBUTMF

38,8286

34,9707

32,6247

30,6118

27,1889

24,2666

23,225

15,3942

15,3997

 

NAFSM

34,6116

31,4578

29,5988

28,2863

27,2266

24,7258

25,229

18,2933

20,9087

 

INRHGA

38,6923

35,0506

32,6346

30,8723

28,9528

26,2601

25,3163

24,2971

22,7802

Girlface

AMF

25,9081

25,7956

24,3552

21,4275

12,3631

8,3342

15,18

12,6008

8,9335

 

MDBUTMF

40,9269

39,2026

36,7941

27,8005

24,3342

20,9944

23,3093

19,1281

15,0042

 

NAFSM

37,9844

35,763

33,9727

31,4295

28,8787

26,044

28,4429

26,3813

19,1511

 

INRHGA

37,2819

38,2856

33,6955

31,9982

31,3146

29,8498

28,5719

28,1635

24,5959

Lenna

AMF

24,4611

24,3632

24,2775

23,6891

21,7659

17,15

16,1279

6,3904

5,7879

 

MDBUTMF

42,9293

39,1671

36,761

34,501

30,942

28,4891

24,5797

15,0837

11,1496

 

NAFSM

38,7396

35,5846

33,7161

32,3598

30,8756

29,6132

28,6649

17,3033

14,2669

 

INRHGA

42,7286

39,1743

36,7786

34,6075

31,9927

29,9361

28,7636

27,4954

25,3531

Mean

AMF

23,2724

23,1642

22,5261

21,5721

17,7893

11,8809

13,4886

8,4138

7,6640

 

MDBUTMF

39,2457

36,0759

33,6642

30,0408

26,8022

24,2706

22,5649

16,7000

14,0599

 

NAFSM

35,7420

32,8573

31,1107

29,4359

27,9193

25,9450

25,9119

20,6082

18,4757

 

INRHGA

38,2378

35,9222

33,0625

31,2270

29,4792

27,3842

26,3352

25,4815

23,2500

Table 5. SSIM results in the methods of model 2 for four some images

Image

Filter

10%

20%

30%

40%

50%

60%

70%

80%

90%

Bridge

AMF

0,4917

0,4824

0,4711

0,4638

0,2959

0,1634

0,0847

0,0486

0,0426

 

MDBUTMF

0,9785

0,9519

0,9218

0,885

0,8186

0,7191

0,5615

0,4037

0,2056

 

NAFSM

0,9618

0,9207

0,8781

0,8303

0,7762

0,7041

0,6161

0,5025

0,4365

 

INRHGA

0,979

0,9529

0,9212

0,8832

0,8306

0,7369

0,6513

0,5723

0,4534

Couple

AMF

0,6087

0,6044

0,5766

0,5623

0,5584

0,0729

0,2346

0,0357

0,0288

 

MDBUTMF

0,9869

0,9675

0,9447

0,9149

0,8307

0,7413

0,6424

0,2798

0,1874

 

NAFSM

0,9726

0,9407

0,9066

0,8711

0,8322

0,7366

0,731

0,3968

0,4899

 

INRHGA

0,9871

0,968

0,9451

0,9182

0,875

0,7876

0,737

0,6733

0,5769

Girlface

AMF

0,8127

0,8078

0,746

0,6806

0,2095

0,055

0,2848

0,1653

0,0887

 

MDBUTMF

0,9843

0,9805

0,948

0,9232

0,8676

0,716

0,6253

0,3541

0,1481

 

NAFSM

0,9812

0,9645

0,9454

0,9295

0,8991

0,8341

0,854

0,8068

0,405

 

INRHGA

0,9798

0,9738

0,9667

0,9314

0,9115

0,8935

0,8665

0,8272

0,767

Lenna

AMF

0,7624

0,7558

0,7488

0,729

0,6417

0,4009

0,3239

0,0419

0,0662

 

MDBUTMF

0,9923

0,9804

0,967

0,9476

0,908

0,8269

0,6542

0,2452

0,1013

 

NAFSM

0,9859

0,9682

0,9502

0,9304

0,9066

0,8788

0,8497

0,352

0,1874

 

INRHGA

0,9919

0,9804

0,9671

0,9484

0,9136

0,8837

0,8535

0,816

0,7443

Mean

AMF

0,6689

0,6626

0,6356

0,6089

0,4264

0,1731

0,2320

0,0729

0,0566

 

MDBUTMF

0,9855

0,9701

0,9454

0,9177

0,8562

0,7508

0,6209

0,3207

0,1606

 

NAFSM

0,9754

0,9485

0,9201

0,8903

0,8535

0,7884

0,7627

0,5145

0,3797

 

INRHGA

0,9845

0,9688

0,9500

0,9203

0,8827

0,8254

0,7771

0,7222

0,6354

4. Conclusions

In this paper, we have proposed a new impulse noise removal by applying a hybrid genetic algorithm (INRHGA), we address the reduction of impulse noise in images as an optimization problem, which gives better performance in comparison with known noise removal methods in terms of PSNR and SSIM. The performance of the algorithm has been tested an all noise densities on grayscale images. The proposed method is effective for impulse noise removal. An important advantage of INRHGA is impulse noise removal in noisy image without the original image, so it works without a clue about how far we are from the original image.

Finally, our scope of work did not focus on the arithmetic cost of the algorithm, but on the quality of the recovered images. We intend to verify the computational cost and reduce the current implementation time of the proposed algorithm as future work.

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