A Adaptive Image Deoisig Method based o Thresholdig HARI OM AND MANTOSH BISWAS Departmet of Computer Sciece & Egieerig Idia School of Mies, Dhabad Jharkad-86004 INDIA {hariom4idia, matoshb}@gmail.com Abstract - This paper proposes a Adaptive Image Deoisig Method based o Thresholdig that follows the similar approach as i the NeighShrik method. This method shriks the oisy wavelet coefficiets usig a adaptive threshold. The NeighShrik ad its versios amely, IAWDMBNC ad IIDMWT always produce ufavourable smoothig of edges ad details of the oisy image because these methods kill more oisy coefficiets durig the shrikage. Our proposed method overcomes these drawbacks ad performs better tha the NeighShrik, IAWDMBNC, ad IIDMWT i terms of Peak Sigal-to-Noise Ratio (PSNR) usig shrikage based o our proposed threshold. Key-Words - Image Deoisig, Thresholdig method, Coefficiet, Peak Sigal-to-Noise Ratio (PSNR). 1 Itroductio The oise removal from a oisy image is a problem that exists from the very begiig of the digital image processig. This problem still attracts research attetio ad wide rages of various approaches have bee discussed to remove the oise ad preserve the image iformatio. The aim of oise removal is to costruct the origial image from the oisy observatio. I recet years, the wavelets trasform (WT) based approaches have led to a substatial success i image deoisig due to good localizatio i both the spatial ad spectral domais [1-]. The image deoisig methods may be based o term-by-term or block-by-block thresholdig [3-11]. Dooho et al. discuss the termby-term thresholdig such as VisuShrik, SureShrik ad the block-by-block thresholdig such as NeighBlock, NeighShrik, IAWDMBNC, ad IIDMWT have bee discussed by Cai et al., Bui et al., Ju Jiag et al., ad Om et al., respectively. The block-by-block thresholdig methods are based o subbad adaptive eighborig widow ad have better performace tha the term-by-term based methods. The VisuShrik [3-4] method offers the advatages of smoothess ad adaptatio; however, it exhibits visual artifacts due to Gibbs pheomea i the eighbourhood of discotiuities. Overcomig this problem, Coifma ad Dooho have discussed SureShrik. It is based o Stei s Ubiased Risk Estimator (SURE) that miimizes the mea squared error [5]. The NeighBlock method discussed takes the eighbourig coefficiets ito accout [6]. Che ad Bui have exteded the eighborig wavelet thresholdig idea, called NeighShrik, for multiwavelet that outperforms the sigle wavelet deoisig method for the stadard test sigals ad real-life images [7-8]. Ju Jiag et al. ad Om et al. have improved the NeighBlock ad NeighShrik methods [9-10]. Our proposed method is also based o Ju Jiag et al.s method, which takes ito accout the local characteristics of the eighborig widow, size of the subbad, ad the oise distributio at differet decompositio levels of the oisy image. The effectiveess of our method over the NeighShrik, IAWDMBNC, ad IIDMWT is due to the oise removal, which is also show i experimetal results i terms of peak-to-sigal ratio (PSNR). The orgaizatio of rest of the paper is as follows. Sectio describes the proposed method i detail. Sectio 3 discusses the experimetal results carried out, ad fially the paper is cocluded i Sectio 4. Proposed Method Let a oise-free image X be corrupted by idepedet ad idepedet idetically distributed (i.i.d.) additive white Gaussia oise N that has zero-valued mea ad variace as σ. The E-ISSN: 4-3488 1 Volume 10, 014
correspodig oisy image is deoted by Y. Mathematically, we ca write Y = X + N (1) Here, 1 m, M; M M is origial image size. The mai goal of our method is to miimize the mea square error (MSE) of the oisy image Y ad origial image X. Let W(. ) ad W -1 (. ) deote the forward ad backward wavelet trasform operators ad D(., T) deote the deoisig operator with threshold T []. We deoise Y to recover Xˆ as a estimate of the origial image X after applyig the followig three steps: (i) Forward operator to oisy image Y i.e. Z = W(Y). (ii) Deoisig operator to Z i.e. O = D (Z, T). (iii) Iverse wavelet trasform to recostruct the image Xˆ from O i.e., Xˆ = W -1 (O). For carryig out above steps, we eed to derive threshold usig which the shrikage factor is evaluated ad fially the deoisig procedure is applied..1 Parameter Estimatio Let Sq be a summatio square of the wavelet coefficiets by icorporatig eighbourig coefficiets i thresholdig process. I other words, we have Sq = ( p, q) d p q B m,, () where, B represets the eighborhood widow whose elemets are deoted by d p,q. For every wavelet coefficiet, we cosider a square eighborhood widow B of size L L cetered at that pixel, where L is a positive odd iteger. We take several useful values of eighborig coefficiets that are eeded for choosig a appropriate threshold. Let Sqmax ad Sq mi represet maximum ad miimum summatio square, respectively, of Sq at the same decompositio level as defied below [9]: Sq = max ( Sq max mi ), ad Sq = mi ( Sq ) (3). Threshold Estimatio The NeighShrik deoisig method uses the VisuShrik threshold that produces the oversmoothed sigal sice its threshold is large [7-8]. This problem has bee overcome i IAWDMBNC ad IIDMWT by usig their shrikages followed by the modified threshold of the VisuShrik threshold with maximum ad miimum sums of the wavelet coefficiets widow at the same level [9-10]. However, theses methods are ot able to remove the oise ad restore the modified oisy coefficiets efficietly sice they kill may oisy coefficiets because of their large thresholds. I this proposed work, we try to overcome this problem by usig the shrikage followed by our proposed threshold fuctio. Here, we chage the VisuShrik threshold ad other parameters of the oisy image i such a way that the threshold value is either large or less of the oisy coefficiets. Hece, this proposed method removes the oise effectively as the small threshold keeps more features of the sigal, whereas large threshold elimiates the oise as much as possible. Therefore, we eed to defie our threshold as follows. NEW Sq Sq T m, = m, * t Sq Sq max (4) max where, the scale factor, t, is give by [10] t = σ mi Mˆ log (5) l Here, l = 1,,, J; J deotes the decompositio level to be cosidered ad Mˆ = M/ l..3 Shrikage Estimatio After estimatig the thresholdt NEW m,, we eed shrik the wavelet coefficiets usig the followig formula. X m, = New l Tm, Zm, 1 (6) Sq m, The shrikig operatio couterbalaces the deficiecy of soft thresholdig that ca keep more iformatio of the sigal. The degree of shrikage i our thresholdig decreases as the decompositio level l icreases. The shrikage factor correlates the wavelet coefficiets ad decompositio levels (i.e. l) ad + sig at ed of the expressio sigifies that the positive value should be kept ad the egative value should be set as zero. E-ISSN: 4-3488 Volume 10, 014
(a) (c) Fig. 1: Origial test gray images: (a) Lea (b) Madrill ad (c) Barbara each of size 51 51 pixels.3 Deoisig Procedure The followig steps are performed i the deoisig scheme: (i) Perform multiscale decompositio o the corrupted image. For this, apply -D wavelet trasform W o the oisy image Y up to J th level to geerate several subbads: HH, HL, ad LH, called details, ad LL, called approximatio. (ii) For each level, compute NEW T m, (b) usig (4). (iii) For each subbad (except the low pass residual, i.e. approximatio), shrik the wavelet coefficiets usig (6) to obtai the modified wavelet coefficiets. (iv) Perform iverse wavelet trasform o the modified coefficiets to obtai the deoised estimate image Xˆ. 3 Experimetal Results Our experimets have bee carried out o the oisy images, which iclude Lea, Madrill, ad Barbara (refer Fig. 1). Differet oise levels: 10, 0, 30, 50, 75, ad 100 are geerated by addig Gaussia white oise to the origial oise-free images. We take three, four, ad five levels of wavelet decompositios usig the Symlet wavelet with a vaishig momet of eight. We have computed the results by usig NeighShrik, IAWDMBNC, IIDMWT, ad our proposed methods i terms of PSNR (i db) for test images usig two differet widow sizes: 3 3 ad 5 5. The results for decompositio levels: three, four, ad five are show i Tables 1-3. For the purpose of visual quality, we have take oisy image with oise level 50 ad 10 of Lea ad Goldhill (refer Figs. (a) ad 3(a)) ad the oise free images obtaied by applyig the cosidered deoisig methods (refer Figs. (b)- (i) ad 3(b)-3(i)) for the decompositio level three, respectively. We have also show these PSNR values graphically i Fig. 4(a) for 3 3 widow size ad Fig. 4(b) with 5 5 widow size for decompositio level three oly. We observe that the results of our proposed method are better tha that of the NeighShrik, IAWDMBNC, ad IIDMWT for all test images, oise, ad decompositio levels, for widow size 3 3 (refer Tables 1-3, Figs., 3 & 4(a)). For widow size 5 5, our results are better for almost all oise levels ad for all decompositio levels for Lea image (refer Tables 1-3, Figs. (b)-(i)). We observe that our method outperforms the NeighShrik, IAWDMBNC ad IIDMWT for all oise ad decompositio levels i widow size 5 5 for Madrill (refer Tables 1-3, Figs. 3(b)-3(i)). For widow size 5 5, our results are better for almost all oise levels ad for all decompositio levels for Barbara (refer Tables 1-3, Figs. 4(b)). It is evidet from tables 1-3 ad Figs., 3 & 4 that our method removes oise sigificatly as compared to the NeighShrik, IAWDMBNC ad IIDMWT for widow size 3 3. For widow size 5 5, it removes oise sigificatly for higher oise level as compared to the NeighShrik, IAWDMBNC ad IIDMWT; but it does ot remove oise for low oise level. Similar results were obtaied for other images also. We however have give the umerical results for all images i tables 1-3. E-ISSN: 4-3488 3 Volume 10, 014
Table 1: PSNR (i db) for images: Lea, Madrill, ad Barbra with oise levels: 10, 0, 30, 50, 75, ad 100 for NeighShrik, IAWDMBNC, IIDMWT ad our proposed method with decompositio level three (3) Images Noise levels Deoise Methods with decompositio level:3 NeighShrik IAWDMBNC IIDMWT Proposed 3x3 5x5 3x3 5x5 3x3 5x5 3x3 5x5 10 33.3 34.5 33.83 33.34 33.65 33.84 34.0 3.53 Lea 0 8.73 30.37 9.69 30.53 9.8 30.77 30.85 30.03 30 6.54 7.65 7.30 8.43 6.98 8.16 8.55 8.81 50 4.85 5.11 5.4 5.85 4.93 5.40 5.95 6.46 75 3.91 3.91 3.96 4.03 3.91 3.91 4.13 4.49 100.89.89.87.85.89.89.90.9 Madrill Barbara 10 7.6 9.64 8.5 9.78 7.91 9.84 9.13 9.99 0 1.96 4.3.83 5.13.51 4.93 3.94 5.64 30 0.38 1.41 0.83.37 0.6 1.96 1.85 3.5 50 19.81 19.89 19.93 0.16 19.84 0.00 0. 0.98 75 19.51 19.51 19.51 19.54 19.51 19.51 19.57 19.75 100 19.11 19.11 19.10 19.10 19.11 19.11 19.10 19.15 10 31.06 3.5 31.83 3.37 31.61 3.39 3.3 31.97 0 5.35 7.64 6.37 8.7 6.0 8.11 7.37 8.48 30.87 4.54 3.77 5.51 3.0 5.1 4.65 6.3 50 1.98.14.19.8.04.7.63 3.55 75 1.46 1.46 1.49 1.59 1.46 1.47 1.59 1.91 100 0.85 0.85 0.84 0.87 0.85 0.85 0.86 0.96 Table : PSNR (i db) for images: Lea, Madrill, ad Barbra with oise levels: 10, 0, 30, 50, 75, ad 100 for NeighShrik, IAWDMBNC, IIDMWT ad our proposed method with decompositio level four (4) Images Noise levels Deoise Methods with decompositio level:4 NeighShrik IAWDMBNC IIDMWT Proposed 3x3 5x5 3x3 5x5 3x3 5x5 3x3 5x5 10 33. 34.5 33.83 33.35 33.65 33.48 34.0 3.53 Lea 0 8.58 30.39 9.64 33.56 9. 30.8 30.90 30.03 30 6.09 7.58 7.07 8.50 6.74 8. 8.64 8.88 50 3.47 4.60 4.47 5.71 4.01 5.18 6.0 6.71 75.5.93.96 3.66.77 3.8 4.14 4.93 100.06.09.51.76.17.36.97 3.58 Madrill Barbara 10 7.6 9.64 8.5 9.78 7.91 9.48 9.13 9.99 0 1.90 4.3.80 5.13.48 4.93 3.94 5.64 30 0.1 1.38 0.66.37 0.47 1.95 1.85 3.6 50 19.37 19.59 19.60 0.0 19.46 19.83 0.13 1.01 75 19.14 19.0 19.4 19.40 19.14 19.9 19.47 19.84 100 19.04 19.04 19.05 19.13 19.04 19.04 19.17 19.36 10 31.05 3.5 31.83 3.37 31.60 3.39 3.3 31.97 0 5.4 7.64 6.3 8.7 5.96 8.1 7.38 8.49 30.57 4.45 3.59 5.51 3.01 5.10 4.66 6.5 50 1.07 1.74 1.60.67 1.36.06.59 3.63 75 0.39 0.54 0.76 1.09 0.48 0.9 1.38.08 100 0.18 0. 0.37 0.44 0.0 0.6 0.68 1.13 E-ISSN: 4-3488 4 Volume 10, 014
Table 3: PSNR (i db) for images: Lea, Madrill, ad Barbra with oise levels: 10, 0, 30, 50, 75, ad 100 for NeighShrik, IAWDMBNC, IIDMWT ad our proposed method with decompositio level five (5) Images Noise levels Deoise Methods with decompositio level:5 NeighShrik IAWDMBNC IIDMWT Proposed 3x3 5x5 3x3 5x5 3x3 5x5 3x3 5x5 10 33.1 34.5 33.83 33.35 33.65 33.84 34.0 3.53 Lea 0 8.55 30.38 9.63 30.56 9.0 30.81 30.90 30.04 30 6.00 7.57 7.01 8.50 6.70 8.0 8.64 8.88 50 3.00 4.43 4.7 5.67 3.76 5.1 6.01 6.71 75 1..36.7 3.47 1.89.99 4.08 4.95 100 0.1 0.86 1.7.6 0.60 1.66.71 3.6 Madrill Barbara 10 7.5 9.64 8.5 9.78 7.91 8.84 9.13 9.99 0 1.89 4.3.80 5.13.48 4.93 3.94 5.64 30 0.07 1.37 0.64.36 0.45 1.95 1.85 3.6 50 19.16 19.50 19.49 0.00 19.3 19.79 0.1 1.01 75 18.71 19.00 19.05 19.36 18.8 19.17 19.43 19.84 100 18.58 18.70 18.79 19.05 18.61 18.77 19.11 19.39 10 31.05 3.5 31.83 3.37 31.60 3.39 3.3 31.97 0 5.4 7.64 6.3 8.7 5.96 8.1 7.38 8.49 30.53 4.45 3.58 5.50.99 5.10 4.66 6.5 50 0.73 1.69 1.46.66 1.17.04.58 3.63 75 19.43 0.11 0.10 0.98 19.90 0.71 1.3.09 100 18.8 19.19 19.3 0.10 19.07 19.68 0.49 1.1 (a) (b) (c) (d) (e) (f) (g) (h) (i) Fig. : Comparative performace of various deoisig methods o Lea with oise level 50 (a) Noisy image with oise level 50; Deoised image usig NeighShrik with widow size (b) 3 3, (c) 5 5; Deoised image usig IAWDMBNC with widow size (d) 3 3, (e) 5 5; Deoised image usig IIDMWT with widow size (f) 3 3, (g) 5 5; Deoised image usig Proposed method with widow size (h) 3 3, (i) 5 5 for decompositio level three (3) E-ISSN: 4-3488 5 Volume 10, 014
(a) (b) (c) (d) (e) (f) (g) (h) (i) Fig. 3: Comparative performace of various deoisig methods o Madrill with oise level 10 (a) Noisy image with oise level 10; Deoised image usig NeighShrik with widow size (b) 3 3, (c) 5 5; Deoised image usig IAWDMBNC with widow size (d) 3 3, (e) 5 5; Deoised image usig IIDMWT with widow size (f) 3 3, (g) 5 5; Deoised image usig Proposed method with widow size (h) 3 3, (i) 5 5 for decompositio level three (3) (a) E-ISSN: 4-3488 6 Volume 10, 014
(b) Fig. 4: PSNR gai vs. Noise level of the proposed, NeighShrik, IAWDMBNC, ad IIDMWT methods for Barbara image with widow size: (a) 3 3 ad (b) 5 5 for decompositio level three (3) 4 Coclusio We have proposed a adaptive image deoisig techique that succeeds i removig the oise from a image. This method is completely a data-drive that improves the visual quality of a oisy image cosiderably ad preserves the image details. Simulatio results show that our proposed method outperforms over the NeighShrik, IAWDMBNC, ad IIDMWT deoisig methods. Refereces: [1] A. Graps, A Itroductio to Wavelets, IEEE Computatioal Sciece ad Egieerig, Vol., No., 1995. [] T. Edwards, Discrete Wavelet Trasforms: Theory ad Implemetatio, Discrete Wavelet Trasforms, Staford Uiversity, 199. [3] D. L. Dooho ad I. M. Johstoe, Ideal spatial adaptatio via wavelet shrikage, Biometrika, Vol. 81, No. 3, 1994, pp. 45-455. [4] D. L. Dooho, De-Noisig by Soft Thresholdig, IEEE Trasactio Iformatio Theory, Vol. 41, No. 3, 1995, pp. 613 67. [5] D. L. Dooho ad I. M. Johstoe, Adaptig to Ukow Smoothess via Wavelet Shrikage, Joural of America Statistical Associatio, Vol. 90, No. 43, 1995, pp. 100-14. [6] T. T. Cai ad H. H. Zhou, A Data-Drive Block Thresholdig Approach To Wavelet Estimatio, Aals Statistics, Vol. 37, No., 009, pp. 569 595. [7] G. Y. Che ad T. D. Bui., Multiwavelets Deoisig Usig Neighborig Coefficiets, IEEE Sigal Processig Letters, Vol. 10, No. 7, 003, pp. 11-14. [8] G. Y. Che, T. D. Bui ad A. Krzyzak, Image Deoisig Usig Neighbourig Wavelet Coefficiets, ICASSP, 004, pp. 917-90. [9] J. Jiag, J. Guo, W. Fa, ad Q. Che, A Improved Adaptive Wavelet Deoisig Method Based o Neighborig Coefficiets (IAWDMBNC), World Cogress o E-ISSN: 4-3488 7 Volume 10, 014
Itelliget Cotrol ad Automatio, Chia, 010, pp. 894-898. [10] H. Om ad M. Biswas, A Improved Image Deoisig Method based o Wavelet Thresholdig (IIDMWT), Joural of Sigal ad Iformatio Processig (USA), Vol. 3, No. 1, 01, pp.109-116. [11] Y. Yag ad Y. Wei, Neighborig Coefficiets Preservatio for Sigal Deoisig, Circuits, Systems, ad Sigal Processig, Vol. 31, No., pp. 87-83, 01. E-ISSN: 4-3488 8 Volume 10, 014