research article a new method of image denoising for

Research ArticleA New Method of Image Denoising for Underground Coal MineBased on the Visual Characteristics

Gang Hua1 and Daihong Jiang12

1 School of Information and Electrical Engineering China University of Mining and Technology Xuzhou Jiangsu 221008 China2 School of Information and Electronic Engineering Xuzhou Institute of Technology Xuzhou Jiangsu 221008 China

Correspondence should be addressed to Gang Hua ghua3323163com

Received 15 January 2014 Accepted 12 March 2014 Published 6 April 2014

Academic Editor Feng Gao

Copyright copy 2014 G Hua and D JiangThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Affected by special underground circumstances of coal mine the image clarity ofmost images captured in themine is not very highand a large amount of image noise is mingled with the images which brings further downhole images processing many difficultiesTraditional image denoising method easily leads to blurred images and the denoising effect is not very satisfactory Aimed atthe image characteristics of low image illumination and large amount of noise and based on the characteristics of color detailblindness and simultaneous contrast of human visual perception this paper proposes a new method for image denoising basedon visual characteristics The method uses CIELab uniform color space to dynamically and adaptively decide the filter weightsthereby reducing the damage to the image contour edges and other details so that the denoised image can have a higher clarityExperimental results show that thismethod has a brilliant denoising effect and can significantly improve the subjective and objectivepicture quality of downhole images

1 Introduction

The application environment in the coal industry is alwaysspecial and downhole images are always mingled with largeamount of image noise interfered by complex undergroundenvironment mechanical vibration and dust noise Thisbrings many difficulties for the subsequent processing of theimage Therefore the denoising process on images capturedand transmitted from downhole becomes very necessaryso as to provide better image quality and better followupprocessing

There are many ways in terms of denoising such as themean denoising median denoising and wavelet denoisingA representative study is from Narendra who raised therow-column decomposition median filtering algorithm [1]moreover He et al have put forward a multimedian filteralgorithm [2] which can effectively remove the image impulsenoise additionally Darsow and Olsen have proposed threedenoising methods based on phases of wavelet local phasevariance threshold edge tracking and scale phase fluctuationthreshold method [3] In order to overcome the weaknessthat wavelet transform can only carry out point singularity

detection Minh N Do and Martin Vetterli proposed con-tourlet transform in 2002 [4] With the gradual deepeningof the various branches of mathematics in the theory andapplications great progress in image denoising technologyhas been achieved in terms of mathematical morphologypartial differential equations genetic algorithms informationtheory and so forth producing a number of new denoisingalgorithms [5ndash8] including denoising algorithm based onmathematicalmorphology [9ndash12] denoising algorithmbasedon fuzzy theory [13 14] denoising algorithmbased on geneticalgorithms [15] neural network-based denoising algorithm[16] and denoising algorithm based on information entropy

Although with the maturity and improvement of thevarious theories image denoising methods have gained a lotof progress these methods have their respective advantagesdisadvantages and application areas For example the meandenoising is suitable for removing grain noise in images butthe images always easily become blur because this methodis too average median denoising is good for removingimpulse noise in the image but the denoising effect isnot very ideal when the noise area inside the window istoo large Wiener filter is suitable for removing the white

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 362716 7 pageshttpdxdoiorg1011552014362716

2 Journal of Applied Mathematics

noise in the image however the calculation amount is toolarge wavelet denoising has a wide range of algorithms andsuperior performances but the realization is very difficultand complex Moreover the effect of the above algorithmswill not be satisfactory when an image is simultaneouslyinterfered by a variety of noise in other words while theimage smoothens the quality declines Besides denoisingresearch on specific areas with complex environment is alsovery rare The aforementioned are the current research statusof image denoising therefore with the combination of noisecharacteristics of the coal mine finding a method that canpreserve the image detail and textural features while at thesame time reducing image noise has become the research goalof this paper

2 CIELab Color Space

CIELab color space is defined by the International Commis-sion on Illumination (CIE) in 1976 and it is currently one ofthe most uniform color spaces with a set data of 119871 119886 and119887 representing one color and one Lab values group formedone corresponding relationship with one color In the set 119871indicates the luminance value 119886 and 119887 are the chromaticitycoordinates Value 119886 indicates the color change direction ofred-green +119886 indicates the change towards the red directionand minus119886 shows the change in the direction of green 119887 showsthe change in the yellow-blue direction +119887 shows the changein the direction of yellow andminus119887 shows the change in the bluedirection As shown in Figure 1 119886 represents axis of red andgreen and 119887 represents axis of yellow and blue Their valuesrange from 0 to 10 119886 = 119887 = 0 means colorlessness and 119871

represents scale factor from black to white

3 Interconversion of RGB and CIELab ColorSpace

The interconversion of RGB and CIELab color space needs toconvert RGB to CIEXYZ color space first and then to CIELabcolor space [5]

The conversion formula of RGB color space to119883119884119885 colorspace is

[

[

119883

119884

119885

]

]

= (

04303 03416 01784

02219 07068 00713

00202 01296 09393

)[

[

119877

119866

119861

]

]

(1)

Then convert 119883119884119885 color space to LAB color space and theconversion formula is

119886 = 500 [119891(119883

119883119899

) minus 119891(119884

119884119899

)]

119887 = 200 [119891(119884

119884119899

) minus 119891(119885

119885119899

)]

119891 (119909) =

11990913

119884

119884119899

gt 0008856

7787 times 119909 +16

116

119884

119884119899

le 0008856

(2)

Yellowish

minusb

lowast

b

lowast

Greenishminusa

lowast

L

lowast

= 0

(black)

L

lowast

= 100

(white)

a

lowast

Reddish

Blueish

Figure 1 CIELab color space

where 119871 = 119891(119909) 119883119899

= 9504 119884119899

= 10000 and 119885119899

=

10889 are white tristimulus values of 11986365 the CIE standard

illuminant 119883119884 and 119885 are coordinate value of CIEXYZspace

The computational formula of aberration Δ119864lowast

119886119887between

two colors in CIEXYZ space is as follows

Δ119864119886119887

= [(Δ119871lowast

)2

+ (Δ119886lowast

)2

+ (Δ119887lowast

)2

]12

(3)

where

Δ119871lowast

= 119871lowast

1minus 119871lowast

2

Δ119886lowast

= 119886lowast

1minus 119886lowast

2

Δ119887lowast

= 119887lowast

1minus 119887lowast

2

(4)

4 New Adaptive Image Denoising MethodBased on Visual Characteristic

The classic image denoising methods are done in the RGBcolor space while RGB color space is a nonuniform colorspace and it does not take into account important infor-mation such as the image brightness and chroma Due tothe fact that images captured from downhole are affectedby low light or uneven illumination it is very hard to reachsatisfactory denoising effect by adopting the classic imagedenoising method In order to improve the image denoisingperformance a more uniform CIELab color space is neededIn this color space human visual sensitivity to the colordifferences of different wavelengths is not the same therelevant data are shown in Table 1 Aimed at the specialdownhole circumstances and based on CIELab uniformcolor space the characteristics of color detail blindness andsimultaneous contrast of human visual perception this paperpresents a new image denoising method to improve thesubjective and objective image quality

41 Algorithm Thought In uniform color space the chro-matism value of two human-eye distinguishable colors isequal that is when the chromatism is smaller than a certain

Journal of Applied Mathematics 3

Table 1 Value of chromatism and sensitivity level to the colordifferences

Value ofchromatism Sensitivity level to the color differences

00sim050 (Tiny chromatic aberration) trivial feeling05sim151 (Small chromatic aberration) slight feeling15sim3 (Lesser chromatic aberration) noticeable feeling3sim6 (Larger chromatic aberration) appreciable feelingAbove 6 (Large chromatic aberration) strong feeling

threshold human eyes consider them as the same color butwhen the chromatism is greater than a threshold human eyewill be able to distinguish the two different colors In CIELabcolor space the value of this threshold is generally 3 In viewof this the paper will divide image noise into two typesflat region noise and nonflat region noise The algorithmcarries out different processing self-adaptively according tothe different region of the pixel

In a region let 119909119894119895represent the polluted pixel value of

point (119894 119895) and then let the CIELabmedian of the pixel in thearea with 119909

119894119895being the center point and neighborhood being

(2119873 + 1) times (2119873 + 1) be

119910119894119895

= median = 119909119894minus119873119869minus119899

119909119894119895 119909

119894+119873119869+119873 (5)

Let the CIELab chromatic aberration of current pixel pointand center point be 119889 = |119909

119894119895

minus 119910119894119895

| preset a threshold 119905 andcompare it with 119889

120572119894119895

= 1 119889 gt 119905

0 else(6)

If 120572119894119895of all pixels within the neighborhood of (2119873+1)times(2119873+

1) are 1 then it is called flat region noise the color of flatregion noise point can be affected by the rest of pixels withinthe same neighborhood and convolution denoising can beconducted by using traditional Gaussian filter template Ifthere are pixels within the neighborhood of (2119873+1) times (2119873+

1) whose 120572119894119895are 0 then this area is nonflat region Noise

in nonflat region is not entirely affected by other pixels inthe neighborhood and is only related to pixels in the samearea that is the noise is only related to pixels whose CIELabchromatic aberration is less than the relevant threshold ifit is greater than the threshold then it is considered thatthe contribution of the pixel color value to the center pointremains conforming to Gaussian distribution otherwise thepixel does not have any contribution to the center pointLet the convolution weights be 0 Thus the pixel color willbe more consistent within the same region achieving thepurpose of preserving image detail

42 Gaussian Filter Gaussian filter [7] is the linear smooth-ing filter which determines weights according to the shape ofthe Gaussian function One-dimensional Gaussian functionis

119892 (119909) = 119890minus119909221205902

(7)

wherein 120590 determines the width of the Gaussian filter Thegreater 120590 becomes the wider the band of the Gaussian filterwill be and the better the smoothness will be Moreover 119886compromise can be obtained by adjusting the smoothnessdegree parameter 120590 when the image features are too vagueand when excessive unwelcome break variables are caused bynoise and texture in smooth images For image processingtwo-dimensional Gaussian function is commonly used assmoothing filter The function expression is

119892 [119894 119895] = 119890minus(1198942+1198952)21205902

(8)

The convolution and denoising formula of the input image119891[119894 119895] via Gaussian filter is

119892 [119894 119895] lowast 119891 [119894 119895] =

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119892 [119896 119897] 119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119890minus(1198962+1198972)21205902

119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119890minus119896221205902

119899minus1

sum

119897=0

119890minus119897221205902

119891 [119894 minus 119896 119895 minus 119897]

(9)

In order to reduce the time complexity of Gaussian fil-ter convolution calculation the two-dimensional Gaussianfunction can be converted to the combination of two one-dimensional convolution templates [8] First convolve theinput image119891[119894 119895] and the Gaussian template in the horizon-tal direction set a temporary array store the result in thetemporary array then convolve the image and the Gaussiantemplate in the horizontal direction and transpose the resultthe final smooth image can be obtained

Figure 2 is a schematic diagram of the separability of theGaussian function convolution This method is completedthrough the combination of two horizontal convolution tem-plates First convolve the input image119891[119894 119895] and theGaussianfunction in the horizontal direction and then transpose andstore the result in the temporary array after that take thetemporary array as the input and carry out the convolutionwith the same Gaussian function to realize the purposeof replacing the vertical convolution with the horizontalconvolution Transpose the output information after thesecond convolution and then the final smoothed outputimage can be obtained Since the separability of the Gaussianfunction is high Gaussian filter can be effectively achievedTwo-dimensional Gaussian function can be carried out intwo steps First convolve the imagewith the one-dimensionalGaussian function then convolve the result with the sameone-dimensionalGaussian function perpendicular to the firstresult Therefore the calculation amount of two-dimensionalGaussian filter presents a linear growth along with the widthof the filter template rather than a square growth

43 Algorithm Flow Define the size of denoising template as120575 times 120575 and the distinguishable color threshold as 119879 traverseany pixel (119903 119892 119887) in the image the specific realization stepsof this algorithm are as follows


(a) Longitudinal template convolution (b) Horizontal template convolution

Figure 2 Schematic diagram of the separability of Gaussian function convolution

(1) Input the pending image119891 and initialize the Gaussianconvolution template whose size is 120575 times 120575

(2) Use the chromatic aberration computational formulaof CIELab space color to calculate the value of chro-matism between the center pixel and pixels withinneighborhood 120575 collect number 119899 which stands forthe value of chromatism that is greater than thethreshold 119879

(3) If 119899 = 120575 times 120575 minus 1 then it indicates that except thecenter pixel all the values of chromatism betweenany two pixels in the region are greater than thethreshold 119879 This is flat region noise convolution anddenoising can be reached via traditional Gaussianfilter template Turn to Step (4)

(4) If 119899 = 120575 times 120575 minus 1 119899 = 0 and if the value of chromatismbetween center pixel and pixel (119894 119895) in the regionis greater than threshold 119879 then this is nonflatregion noise Set the value of pixel (119894 119895) in Gaussianconvolution template to be 0 Turn to Step (5)

(5) If none of the above is satisfied no operation isrequired keep the original value

(6) Process the next pixel and turn to Step (2)

(7) Judge whether all the pixels are processed if yesend the algorithm otherwise turn to Step (6) andcontinue the processing

The algorithm flow is as shown in Figure 3

5 Experimental Performance andComparative Analysis

A noisy downhole image was selected and denoising process-ing was carried out by respectively using methods of meandenoising median denoising hybrid denoising traditional

Noise point

Traverse pixels

Nonnoise point

Judging

Flat region noise Nonflat region noise

Keep theoriginal

value

Input image

Traditional Gaussiandenoising

Statistical-basedGaussian template

denoising

End of algorithm

Processing all pixels

No

No

No

Yes

Figure 3 Algorithm flow

Gaussian denoising and the method proposed in this paperImage RMSE (root mean square error) and PSNR (peaksignal to noise ratio) were calculated so as to evaluate theperformance of different algorithms


(a) Noise polluted image (b) Mean denoising

(c) Median denoising (d) Hybrid denoising

(e) Traditional Gaussian denoising (f) Paper-proposed denoising

Figure 4 Effect contrast of different denoising methods

RMSE and PSNR are defined as follows [17 18]

RMSE =1

119872119873

119873

sum

119895=1

119872

sum

119894=1

1003816100381610038161003816119891 (119909 119910) minus 119892 (119909 119910)1003816100381610038161003816

2

PSNR = 10 log10

(2552

times 119872 times 119873

sum119873

119895=1sum119872

119894=1(119891 (119894 119895) minus 119892 (119894 119895))

2)

(10)

wherein 119892 indicates source image 119891 stands for images whichgoes through scales addressing first and then same multiple

processing second with the use of relevant algorithm and 119872

and 119873 represent the length and width of the image RMSEreflects the approximate extent of the scaled image to thesource image the smaller the RMSE is themore approximatethe scaled image is to the source image PSNR reflects theimage magnification effect The higher the PSNR is theclearer the scaled image will be

The experimental hardware environment is Pentium 4CPU (280GHz) memory capacity 15 GB and resolution1024 times 768 the software environment is Microsoft WindowsXP Professional SP3 operating systems The effect contrast of


Table 2 Evaluation index of denoising effect of different denoisingalgorithms

Denoising method RMSE PSNRMean denoising 30714593 2103142Median denoising 25965736 3273148Hybrid denoising 24247657 3345765Traditional Gaussian denoising 21032459 3487167Paper-proposed denoising 19010174 3691472

different denoising methods is as shown in Figure 4 and thecomparison of denoising experimental data is as shown inTable 2

It can be seen from Table 2 that RMSE of mean denoisingis the maximum and that of the PSNR is minimum whichmeans the denoising effect of this method is the most unsat-isfactory RMSE of median and hybrid denoising method isgreatly lower than that of mean denoising and PSNR hasalso been improved Compared with traditional Gaussiandenoising and other methods the algorithm proposed bythis paper has further improved the objective quality of theimage Moreover it can also be seen from Figure 3 thatthe contours of the image processed by mean denoising arevague and the image also contains a lot of noise what isworse there is a serious loss of image detail informationthe performance of median and hybrid denoising is a littlebit better but the processed image still contains residualnoise traditionalGaussian denoisingmethod did notmanageto eliminate the obvious noise within the visual range andthe effect is not very ideal the algorithm proposed in thispaper successfully improved the peak signal to noise ratio andat the same time managed to reserve image detail featuresand texture changing features well more importantly theprocessed image has higher resolution and better visualeffects

6 Conclusions

Denoising processing on underground images has beenconducted in this paper based on CIELab color space andCIELab chromatism aberration computational formula Thepaper has proposed that weight should be determined byvisual chromatism aberration which makes up the insuffi-ciency of letting space coordinates distance decide weight inRGB space in the meantime the characteristic that CIELabcolor space is more uniform in visual perception is usedtaking fully into account the luminance and chrominanceinformation of the processed image making the denoisedimages and human vision maintain better correlation Theexperimental results have demonstrated the effectiveness ofthe algorithm from aspects of the subjective quality andthe objective quality This method is very helpful to furtherprocessing and application of downhole images

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by advancing projects of the industri-alization of scientific research achievements in Universitiesof Jiangsu Province (Grant JHB2012-36) and the science andtechnology fund of theMinistry of Housing andUrban-RuralDevelopment of China (Grant 2013-K2-5)

References

[1] P M Narendra ldquoA separable median filter for image noisesmoothingrdquo IEEETransactions on PatternAnalysis andMachineIntelligence vol 3 no 1 pp 20ndash29 1981

[2] J-M He Q Li and Y Ming ldquoRealization and performance testof improved median filterrdquo Computer Systems amp Applicationsvol 18 no 8 pp 172ndash174 2009

[3] W F Darsow and E T Olsen ldquoCharacterization of idempotent2-copulasrdquo Note di Matematica vol 30 no 1 pp 147ndash177 2010

[4] J J Li H Fan and Y Wang ldquoImage denoising algorithmbased on dyadic contourlet transformrdquo Applied Mechanics andMaterials vol 40-41 pp 591ndash597 2011

[5] G Hernandez-Gomez R E Sanchez-Yanez V Ayala-Ramirezand F E Correa-Tome ldquoNatural image segmentation usingthe CIELab spacerdquo in Proceedings of the 19th InternationalConference on Electronics Communications and Computers(CONIELECOMP rsquo09) pp 107ndash110 February 2009

[6] G Cui M R Luo B Rigg G Roesler and K Witt ldquoUniformcolour spaces based on the DIN99 colour-difference formulardquoColor Research and Application vol 27 no 4 pp 282ndash290 2002

[7] D-H Shin R-H Park S Yang and J-H Jung ldquoBlock-based noise estimation using adaptive Gaussian filteringrdquo IEEETransactions on Consumer Electronics vol 51 no 1 pp 218ndash2262005

[8] S Gao C Li and D Bi ldquoImage enhancement algorithm basedon NF-ICMrdquo Chinese Optics Letters vol 8 no 5 pp 474ndash4772010

[9] A Saffor A R Ramli and K-H Ng ldquoA comparative studyof image compression between JPEG and waveletrdquo MalaysianJournal of Computer Science vol 14 no 1 pp 39ndash45 2001

[10] R R Coifinan and D L Donoho ldquoTranslation-invariantdenoisingrdquo in Wavelet in Statistics vol 103 of Lecture Notes inStatistics pp 125ndash150 Springer New York NY USA 1994

[11] A G Bruce and H-Y Gao ldquoWaveShrink with firm shrinkagerdquoStatistica Sinica vol 7 no 4 pp 855ndash874 1997

[12] M Jansen M Malfait and A Bultheel ldquoGeneralized crossvalidation for wavelet thresholdingrdquo Signal Processing vol 56no 1 pp 33ndash44 1997

[13] L Sendur and I W Selesnick ldquoBivariate shrinkage functionsfor wavelet-based denoising exploiting interscale dependencyrdquoIEEE Transactions on Signal Processing vol 50 no 11 pp 2744ndash2756 2002

[14] C S Lee and Y H Kuo Fuzzy Techniques in Image Processingvol 52 Springer New York NY USA 2000

[15] C S Lee Y H Kuo and P T Yu ldquoWeighted fuzzy mean filtersfor image processingrdquo Fuzzy Sets and Systems vol 89 pp 15ndash180 1997


[16] S H Wang L N Wu Y D Zhang et al ldquoAnt colonyalgorithm used for bankruptcy predictionrdquo in Proceedings ofthe 2nd International Symposium on Information Science andEngineering (ISISE rsquo09) pp 137ndash139 Shanghai China 2009

[17] D S Levine and M Aparicio IV Eds Neural Networks forKnowledge Representation and Inference Psychology Press 2013

[18] S Yuying and L Jingjing ldquoA semi-implicit image denoisingalgorithm in matrix formrdquo Journal of Xuzhou Institute ofTechnology (Natural Sciences Edition) vol 27 no 4 2012

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noise in the image however the calculation amount is toolarge wavelet denoising has a wide range of algorithms andsuperior performances but the realization is very difficultand complex Moreover the effect of the above algorithmswill not be satisfactory when an image is simultaneouslyinterfered by a variety of noise in other words while theimage smoothens the quality declines Besides denoisingresearch on specific areas with complex environment is alsovery rare The aforementioned are the current research statusof image denoising therefore with the combination of noisecharacteristics of the coal mine finding a method that canpreserve the image detail and textural features while at thesame time reducing image noise has become the research goalof this paper

2 CIELab Color Space

CIELab color space is defined by the International Commis-sion on Illumination (CIE) in 1976 and it is currently one ofthe most uniform color spaces with a set data of 119871 119886 and119887 representing one color and one Lab values group formedone corresponding relationship with one color In the set 119871indicates the luminance value 119886 and 119887 are the chromaticitycoordinates Value 119886 indicates the color change direction ofred-green +119886 indicates the change towards the red directionand minus119886 shows the change in the direction of green 119887 showsthe change in the yellow-blue direction +119887 shows the changein the direction of yellow andminus119887 shows the change in the bluedirection As shown in Figure 1 119886 represents axis of red andgreen and 119887 represents axis of yellow and blue Their valuesrange from 0 to 10 119886 = 119887 = 0 means colorlessness and 119871

represents scale factor from black to white

3 Interconversion of RGB and CIELab ColorSpace

The interconversion of RGB and CIELab color space needs toconvert RGB to CIEXYZ color space first and then to CIELabcolor space [5]

The conversion formula of RGB color space to119883119884119885 colorspace is

[

[

119883

119884

119885

]

]

= (

04303 03416 01784

02219 07068 00713

00202 01296 09393

)[

[

119877

119866

119861

]

]

(1)

Then convert 119883119884119885 color space to LAB color space and theconversion formula is

119886 = 500 [119891(119883

119883119899

) minus 119891(119884

119884119899

)]

119887 = 200 [119891(119884

119884119899

) minus 119891(119885

119885119899

)]

119891 (119909) =

11990913

119884

119884119899

gt 0008856

7787 times 119909 +16

116

119884

119884119899

le 0008856

(2)

Yellowish

minusb

lowast

b

lowast

Greenishminusa

lowast

L

lowast

= 0

(black)

L

lowast

= 100

(white)

a

lowast

Reddish

Blueish

Figure 1 CIELab color space

where 119871 = 119891(119909) 119883119899

= 9504 119884119899

= 10000 and 119885119899

=

10889 are white tristimulus values of 11986365 the CIE standard

illuminant 119883119884 and 119885 are coordinate value of CIEXYZspace

The computational formula of aberration Δ119864lowast

119886119887between

two colors in CIEXYZ space is as follows

Δ119864119886119887

= [(Δ119871lowast

)2

+ (Δ119886lowast

)2

+ (Δ119887lowast

)2

]12

(3)

where

Δ119871lowast

= 119871lowast

1minus 119871lowast

2

Δ119886lowast

= 119886lowast

1minus 119886lowast

2

Δ119887lowast

= 119887lowast

1minus 119887lowast

2

(4)

4 New Adaptive Image Denoising MethodBased on Visual Characteristic

The classic image denoising methods are done in the RGBcolor space while RGB color space is a nonuniform colorspace and it does not take into account important infor-mation such as the image brightness and chroma Due tothe fact that images captured from downhole are affectedby low light or uneven illumination it is very hard to reachsatisfactory denoising effect by adopting the classic imagedenoising method In order to improve the image denoisingperformance a more uniform CIELab color space is neededIn this color space human visual sensitivity to the colordifferences of different wavelengths is not the same therelevant data are shown in Table 1 Aimed at the specialdownhole circumstances and based on CIELab uniformcolor space the characteristics of color detail blindness andsimultaneous contrast of human visual perception this paperpresents a new image denoising method to improve thesubjective and objective image quality

41 Algorithm Thought In uniform color space the chro-matism value of two human-eye distinguishable colors isequal that is when the chromatism is smaller than a certain









(2119873 + 1) times (2119873 + 1) be

119910119894119895


119909119894119895 119909

119894+119873119869+119873 (5)


119894119895

minus 119910119894119895


120572119894119895

= 1 119889 gt 119905

0 else(6)






119892 (119909) = 119890minus119909221205902

(7)


119892 [119894 119895] = 119890minus(1198942+1198952)21205902

(8)


119892 [119894 119895] lowast 119891 [119894 119895] =

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119892 [119896 119897] 119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119890minus(1198962+1198972)21205902

119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119890minus119896221205902

119899minus1

sum

119897=0

119890minus119897221205902

119891 [119894 minus 119896 119895 minus 119897]

(9)

















Noise point

Traverse pixels

Nonnoise point

Judging


Keep theoriginal

value

Input image



denoising

End of algorithm


No

No

No

Yes









RMSE =1

119872119873

119873

sum

119895=1

119872

sum

119894=1

1003816100381610038161003816119891 (119909 119910) minus 119892 (119909 119910)1003816100381610038161003816

2

PSNR = 10 log10

(2552


sum119873

119895=1sum119872

119894=1(119891 (119894 119895) minus 119892 (119894 119895))

2)

(10)










6 Conclusions




Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















(2119873 + 1) times (2119873 + 1) be

119910119894119895


119909119894119895 119909

119894+119873119869+119873 (5)


119894119895

minus 119910119894119895


120572119894119895

= 1 119889 gt 119905

0 else(6)






119892 (119909) = 119890minus119909221205902

(7)


119892 [119894 119895] = 119890minus(1198942+1198952)21205902

(8)


119892 [119894 119895] lowast 119891 [119894 119895] =

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119892 [119896 119897] 119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119899minus1

sum

119897=0

119890minus(1198962+1198972)21205902

119891 [119894 minus 119896 119895 minus 119897]

=

119898minus1

sum

119896=0

119890minus119896221205902

119899minus1

sum

119897=0

119890minus119897221205902

119891 [119894 minus 119896 119895 minus 119897]

(9)

















Noise point

Traverse pixels

Nonnoise point

Judging


Keep theoriginal

value

Input image



denoising

End of algorithm


No

No

No

Yes









RMSE =1

119872119873

119873

sum

119895=1

119872

sum

119894=1

1003816100381610038161003816119891 (119909 119910) minus 119892 (119909 119910)1003816100381610038161003816

2

PSNR = 10 log10

(2552


sum119873

119895=1sum119872

119894=1(119891 (119894 119895) minus 119892 (119894 119895))

2)

(10)










6 Conclusions




Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra






















Noise point

Traverse pixels

Nonnoise point

Judging


Keep theoriginal

value

Input image



denoising

End of algorithm


No

No

No

Yes









RMSE =1

119872119873

119873

sum

119895=1

119872

sum

119894=1

1003816100381610038161003816119891 (119909 119910) minus 119892 (119909 119910)1003816100381610038161003816

2

PSNR = 10 log10

(2552


sum119873

119895=1sum119872

119894=1(119891 (119894 119895) minus 119892 (119894 119895))

2)

(10)










6 Conclusions




Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra















RMSE =1

119872119873

119873

sum

119895=1

119872

sum

119894=1

1003816100381610038161003816119891 (119909 119910) minus 119892 (119909 119910)1003816100381610038161003816

2

PSNR = 10 log10

(2552


sum119873

119895=1sum119872

119894=1(119891 (119894 119895) minus 119892 (119894 119895))

2)

(10)










6 Conclusions




Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














6 Conclusions




Acknowledgments


References



























Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article a new method of image denoising for

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