ISSN: [Husain * et al., 6(8): August, 2017] Impact Factor: 4.116

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1 [Husain * t al., 6(8): ugust, 2017] Impact Factor: IJESRT INTERNTIONL JOURNL OF ENGINEERING SCIENCES & RESERCH TECHNOLOGY IMGE DE-NOISING USING MULTI-SCLE TRNSFORM BSED TECHNIQUE Dawar Husain *1, Upndra kumar 2 & Munnaur lam 3 *1&2 Dpartmnt of Elctronics.I.M.T LUCKNOW. 3 Dpartmnt of Elctronics INTEGRL UNIVERSITY.LUCKNOW DOI: /znodo BSTRCT This papr aims in prsnting a comparativ analysis of Multi-scal Transform (MST) basd d-noising tchniqus. MST basd imag d-noising tchniqus ovrcom th limitation of Fourir transform and spatial basd d-nosing tchniqus, as it provids th local information of non stationary imag in a mor comprhnsiv mannr. Th MST tchniqus, namly, Discrt Wavlt Transform (DWT), Stationary Wavlt Transform (SWT) and Contour-lt Transform (CT) hav bn slctd for th d-nosing of standard and mdical imags. Furthr, th comparison of prformanc of diffrnt imag d-noising tchniqu has bn carrid out in trms of diffrnt nois variancs, subjctiv and quantitativ masurs. nalysis of rsult shows that CT tchniqu outprforms SWT and DWT tchniqus in trms of both qualitativly and quantitativly. KEYWORDS: Spatial-scal, SWT, CT. I. INTRODUCTION Ovr th yars, digital imags play an indispnsabl rol both in daily lif applications such as, satllit tlvision, computr tomography, gographical information systms and astronomy. Imags acquird by imag snsors ar gnrally contaminatd by nois. Thr ar various factors rsponsibl for affcting th quality of imags such as, imprfct instrumnts, problms with th data acquisition procss, and intrfring natural phnomna. Thus, d-noising is oftn an indispnsabl stp to b takn bfor th imags data is analyzd. This can b achivd by applying an fficint d-noising tchniqu to compnsat for such data corruption [1-2]. nalysis of non-stationary imag corruptd with nois, is a challnging job, as thir proprtis chang with tim. Such 2D-signals cannot b analyzd wll by pur spatial and frquncy domain rprsntations. Th joint spatial-scal domain has bn provn to b a ffctiv tool for analyzing and dtction of spatial-frquncy charactristics of non-stationary imags in a mor dscriptiv mannr. Spatial-scal domain-basd imag analysis mthods such as, Non Sub-sampld Contourlt Transform(SWT)ovrcom th shortcomings of th traditional Fourir-basd mthods and Contourlt Transform (CT). Howvr, it is found that CT suffrs with th problm of shift invarianc du to aliasing btwn sub-bands. Thus, to rsolv th limitation of CT, SWT has bn introducd [10-13]. SWT is th multi-dirction and shift-invariant tchniqu which is dsirabl in imag analysis applications, such as, dg dtction, contour charactrization and imag d-nosing Thus, in this study, th comparison of prformanc of SWT and CT in trms of diffrnt nois variancs, subjctiv and objctiv prformancs, is th cntral thm of this articl II. IMGE DE-NOISING TECHNIQUES Bfor discussing th imag d-noising tchniqus, first of all, it would b appropriat to discuss in gnral diffrnt typs of noiss, such as Poisson nois, Spckl nois, Gaussian nois, Salt and Pppr nois. Hr, in this study, Salt & Pppr and Gaussian noiss hav bn slctd for analysis and implmntation purpos. Salt & pppr Nois also known as intnsity spiks, ariss du to rrors in data transmission and impairmnts of pixl lmnts in th camra snsors, timing rrors in th digitization procss, or faulty mmory locations, whil Gaussian nois ariss du to amplifirs or dtctors and is uniformly distributd ovr th signal. Furthr, imag d-nosing tchniqus ar broadly classifid into Spatial and Transform domain filtring tchniqus. Hr, in this study, mphasis has bn givn to transform domain filtring, as it is mor suitabl for [28]

2 [Husain * t al., 6(8): ugust, 2017] Impact Factor: information rprsntation, intrprtation and analysis. Multi-scal Transform basd d-nosing tchniqus, such as SWT and CT has bn slctd for th implmntation purposs. Th dtaild dscription of CT and SWT basd d-noising tchniqus ar outlind blow: Imag D-nosing by Contourlt Transform (CT) To ovrcom th shortcomings of wavlts and curvlts, [10] rcntly pionrd a nw systm of imag rprsntations namd contourlts. Contourlt is a "tru" two dimnsional transform that can captur th intrinsic gomtrical structurs information of imags, as wll as, provids flxibl numbr of dirctions. In othr words, CT is drivn basd on curvlt concpts [12]. Th Contourlt Transform (CT) proposd by [10] is a ral two-dimnsional transform, which is basd on nonsparabl filtr banks and provids an fficint dirctional multi-rsolution imag rprsntation. Th Contourlt Transform is also known as Pyramidal Dirctional Filtr Bank (PDFB). Implmntation of th CT is achivd via two major stps: Th Laplacian Pyramid (LP) is first usd to captur th point discontinuitis (Starck t al., 1998), and thn followd by a Dirctional Filtr Bank (DFB) to link point discontinuitis into linar structurs. Th procdur for th d-noising of imags by DWT has bn xplaind in th sction 2.2. Imag D-nosing by Stationary Wavlt Transform (SWT) In ordr to rduc th frquncy aliasing of contourlts, nhanc dirctional slctivity and shift-invarianc, [11] proposd Non Sub-sampld Contourlt Transform. This is basd on th Non Sub-sampld Pyramid Filtr Banks (NSPFB) and th Non Sub-sampld Dirctional Filtr Banks (NSDFB) structur. Th formr provids multiscal dcomposition using two channl non sub-sampld 2-D filtr banks, whil th latr provids dirctional dcomposition i.. it is usd to split band pass sub-bands in ach scal into diffrnt dirctions [9-12]. s a rsult, SWT is shift-invariant and lads to hav bttr frquncy slctivity and rgularity than CT. Th schm of SWT structur is shown in Fig. 1(a). Th SWT structur classify 2-Dimnsional frquncy domain into wdg-shapd dirctional sub-band as shown in Fig. 1(b) Th gnral mthodology adoptd for th d-noising of imags using CT and SWT tchniqus can b summarizd as follows (Figur. 2): Dcompos th noisy imag into a contourlt domain.pply a spcific thrsholding rul to th cofficints in contourlt domainth d-noisd cofficints ar subjct to an invrs Contourlt Transform to construct th d-noisd imag. III. EVLUTION CRITERI It is obvious that thr is slight variation among d-noisd rsults. Thrfor, in ordr to assss th quality of th d-noisd imag othr than simpl visual inspction of th imags, som quantitativ assssmnt critria hav bn dfind. Th quantitativ indicators which hav bn usd for this purpos ar Pak Signal-to-Nois Ratio (PSNR), Root Man Squar Error (RMSE) [14-1] ar outlind blow. RMSE Th RMSE is th most valuabl prformanc valuation critrion whn original imag is prsnt. RMSE is a good masur of accuracy [14]. M N RMSE = (F(i, j) R o (i, j))2 (4) M N i=1 j=1 whr, M, N indicat th siz of th imag is M N. F(i, j), R o (i, j) indicat th gray valu of th pixl which is in th row i and in th column j of th imag. With smallr RMSE, thr is lss diffrnc btwn thm. PSNR Th PSNR indicator masur th distortion of th d-noisd imag compard with th rfrnc imag. For lss amount of imag distortion, th valu of PSNR should b larg [1]. PSNR = 10log ( 2 2 RMSE ) () [29]

3 [Husain * t al., 6(8): ugust, 2017] Impact Factor: IV. EVLUTION OF RESULTS ND DISCUSSION Th analysis of rsults of various imag d-noising tchniqus blonging to multi-scal transform basd domain, has bn carrid out using standard imags. In ordr to analyz th prformanc and capability of th d-noising tchniqus usd in this study, it is, ncssary to prform th assssmnt of accuracy and rviw th rsults. Furthr, a thorough analysis of th prformanc of th imag d-noising tchniqus has bn carrid out for datast, both visually and quantitativly. Visual (Qualitativ) nalysis Th visual comparison of th d-noisd imags is carrid out for th subjctiv (qualitativ) assssmnt, sinc, it is a simpl, yt on of th ffctiv mthod for assssing advantags and disadvantags of any d-noising tchniqu. Hr, in this study for th simulation purpos, imag of siz has bn takn. Th dnoisd imags ar visually valuatd in trms of diffrnt paramtrs as listd blow: Shap of th objct (SO) Colour Radiomtry (CR), Edg Sharpning(ES) [30]

4 [Husain * t al., 6(8): ugust, 2017] Impact Factor: a) nalysis of Boat Imag Corruptd with Gaussian Nois for diffrnt nois variancs It is obsrvd that th spatial information of all th d-noisd imags has improvd whn compard to th noisy imag indicating that th small faturs that wr not noticabl in th noisy imag ar now b distinguishabl and idntifiabl. Fig. 3 shows th d-noisd imags gnratd by diffrnt d-nosing tchniqus for datast DS corruptd with Gaussian nois, for diffrnt nois variancs Figur 2 Mthodology adoptd for imag d-noising by CT and SWT tchniqus With rfrnc to Fig. 3, it is obsrvd that th d-noisd imags gnratd by SWT tchniqu (Fig. 3 (d), () & (f)), for diffrnt nois variancs xhibit good gomtric dtails, whn compard to th original imag. This is followd by CT (Fig. 3(a), (b) & (c) tchniqu. Howvr, th intnsity of colour in th d-noisd imags gnratd by SWT is slightly lightr, whn compard to th original imag, followd by CT basd d-noising tchniqus. Furthr, th d-noisd imag gnratd by CT tchniqu yilds lowr spatial quality, whn compard to SWT basd d-nosing tchniqu. This is du to th sub-sampling procss involvd in CT tchniqu, lading to th introduction of artifacts such as, xistnc of squar blocks, making th linar faturs zigzag in th imag, whn imags ar zoomd in to s vry small objcts. b) nalysis of Boat Imag corruptd with Salt & Pppr Nois for diffrnt nois variancs With rfrnc to Fig. 4, it is obsrvd that th d-noisd imags gnratd by SWT (Fig. 4(d), () & (f)), and CT (Fig. 4(a), (b) & (c)), tchniqus xhibit good gomtric dtails, whn compard to th original imag. Howvr, th intnsity of colour in th d-noisd imags gnratd by SWT tchniqu ar slightly lightr, whn compard to th original imag, followd by CT basd d-noising tchniqu. Howvr, th d-noisd imag gnratd by CT tchniqu yilds lowr spatial quality. This may b du to th limitd dirctional slctivity i.. horizontal, vrtical and diagonal dirctions possss by th tchniqu, Which in turn dtriorat th gomtry of th faturs in th d-noisd imags. Th comparison rsults of diffrnt d-nosing tchniqus on th basis of visual objct dtction ar listd in Tabl 2. Fig. 3 D-noisd imags gnratd by diffrnt d-nosing tchniqus for DS corruptd with Gaussian nois. Fig. 4 D-noisd imags gnratd by diffrnt d-nosing tchniqus for DS corruptd with Salt & Pppr nois. Tabl 2 Comparison of d-noising tchniqus on th basis of visual objct dtction [31]

5 [Husain * t al., 6(8): ugust, 2017] Impact Factor: D-noising Tchniqu D at as t D S Typ of Nois GUS SIN SLT & PEPPE R Noi s Var ian c C ol ou r SWT S h a p E d g Co lo ur CT Sh ap E d g G G G G Tabl 2 shows that SWT basd d-nosing tchniqu yilds th highst prformanc for diffrnt typs of noiss of diffrnt variancs, whn compard to CT basd d-nosing tchniqu. In othr words, th background of th d-noisd imags with SWT appars smoothr and rmovs th nois prtty wll in th smooth rgions, as wll as, along th dgs. Thus, visually, it can b infrrd that SWT d-nosing tchniqu for diffrnt nois variancs works wll and yilds th bttr prformanc in trms of prsrvation of spctral, spatial and structural similarity information, followd by CT basd d-nosing tchniqu. Quantitativ nalysis Th analysis and invstigation of rsults obtaind from diffrnt d-noising tchniqus hav bn carrid out using quantitativ indicators, as mntiond in th Tabl 3. It is obsrvd that all typs of noiss causs dgradation in th imag quality which in turn rsults in loss of information. Th d-noising of dgradd imag is prformd using SWT and CT tchniqus. Th d-noisd imag which will bst prsrv th spctral, spatial and structural similarity information of th original imag is th on that has satisfid th following conditions (Tabl 3). Basd on ths paramtrs, th prformanc and accuracy of th d-noising tchniqus will b carrid out. Tabl 3 Th idal and rror valu of diffrnt quantitativ indicators S. No. 1 2 Mtric Root Man Squar Error (RMSE) Pak Signal-to-Nois Ratio (PSNR) Idal Valu Error Valu 0 > 0 N > 1 nalysis basd on RMSE Gnrally, smallr RMSE valu rprsnts a gratr accuracy masur in trms of imag fidlity. Th rsults of RMSE gnratd by diffrnt imag d-nosing tchniqus for diffrnt datasts ar tabulatd in Tabl 4. Tabl 4 show th comparison of RMSE for Boat imag for various nois variancs. Tabl 4 Comparison of RMSE for Boat Imags corruptd with Gaussian and Salt & Pppr at diffrnt nois variancs. a) of DS-I datast With rfrnc [32]

6 [Husain * t al., 6(8): ugust, 2017] Impact Factor: Datast RMSE Typ of Nois D-noising Mtric Nois Varianc Tchniqus CT SWT GUSSIN DS SLT & PEPPER a) nalysis of DS-I datast nalysis of rsult shows that th Gaussian and Salt & Pppr nois affctd imags ar ffctivly d-noisd with SWT basd d-nosing tchniqu, as indicatd by low RMSE valu, whn compard to CT basd d-nosing tchniqu. mongst d-nosing tchniqus, CT basd d-nosing tchniqu xhibits low prformanc in trms of RMSE mtric. This is du to th sub-sampling procss involvd in CT tchniqu, lading to th introduction of artifacts such as, xistnc of squar blocks, making th linar faturs zigzag in th imag. Thus, it can b concludd that SWT basd d-nosing tchniqu yilds th highst prformanc in trms of prsrvation of dg information, whn compard to CT d-nosing tchniqu. In othr words, SWT tchniqu is suitabl for dnosing of imags corruptd with Gaussian and Salt & Pppr nois, whn compard to CT basd d-nosing tchniqu. Th RMSE valus corrsponding to diffrnt d-noising tchniqus has bn plottd for DS, as shown in Fig.. nalysis basd on PSNR Gnrally, highr valus of PSNR rflct lss amount of imag distortion. Th analysis of PSNR valus for diffrnt d-nosing tchniqus ar tabulatd in Tabl 6. Tabl 6 Comparison of PSNR for Boat Imags corruptd with Gaussian, Salt & Pppr Nois for diffrnt nois variancs PSNR Mtric Typ of Nois Datast D-noising Nois Varianc CT Tchniqus SWT DS GUSSIN SLT & PEPPER nalysis to Tabl 6, a high valu for PSNR is obsrvd for SWT basd d-noising tchniqu. In othr words, SWT tchniqu producs good quality d-noisd imag with high PSNR valus in comparison to CT basd dnosing tchniqu. Furthr, th d-noisd imag gnratd by CT tchniqu yilds low valus of PSNR, amongst th tchniqus. This may b du to th sub-sampling procss associatd with th CT tchniqu, lading to th introduction of artifacts in th rsulting d-noisd imag. Th diffrnt d-nosing tchniqus outputs corrsponding to PSNR valus ar shown for Boat imags in Fig 6. visual intrprtation of PSNR valus (Fig. 6) suggsts that SWT basd d-nosing tchniqu using yilds th highst prformanc in trms of prsrvation of spctral, spatial and structural similarity information, whn compard to CT basd d-nosing tchniqus. Thus, it can b concludd that SWT tchniqu is bst in prsrving th structural similarity, spatial and spctral information, whn compard to CT basd d-nosing tchniqu. In othr words, SWT basd d-nosing tchniqu mrgd as on of th most ffctiv d-nosing tchniqu, followd by CT basd d-nosing tchniqu. [33]

7 [Husain * t al., 6(8): ugust, 2017] Impact Factor: V. CONCLUSION In this study, a comparativ assssmnt of spatial-scal domain basd d-noising tchniqus, has bn carrid out in trms of quantitativ and qualitativ masurs. Th imag is corruptd with Gaussian and Salt & pppr noiss for diffrnt nois variancs. Th rsult shows that d-noising of imags by SWT tchniqu provids th good rsult in trms of qualitativly and quantitativly paramtrs. Furthr, SWT tchniqu xhibits good prformanc in trms of PSNR and RMSE. This may b du to th rason that SWT tchniqu possss shiftinvariant proprty, which avoids th introduction of artifacts in th rsulting imag. Thus, it can b ascrtaind from this study that analysis and d-nosing of non-stationary imag can b analyzd ffctivly by using shift-invariant SWT tchniqu, whn compard to shift-varianc CT tchniqu. Th outcom of this study could thrfor b utilizd for furthr imag procssing tasks VI. REFERENCES [1] S. G. Mallat and W. L. Hwang, Singularity dtction and procssing with wavlts, IEEE Trans. Inform. Thory, 38, [2] D. L. Donoho, D-noising by soft-thrsholding, IEEE Trans. Information Thory, 41(3), [3] R. Coifman and D. Donoho, 199. Translation invariant d-noising," in Lctur Nots in Statistics: Wavlts and Statistics, vol. Nw York: Springr-Vrlag, [4] R. Yang, L. Yin, M. Gabbouj, J. stola, and Y. Nuvo, 199. Optimal wightd mdian filtrs undr structural constraints, IEEE Trans. Signal Procssing, 43, [].K. Jain, Fundamntals of digital imag procssing. Prntic-Hall,1989 [6] T. D. Bui and G. Y. Chn, Translation-invariant D-noising using multi-wavlts", IEEE Transactions on Signal Procssing, 46 (12), [7] J. Lu, J. B. Wavr, D.M. Haly, and Y. Xu, Nois rduction with multiscal dg rprsntation and prcptual critria, in Proc. IEEE-SP Int. Symp. Tim- Frquncy and Tim-Scal nalysis, Victoria, BC, 8. [8] P. Moulin and J. Liu, nalysis of multi-rsolution imag D-noising schms using gnralizd Gaussian and complxity priors, IEEE Information Thory, 4(3), [9] Bambrgr, R. H., & Smith, M. J. T., filtr bank for th dirctional dcomposition of imags: Thory and dsign. IEEE Transaction Signal Procssing, 40(4), [10] Do, M.N. and Vttrli, M., 200. Th contourlt transform: an fficint dirctional a multi-rsolution imag rprsntation. IEEE Transactions on Imag Procssing, 14(12), [11] Cunha,.L., Zhou, J. and Do, M.N., 200. Non sub sampld Contourlt Transform: Filtr Dsign and pplications in D-noising. In IEEE Intrnational Confrnc on Imag Procssing, 1, pp [12] Cunha,.L., Zhou, J. and Do, M.N., Th Non Sub- sampld Contourlt Transform: Thory, Dsign and pplications. IEEE Transactions on Imag Procssing, 1(10), [13] Ji, L. and Gallo, K., n grmnt Cofficint for Imag Comparison. Photogrammtry Enginring and Rmot Snsing Journal, 72(7), [14] Li, S., Li, Z. and Gong, J., Multi-variat statistical analysis of masurs for assssing th quality of imag fusion. Intrnational Journal of Imag and Data Fusion, 1(1), [1] K. Sasirkha; K. Thangavl, novl wavlt basd thrsholding for dnoising fingrprint imag [16] Intrnational Confrnc on Elctronics, Communication and Computational Enginring (ICECCE), [17] ravind B. N; Sursh K. V;201. n improvd imag dnoising using wavlt transform [18] Intrnational Confrnc on Trnds in utomation,communications and Computing Tchnology (I- TCT-1) pp1 - [19] Li, S., Yang, B. and Hu, J., Prformanc comparison of diffrnt multi-rsolution transforms for imag fusion. Information Fusion, 12(2), CITE N RTICLE Husain, Dawar, Upndra Kumar, and Munnaur lam. "IMGE DE-NOISING USING MULTI-SCLE TRNSFORM BSED TECHNIQUE." INTERNTIONL JOURNL OF ENGINEERING SCIENCES & RESERCH TECHNOLOGY 6.8 (2017): Wb. ug [34]