Image Denoising Based on Improved Hybrid Genetic Algorithm

Image Denoising Based on Improved Hybrid Genetic Algorithm

Nail Alaoui* Amel Baha Houda Adamou-Mitiche Lahcène Mitiche Lakhdar Bouhamla

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

Corresponding Author Email: 
n.alaoui@univ-djelfa.dz
Page: 
14-21
|
DOI: 
https://doi.org/10.18280/rces.080103
Received: 
23 January 2021
|
Revised: 
3 March 2021
|
Accepted: 
15 March 2021
|
Available online: 
31 March 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: 

Digital images can be degraded through noise during the transmission and process of acquisition, it is still a fundamental challenge is to eliminate as much noise as possible while preserving the main features of the image, for instance, edges, texture, and corners. This paper proposes for image denoising a new Improved Hybrid Genetic Algorithm (IHGA), whose combined a Genetic Algorithm (GA), with some image denoising methods. Wherein this approach uses mutation operators, crossover, and population reinitialization as default operators available in evolutionary methods with applied some state-of-the-art image denoising methods, such as local search. Tests are conducted on some digital images, commonly used as a benchmark by the scientific community, where different standard deviations are used for digital images. Experimental results indicate that the proposed method is very effective and competitive in comparison with previously published works.

Keywords: 

image denoising, hybrid genetic algorithm, edge preservation, optimization, digital images

1. Introduction

Image denoising is one of the exemplary issues of image handling, numerous methodologies have been acquainted with eliminate commotion from advanced image literature [1], yet eliminating noise from computerized images stay a difficult issue.

Digital images can be collected from various instruments, such as laser scanners, medical scanners, cameras, and weather satellites [2]. It is therefore important to remove the noise while maintaining the important features of the image, such as edges and corners. Noise can eventually corrupt images during processing, transmission, and compression processes.

This research describes a method for suppressing noise with an Improved Hybrid Genetic Algorithm (IHGA) for a digital image that combines genetic algorithm with some image denouncing techniques from BM3D [3], Anisotropic Diffusion [4], and Wiener-chop [5] literature. In this work, the IHGA implemented Improved Genetic Hybrid Algorithm which eliminates Gaussian noise in digital images. Our experimental results display that IHGA improves in general.

The remainder of the paper is as below. Section 2 describes the proposed Improved Genetic Hybrid Algorithm in this paper, and we present in detail the reviews of different techniques to denoise pictures. Section 3 summarizes the findings of the Section 4 experiments, and ends remarks in Section 5.

2. Background

The key aim of the image denoising approach is to restore an original picture that has been polluted with additive noise without losing the image's edge information, such as texture and corners.

Some linear filtering [6] was suggested in the original images to eliminate the uniform and Gaussian noise. The filters used to eliminate the noise in optical images are known as linear filters, for example, is the Wiener filter, while non-linear filters are categorized as a median filter, for example. In linear filters, a kernel filter is transformed to the required result through a noise signal, whereas non-linear filters [7] cannot be regarded as a convolution process [1]. These filters are used to eliminate the noise in the image with white Gaussian noise applied without the need for any previous information.

Rational operators [8] have been applied to progress denoising techniques. Approaches based on computational fluid dynamics (CFD) and partial differential equations (PDE) have also been advanced, total variation (TV) methods [9], level set methods [10] non-linear isotropic and anisotropic diffusion [11].

Other methods have combined filtering techniques to remove impulse to suppress noise and local adaptive filtering in the transform domain [9]. Non-local filtering has been confirmed to be strong for image denoising, one of these methods is the BM3D [3] filter Singular Value Decomposition (SVD) has also been applied in the filtering of image noise [12]. Other methods collected wavelet transformations, spatially adaptive methods and hidden models of Markov [13].

In recent years several methods have been proposed using Evolutionary Algorithms for image denoising. Such methods generally attempt to implement the shrinkage rule by estimating thresholds on an image for the noisy wavelet coefficients [14-16].

A genetic algorithm is used to eliminate noise from image in the process suggested by de Paiva et al. [17, 18]. In this approach, a noisy picture is used as a contribution and certain methods of denotation are used to initialize mutation operators, crossover processing and population growth.

This work improves on several essential aspects of the approach introduced by de Paiva et al. [17]. First, it uses a new collection of mutations based on methods of image restoration. Secondly, a whole new range of crossovers. Second, a new approach to initializing a population is implemented, in this method by randomly crossing two people from the initial population group. In addition, there are other significant differences such as using a different selection method as selection of roulette wheels.

3. Methodologies

Algorithm: Proposed Improved Hybrid Genetic Algorithm

Input: Noisy image I.

Step 1: (Initialization) Create a group of three new individuals G= {IBM3D, IAD, IWiener -Chop} as the initial population by Apply filters BM3D, AD and Wiener-Chop over input image I.

Step 2: while the initial population size is less than PopSize do

Step 3: Select a two individual randomly of individuals from a set G.

Step 4: Procedure a random crossing for two individual of this selected pair and integrate each individua of the resulting individuals into the initial population.

Step 5: end while

Step 6: (Evaluation) Each individual of the initial population is evaluated by a fitness function.

Step 7: while the Runtime is less than MaxTime and the iteration number is less than MaxIter do.

Step 8: repeat

Step 9: (Parent selection) Select a pair of individuals from the population using a Roulette Wheel Selection.

Step 10: (Crossover) The offspring are created by recombining pairs of the selected parents to a new generation.

Step 11: (Mutation) Mutate to each offspring using one of three mutations are proposed which are also selection randomly to be used with probability Pm.

Step 12: (Evaluation) Evaluate the fitness of each offspring.

Step 13: (Local Search) If a randomly selected value from [0, 1] is Less than the local search rate, apply local Search operator at the end of each evolutionary step to the best individual found.

Step 14: end if

Step 15: (Elitism) generate a new generation of PopSize individuals using deterministic fitness-based replacement.

Step 16: (Reset population) if the runtime is less than MaxTime integrate the best individual of the previous generation previous with created a new population by the same process used to the initial population.

Step 17: end if

Step 18: (Evaluation) Evaluate each new population's fitness

Step 19: until complete PopSize generations.

Step 20: end while

Step 21: the best image of the last generation returns.

This section describes IHGA, our proposed Improved Genetic Hybrid Algorithm which suppresses image noise. The input of the proposed algorithm is a gray-scale image that I was interrupted by Gaussian noise. The Denoised image of I is the production of the initial population each person in IHGA is represented as a denoised image of I. The proposed algorithm outlines.

3.1 Initialization

Initial populations with PopSize are generated by Lines 1-5 of our algorithms. In which a double-dimensional (2D) pixel array of values within [0,255] range represents each person in the population. An updated version of image I entry reflects all users. After each of the subsequent denoising filters, the first three population individuals use a denoted graphic. BM3D, AD, Wiener Chop.

These methods are classified as computationally fast filters to take advantage of their strength due to their image denoising competency as well as their short computational time. Those methods are considered to be the best literature findings.

The algorithm IHGA creates the other individuals of the initial population by selecting from the set {IBM3D, IAD, Iwiener-Chop} two individuals IX and IY. The outputs are submitted by a random crossing between the two individuals, which exchanges pixels point-to- point. This new individual recombination operation output is included in the initial population and used this operation repetitively until PopSize individuals were attained by the initial population. Figure 1 shows a block diagram of the initial population created.

Figure 1. Creation of the initial population of IHGA

3.2 Fitness function

Lines 6, 12 and 18 of our Algorithm evaluate the fitness of the population. The algorithm is guided based on a fitness function represented by minimizing Eq. (1). As stated in the study [19].

fitness $(i)=\left\{\sum_{\Omega} \sqrt{1+\beta^{2}|\nabla I|^{2}}+\frac{\lambda}{2}\left(I-I_{0}\right)^{2}\right\}$               (1)

Mindful the edges of the image and attempts to save significant highlights of the image work portrayed in the parameter, I is the picture being assessed, I0 the loud picture, $\beta$ and $\lambda$ are adjusting boundaries and Ω is the group of all focuses in the image.

Full names of authors are required. The middle name can be abbreviated.

3.3 Parent selection

Line 9 of our Algorithm create parents by selects pairs of individuals who are selected through roulette wheel selection.

3.4 Crossover

Following a selection of our algorithm's step parents in line 9, line 10, the new person is generated by randomly selecting one of three crossover operators shows next:

Single-point: On both parents a single crossover picked a point, one of the two that we randomly pick in this process.

One-point column: Random arrangement of a progression of pixels. The pixels over this line originate from one parent. The pixels from the subsequent parent are all beneath this line.

One-point row: Similar to the past methodology yet rather than picking a segment from a column.

Two-point: Two-point hybrid chose two focuses on the two guardians; we arbitrarily pick one of the two in this cycle.

Two point column: two hybrid focuses are chosen haphazardly from the exhibit, all pixels duplicated from the beginning of the chromosome to a parent's first hybrid point, at that point all pixels are replicated from the principal hybrid purpose of the parent to the second traverse purpose of the parent, and the rest of replicated from the first of the parent.

Two-point row: segment like the past structure, yet favor a segment as opposed to a column.

Cross grid: a solitary point and one-point administrator blend is utilized to fragment each image into four quadrants, however not actually equivalent measurements. In several image, he shares a quadrant. In Figure 2, this Fusion reveals the effect.

Figure 2. Examples of the crossover

3.5 Mutation

Line 11 of the proposed Algorithm executes a grid mutation operator which provides population diversity. This operator takes a single Ix with probability mutation rate as its input. Next, it selects two rows and two Ix columns at random. Then it labels the rectangle formed by the rows and columns that were selected. Second, by randomly applying one of the three filters presented next, it treated the area:

Filter motion blur: filters a filter motion in the picture, this filter produces a motion blur.

Median filter: filters the image by means of a median filter, the size is randomly selected between 3 pixels and 5 pixels.

Intensity: Each pixel of the image is multiplied by the same factor chosen randomly between the interval [0.8, 1.2].

This operator created a mutated offspring Ix’, Figure 3 shows a result of this mutation operator.

Figure 3. Example of the grid mutation operator

3.6 Local search

Line 13 of our algorithm explains that when the randomly selected value of [0, 1] is less than the local search rate of the algorithm, a local search operator is applied to the best individual found in a new individual using the denoising method of the three described previously BM3D [3], AD [4], and Wiener-chop [5].

3.7 Population replacement

Line 15 of the proposed algorithm is a modified step that only guarantees that the right person is available. The fitness replacement scheme is formed by the union of some of the parents of the previous generation and some of their offspring’s in order to perform with a sorting algorithm to choose certain people.

3.8 Reset population

The population is reset in line 16 of our algorithm to retain the best people and build the majority of the new people in the same method with the first generation.

3.9 Termination condition

Lines 8 to 19 of our Algorithm repeats the algorithm until it completes Pop Size generations even a condition is met in line 7. Next, the algorithm returns the best individual present in the last generation (see Line 21).

4. Experimental Results

The experimental results from the proposed improved genetic hybrid algorithm (IHGA) for image denoise are presented in this section with the intention of testing the efficiency of our proposed developmental algorithm and compared the proposed algorithm to state-of-the-art images denoise methods. For this function the additive Gaussian noise disrupted each of the seven images with 11 different standard variants σ = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 and 60. For this purpose we used 7 images.

We measure the objective quality metrics to evaluate the quality of the image restored after a filtering process. Eq. (2) presented the Peak Signal to Noise Ratio (PSNR) measure via the Mean Square Error (MSE) of Eq. (3).

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

The MSE is the mean squared error between the original (O) and the recovered images (K). M and N It is dimensions of the image.

$M S E=\frac{1}{M N} \sum_{i=0}^{M-1} \sum_{j=0}^{N-1}[O(i, j)-K(i, j)]^{2}$               (3)

4.1 Setting parameter

To test the performance of IHGA parameters, tests were performed using different parameters for each test, and the target quality metrics were calculated to select the best parameter.

The basic configuration of the IHGA after performing all these tests are shown in Table 1.

Table 1. The basic configuration of the IHGA

Selection Pressure

8

Mutation rate

0.2

Population size

15

β

1.5

MaxTime

20 minutes

MaxIter = 5, locale search rate=0.8, and $\lambda$ was $1 / \sqrt{(v)}$ where ν is the estimated variance of the noise, except for the parameters maxIter, λ and local search rate which were chosen empirically.

4.2 Comparison of the results

The results of the IHGA in this section against the other approaches used in the literature used in contrast were Bayes [20], Wiener [1], median [1], TV [9]. Wavelets. The results of the PSNR were given in Table 2., Wiener-chop [5], AD [4], BM3D [3], and HGA [17]. For the noise ratio, the value displayed in bold is the highest value and the underlined values are the lowest.

Results also demonstrated that IHGA is comparable with some of the best picture denoising approaches available in the literature, even though in some cases its worst results (IHGA Min) also yielded better results. In most cases, IHGA proposed innovative technique gives superior results than those techniques used as local search operators. In addition, the effects of this hybrid technique would be entitled to outperform other available approaches published in the literature.

In order to validate this process, IHGA is compared with HGA, which has been able to obtain better results than the ones described in the study [17]. This indicates that some changes in the HGA and its combining with other techniques will help to provide the better output solution. The suggested HGA was introduced for the same runtime of the IHGA run at [17]. This amendment was introduced in order to allow for a rational distinction of the two approaches.

Table 2 illustrates the minimum (Min), maximum (Max) and average (Avg) PSNR obtained by the IHGA. It is also presented the HGA and other methods found in the literature. When examining the maximum results, the proposed method IHGA was the optimum method in terms of PSNR presented the greater results in 59 out of 77 tests (77%). When examining the number of times that the IHGA, it was top PSNR than the other methods with all tested noise levels, against the 88 results for the other methods. The proposed IHGA is greater than other methods in 84 times for Man (96% of the cases), 96% for Boat image, 97% for Lenna image, 99% for Glasses image, 96% for Peppers image, 99% for Lightning image, and 96% for Cameraman image.

Instead of analyzing the best cases Such as those mentioned in the previous paragraph, we conducted an analysis of the worst cases and the average cases, with taking into account the same comparisons the proposed method. IHGA was best than the other methods. In the average and worst cases, respectively, PSNR found by the proposed IHGA is greater than PSNR values of other methods, for the Man image at 81% and 60% of the time, 73% and 58% for Boat image, 82% and 76% for Lenna image, 97% and 93% for Glasses image, 85% and 77% for Peppers image, 96% and 93% for Lightning image, and 78% and 70% for Cameraman image.

IHGA is now compared against Best methods for denoising images it uses as local search, when making the same comparisons as those that were made in the previous, but taking into account it against only BM3D, AD, and Wiener-chop. The maximum PSNR outperforms these methods for the Man image at 90% of the time, 87% for Boat image, 90% for Lenna image, 100% for Glasses image, 90% for Peppers image, 100% for Lightning image, and 87% for Cameraman image. In the average case and worst cases. Respectively, IHGA has the best PSNR than the theses methods at for the Man image at 63% and 36% of the time, 73% and 30% for Boat image, 66% and 54% for Lenna image, 90% and 78% for Glasses image, 66% and 54% for Peppers image, 87% and 87% for Lightning image, and 51% and 42% for Cameraman image.

When Comparison of the results of the proposed method IHGA for it against only HGA show that the Image quality is improved without losing image features, indicates that our technique has an advantage over HGA. For PSNR metric, our analysis shows that the IHGA is better than HGA 94% of the time in the best case, 92% in the average case, and 72% in the worst result for the 10 executions.

The IHGA algorithm is more efficient in eliminating Gaussian noise than a IHGA, especially at the high noise level For example σ =60 (see Figures 4, 5, 6, 7, 8, 9, and 10).

Table 2. PSNR results for all the tested methods

Images

σ

Bayes

WC

Median

Wiener

AD

BM3D

TV

HGA avg

HGA max

HGA min

IHGA avg

IHGA max

IHGA min

Man

10

31,31

32,11

30,204

30,49

32,57

33,62

30,74

32,51

32,66

32,27

32,58

33,61

32,10

 

15

29,75

30,50

28,744

29,485

30,465

31,718

30,268

30,556

30,719

30,374

30,554

31,605

30,328

 

20

28,69

29,45

27,402

28,562

29,158

30,452

29,182

29,461

29,937

29,215

29,885

30,012

29,248

 

25

27,75

28,56

26,106

27,641

28,136

29,542

27,601

28,990

29,576

28,146

28,980

29,56

28,143

 

30

26,96

27,82

24,964

26,811

27,311

28,821

25,884

27,75

28,526

27,266

28,530

28,846

27,228

 

35

26,41

27,12

23,872

26,063

26,655

28,176

24,232

27,091

27,637

26,407

27,160

28,197

26,824

 

40

25,85

26,61

22,984

25,354

26,129

27,598

22,814

26,301

26,677

25,879

26,570

27,625

26,411

 

45

25,40

26,05

22,039

24,635

25,528

27,057

21,414

25,887

26,236

25,498

26,310

27,088

26,060

 

50

25,00

25,55

21,294

24,027

25,064

26,616

20,307

25,465

25,778

24,975

25,880

26,627

25,574

 

55

24,604

24,967

20,566

23,467

24,623

26,237

19,217

25,039

25,518

24,182

25,559

26,245

24,98

 

60

24,192

24,534

19,907

22,969

24,175

25,742

18,397

24,651

25,087

24,24

25,135

25,756

24,77

Boat

10

30,32

32,24

29,412

30,042

32,338

33,587

30,461

32,30

32,382

32,081

32,252

33,297

32,080

 

15

29,05

30,55

28,178

29,013

30,388

31,930

29,867

30,481

30,598

30,099

30,58

31,631

30,002

 

20

27,94

29,37

26,958

28,120

28,986

30,791

28,879

29,223

30,047

28,711

29,415

30,791

28,652

 

25

26,95

28,39

25,768

27,185

27,867

29,782

27,355

28,281

29,056

27,785

28,405

29,785

27,65

 

30

26,19

27,60

24,673

26,354

26,971

28,978

25,72

27,589

28,678

26,985

27,602

29,252

26,971

 

35

25,59

26,96

23,721

25,627

26,26

28,362

24,125

26,392

27,390

25,410

27,100

28,452

26,884

 

40

24,99

26,35

22,820

24,871

25,599

27,585

22,687

25,859

26,615

24,725

26,560

27,674

26,150

 

45

24,58

25,72

21,954

24,200

25,026

26,906

21,329

25,393

25,854

24,847

26,156

26,987

25,706

 

50

24,15

25,22

21,225

23,626

24,512

26,476

20,228

24,753

25,433

24,122

25,700

26,547

25,420

 

55

23,79

24,66

20,504

23,035

24,003

25,925

19,142

24,389

24,995

23,016

25,147

26,025

24,720

 

60

23,37

24,22

19,877

22,558

23,611

25,426

18,250

23,909

24,585

23,138

24,865

25,777

24,289

Lenna

10

33,33

34,35

32,116

32,661

34,177

35,873

33,06

34,287

34,481

34,084

34,344

35,773

34,178

 

15

31,84

32,72

30,042

31,215

32,155

34,248

32,227

32,456

32,633

32,171

32,720

34,107

32,047

 

20

30,56

31,50

28,361

29,996

30,786

32,999

30,586

31,809

32,717

31,213

32,414

32,901

31,191

 

25

29,48

30,47

26,815

28,847

29,672

32,014

28,457

31,209

32,025

30,095

31,144

32,014

30,017

 

30

28,75

29,65

25,533

27,868

28,831

31,184

26,478

30,09

30,735

29,207

30,012

31,304

29,101

 

35

27,98

28,87

24,38

26,992

28,162

30,507

24,63

28,742

29,079

28,248

30,104

30,611

29,301

 

40

27,51

28,07

23,297

26,084

27,38

29,932

22,991

28,195

28,910

27,599

29,411

29,999

28,61

 

45

27,02

27,423

22,432

25,366

26,867

29,338

21,628

27,477

28,239

27,019

28,438

29,414

28,251

 

50

26,50

26,753

21,589

24,632

26,264

28,775

20,388

26,916

27,372

26,341

28,215

28,810

27,321

 

55

25,99

26,227

20,802

24,043

25,798

28,284

19,369

26,639

27,333

25,643

27,64

28,381

26,984

 

60

25,47

25,645

20,117

23,485

25,288

27,746

18,448

25,966

26,853

25,137

27,248

27,819

26,61

Glasses

10

39,64

40,961

35,166

37,74

40,088

43,348

40,165

40,933

41,296

40,632

43,347

43,610

42,21

 

15

37,32

38,333

31,944

34,895

37,665

41,455

37,928

39,457

40,702

38,457

41,445

41,601

40,278

 

20

35,53

36,018

29,494

32,555

35,844

39,727

33,684

38,709

39,453

37,155

39,727

39,793

38,415

 

25

34,78

34,574

27,652

30,978

34,366

38,458

30,207

38,496

38,501

38,443

38,453

38,501

37,458

 

30

34,05

33,485

26,16

29,798

33,352

37,286

27,566

35,374

36,575

33,669

37,346

37,483

37,286

 

35

33,25

32,475

24,885

28,765

32,36

36,379

25,492

34,165

35,116

32,667

36,489

36,616

36,379

 

40

32,38

31,077

23,627

27,633

31,226

35,390

23,627

32,935

33,825

31,773

35,405

35,495

35,39

 

45

31,56

30,511

22,779

26,863

30,614

34,840

22,344

32,566

33,256

32,121

34,842

34,999

34,105

 

50

30,91

29,502

21,856

26,044

29,696

33,760

21,156

31,577

31,922

30,727

33,765

33,820

33,76

 

55

29,85

28,567

21,024

25,148

28,912

32,455

20,122

30,567

30,975

30,078

32,590

32,877

32,255

 

60

28,94

27,646

20,351

24,502

27,998

31,448

19,21

29,739

30,496

28,747

31,865

31,968

31,148

Peppers

10

30,93

32,617

30,101

30,641

33,378

34,500

32,097

33,444

33,601

33,246

33,517

34,420

33,114

 

15

28,33

30,735

28,63

29,55

31,204

32,578

31,161

31,279

31,701

30,244

31,571

32,575

30,114

 

20

26,52

29,261

27,285

28,422

29,607

31,115

29,646

29,999

30,322

29,798

30,301

31,105

29,625

 

25

24,94

28,017

25,908

27,334

28,379

30,073

27,667

28,795

29,451

28,267

29,412

30,240

28,171

 

30

24,38

27,114

24,821

26,493

27,269

29,070

25,98

27,926

28,521

26,992

28,415

29,178

27,601

 

35

23,75

26,152

23,7

25,605

26,412

28,328

24,269

26,566

27,018

26,184

27,61

28,521

27,008

 

40

23,26

25,253

22,774

24,852

25,637

27,531

22,708

25,769

26,339

25,215

27,031

27,610

26,328

 

45

23,03

24,555

21,935

24,19

24,857

26,784

21,401

25,181

25,501

24,762

26,251

26,888

25,48

 

50

22,48

23,887

21,212

23,555

24,257

25,971

20,372

24,316

25,026

23,847

25,441

26,101

24,81

 

55

22,13

23,329

20,415

22,947

23,644

25,675

19,228

23,719

24,115

23,194

25,257

25,901

24,644

 

60

21,90

22,834

19,837

22,446

23,151

25,101

18,389

23,172

23,575

22,762

24,611

25,301

24,045

Lightning

10

33,52

37,535

33,73

36,009

38,359

40,169

37,477

38,939

39,059

38,695

40,16

40,369

40,017

 

15

31,61

35,202

31,144

33,848

36,101

38,171

35,988

36,909

37,271

36,593

38,247

38,341

38,17

 

20

30,29

33,301

28,989

31,902

34,37

36,662

32,769

35,879

36,457

35,218

36,742

36,777

36,66

 

25

29,43

32,127

27,298

30,445

33,062

35,533

29,819

35,449

35,542

34,933

35,341

35,542

34,633

 

30

28,86

31,117

25,828

29,106

32,006

34,707

27,214

33,756

34,618

33,037

34,814

34,847

34,41

 

35

28,52

30,148

24,581

27,967

31,062

33,659

25,132

32,168

32,548

31,61

33,74

33,744

33,659

 

40

27,74

29,415

23,535

26,898

30,182

33,166

23,441

31,155

31,809

29,927

33,168

33,216

33,166

 

45

27,09

28,692

22,597

26,102

29,483

32,507

22,012

30,802

31,208

29,395

32,617

32,807

32,507

 

50

26,46

27,928

21,667

25,164

28,481

31,711

20,765

29,901

30,422

28,784

31,715

31,810

31,715

 

55

25,90

27,461

20,987

24,655

28,084

31,152

19,787

29,495

30,084

28,427

31,156

31,262

30,156

 

60

25,64

26,61

20,231

23,866

27,100

30,466

18,816

28,379

29,021

27,411

30,468

30,567

30,466

Cameraman

10

31,36

31.194

26.567

29.146

33.086

33.548

29.177

32.747

33.045

31.185

33.087

33.414

32.577

 

15

28,55

29.255

23.810

29.255

30.807

31.538

28.891

30.613

30.839

30.134

30.447

31.417

30,038

 

20

26,98

27.874

23.810

29.255

29.236

30.200

27.907

29.381

29.591

29.176

29.477

30.110

29,047

 

25

25,76

26.806

23.810

29.255

27.906

29.246

26.768

28.218

27.666

27.929

28.147

29.141

27,87

 

30

25,03

26.001

23.810

29.255

26.797

28.260

26.421

27.136

27.481

26.924

27.571

28.310

26,722

 

35

24,25

25.184

23.810

29.255

25.817

27.535

23.882

26.044

26.297

25.531

26.018

27.644

25,541

 

40

23,67

24.563

23.810

29.255

24.992

26.748

22.638

25.230

25.448

24.427

25.351

26.887

24,86

 

45

22,98

23.904

23.810

29.255

24.170

25.789

21.315

24.266

24.662

23.363

24.630

25.977

24,135

 

50

22,25

23.288

23.810

29.255

23.389

25.299

20.237

23.651

23.838

23.185

23.515

25.319

23,425

 

55

21,90

22.833

19.940

21.644

22.785

24.514

19.231

23.166

23.322

22.808

23.208

24.718

23,052

 

60

21,53

22.454

19.481

21.212

22.320

24.162

18.482

22.631

22.851

22.193

22.744

24.241

22,425

Figure 4. Results of the methods for Boat image by HGA and IHGA

Figure 5. Results of the methods for Cameraman image by HGA and IHGA

Figure 6. Results of the methods for Cameraman image by HGA and IHGA

Figure 7. Results of the methods for Lenna image by HGA and IHGA

Figure 8. Results of the methods for Man image by HGA and IHGA

Figure 9. Results of the methods for Lightning image by HGA and IHGA

Figure 10. Results of the methods for Peppers image by HGA and IHGA

5. Conclusions

In this paper, we have presented an Improved Hybrid Genetic Algorithm (IHGA), this method, although inspired by HGA has a number of fundamental changes, such as the use different operators of mutation and crossover, local search operators used only the best candidate that was identified at the conclusion of and evolutionary process. We also have changed the method selection process. IHGA was evaluated against other denoising methods, where were used seven different images with the 11 levels of noise. Experimental results present that IGHA outperformed a previous an approach based on HGA, which indicates that we have found an improves solution for image denoising problem. In comparison with the other denoising image found.

In the literature, especially images with high noise levels. Taking the best solutions into consideration, the average and the worst solutions found, which measured using PSNR. IHGA is still slow compared to some image denoising methods. This problem becomes more apparent when several executions. As future work, we intend to reduce the computational cost through proposed new fitness functions and other image denoising techniques can be proposed as local search.

Acknowledgment

The research being reported in this publication was supported by the Algerian Directorate General for Scientific Research and Technological Development (DGRSDT).

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