Adaptive Pixel Interpolation for Spatial Error Concealment

Transcription

1 J Sign Proess Syst (2010) 60: DOI /s y Aptive Pixel Interpoltion for Sptil Error Conelment Li Song & Xin M Reeive: 9 Novemer 2008 / Revise: 23 Mrh 2009 /Aepte: 30 Mrh 2009 /Pulishe online: 27 My 2009 # 2009 Springer Siene + Business Mei, LLC. Mnufture in The Unite Sttes Astrt Error onelment tehniques re wiely use s effiient wys to reover the lost informtion t the eoer. This pper proposes n ptive pixel interpoltion tehnique for sptil error onelment in the lok se oing system. For missing pixel in orrupte lok, its vlue is erive from four neighorhoos of the lok through interpoltion using multiple preition strtegy. The weighting rules of these four neighorhoo loks re refully esigne with regr to three ftors, the istne to the missing pixels within the given orrupte lok, the perentge of unorrupte pixels, n the similrity to the given orrupte lok. The propose metho works effetively in onseutive lok loss sitution, whih is ommon in rel pplitions of vieo trnsmission. Experimentl results show the propose tehnique gins more urte reovery of the missing pixels thn the existing shemes. Keywors Error onelment. Blok se oing. Pixel interpoltion 1 Introution Nowys, the lok-se vieo n imge ompression stnrs, suh s MPEG-2, H.264 n JPEG, re wiely use throughout the worl. However, the high ompression L. Song (*) : X. M Institute of Imge Communition n Informtion Proessing, Shng Key Lortory of Digitl Mei Proessing n Trnsmission, University of Shnghi Jio Tong University, Shnghi , Chin e-mil: song_li@sjtu.eu.n X. M e-mil: milnloo@hotmil.om effiieny might inrese the vulnerility to the trnsmission errors when multimei ontents re trnsporte over error prone hnnels. In the pst ee, reserhers hve propose three kins of methos to ensure the qulity of the trnsmitte vieo, i.e., error resiliene in enoer, error ontrol in hnnel n error onelment in reeiver [1]. In this pper, we fous on the lst metho whih n reover the orrupte t sptilly n/or temporlly n thus hieve oth goo ojetive n sujetive qulity t reeiver sie. So fr mny sptil error onelment methos hve een propose. To reover the missing pixel vlues n rete imges with goo visul qulity, the sptil error onelment tehnique exploits the orreltion etween the orrupte loks n their jent res. Missing mroloks n e reonstrute using simple iliner interpoltion (BI) from four pixels in surrouning mrolok [2], omplex iretionl interpoltion tehniques [3 5], n the DCT oeffiients interpoltion from the neighoring mro loks [6, 7]. More reently, some results emonstrte the improvements on the iretionl interpoltion methos [8 11], whih use ege piring methos suh s the vergepoints tehnique [9] n the Hough trnsform, to estimte the pixel pirs whih hve the similr ege informtion roun the orrupte res. These pixel pirs re then use to reover the missing ege informtion in the orrupte res. From sttistil point of view, nother populr pproh is vne se on mximum posteriori (MAP) tehniques. The est neighor mthing (BNM) metho propose in [12] mkes use of speil kin of prior informtion-lokwise similrity within the imge to reonstrut the lost loks. In ontrst, the metho propose in [13] employs pixelwise moels to hrterize the orreltion mong imge pixels y using the orienttion ptive interpoltion. Besies, the non uniform rtionl B-

2 292 J Sign Proess Syst (2010) 60: spline (NURBS) interpoltion [14], n lok mthing interpoltion [15] re employe for onseutive lok loss pttern. Other pprohes re lso ville, inluing ontent or moel ptive onelment metho [16, 17], projetion-onto-onvex-set (POCS) [18] n nonliner ptter lignment [19]. Mny methos mentione ove hieve goo onelment results in the se of isolte lok loss pttern, nevertheless they work ineffetively in onseutive lok loss sitution. Inee, it is more ommon to pketize severl onseutive loks into one single pket for most vieo n imge trnsmission pplitions. In this pper, we improve the existing BNM metho y esigning n ptive pixel interpoltion tehnique. Our min ontriutions re three-fol: 1) The missing lok is reovere in pixel-y-pixel mnner; 2) Weighting rules re well-esigne to hieve promising reonstrution of eh pixel; 3) A priority-se oneling orer is resse to gretly llevite the error-propgtion prolem. Experimentl results show our metho hieves superior performne in omprison with severl stte-of-the-rt methos. The rest of this pper is orgnize s follows. Setion 2 provies rief review of the BNM metho. The etile esription of the ptive pixel interpoltion proessing n lso e foun. Setion 3 presents extensive experiment results. Finlly, onluing remrks re given in Setion 4. 2 Aptive Pixel Interpoltion 2.1 Overview of the BNM Metho The BNM metho propose in [12] mkes use of lokwise similrity within the imge to reonstrut the lost loks. It Figure 2 Illustrtion for templte mthing. tkes surrouning neighorhoo of the lost lok s templte n performs templte mthing within given serhing rnge, s shown in Fig. 1. The est nite lok is the one whose neighorhoo most losely resemles the templte of the trget lost lok. The men squre error (MSE) or sum of solute ifferenes (SAD) etween the orresponing neighorhoo pixels is use s the mthing mesure of two loks. The lost lok is reovere using the pixel vlues opie or trnsforme from the orresponing prt of the est nite lok. The BNM metho n perform well in the plin res without omplex eges n textures. However, its ury in omplex res is limite s it oes not tke some importnt ftors into onsiertion, suh s intensity vritions of pixels withine the templte n ontext informtion of eh missing pixel. In the next susetions, we will inite how we perform ptive preitions for eh missing pixel in lost lok y seleting ifferent neighorhoo of the trget lok s the mthing templte. 2.2 Pixel-Wise Preition Through Templte Mthing of Different Neighorhoos Figure 1 The reovery of lost lok in BNM metho. Let p(x,y) n (x,y) represent the pixel vlue n inry sttus t position (x, y) in the imge, respetively. The inry sttus of eh pixel inites whether it is vli, i.e., (x,y)=1 mens (x,y) is originlly goo or hs een onele, n (x,y)=0 mens it is orrupte ut hs not een onele so fr.

3 J Sign Proess Syst (2010) 60: Figure 3 Preition for ifferent missing pixels A n B y top neighorhoo mthing. Lost Blok Lost Blok Suppose tht the lost lok (MxM) hs four neighor regions ville, whih re enote s R L,R R,R T, n R B (Left, Right, Top, n Bottom) n form templte sets {R X : X = L, R, T, B}. In our metho, four nite preition vlues for eh missing pixel will e otine y performing templte mthing for eh neighor region. The preition for missing pixel p involves the following two steps. First, the est nite region R X is etermine within serhing rnge (enote y W) in the imge y using templte mthing. The men solute ifferenes (MAD) etween R X n the trget region with the sme size re use s the riterion to evlute the mthing result. Seon, the orresponing pixel p, whose reltive position to the R is equl to the reltive position of p to R X, oul e set s the preition for p erive from neighor region R X. In orer to improve the ury of preition p, three onstrints re impose s elow: 1) eh pixel in the est nite region R X shoul e vli; 2) p must e vli; 3) p must e pixel outsie urrent lok eing onele, euse we voi to reover the missing pixel from onele pixel in the sme orrupte lok for preventing the possile error propgtion. These onstrints introue some moifitions to the onventionl region mthing metho. As shown in Fig. 2, rel sttisti vlues vlues from similrity ftor funtion Similrity ftor MMAD vlue Figure 4 Similrity ftor from the rel sttisti results n those estimte y formultion with the T s =20. Figure 5 The selete pixels n the iretion long whih the priority of eh lost MB is lulte.

4 294 J Sign Proess Syst (2010) 60: Tle 1 Influene of the prmeter of sttus ftor. T Len Pepper Zel we enote (x,y) s the position of the upper-left pixel in R X (X=Tin Fig. 2), (k,l) s the reltive position offset etween the nite region R X n R X, n (i,j) s pixel s reltive position to the upper-left pixel in the region. M n N re with n height of the missing lok, respetively. Then the first onstrint n e esrie s ¼ xþ ð k þ i; y þ l þ jþ ¼ 1j8ði; jþ 2 R X ð1þ n the other two onstrints n form nother set: 4 2 ¼ fmþ ð k; n þ l ¼ 1jðk; lþ 2 Wg ð2þ Bse on the ove nlysis, the templte mthing for eh pixel p(m,n) n e formulte s follows. ðk; lþ ¼ rg min MADðR X ; k; lþ ð3þ MAD¼ 1 MN R X XM 1 X N 1 i¼0 j¼0 j pxþi; ð yþj ði; jþ ; nðk; lþ Þ pxþiþk; ð yþjþlþj ð4þ Figure 3 gives n illustrtion of the erivtion proess isusse ove, where preitions for two speifi pixels re etermine uring templte mthing of top neighorhoo. Aoring to the onstrints impose on the templte mthing, ifferent pixels woul e ssigne with ifferent est mthing regions though the sme neighor type is selete, s epite in Fig. 3. In sufigure 3 (), the pixel enote y A hs vli orresponing pixel A 1, while the orresponene B 1 of pixel B is not vli in this se. However, pixel B n get vli preition B 2, ut pixel A fils to get preition A 2, s shown in Fig. 3(). Until now, we otin four preitions for eh missing pixel p (m,n) y using four templtes with ifferent orienttion. In the next susetion, we will isuss how to estlish ptive weighting sheme for reonstrution of p. 2.3 Reover Missing Pixel In the preition proess s mentione in the previous susetion, three mjor ftors re eqully importnt for finl reonstrution of missing pixel, one four preitions re hieve from eh neighorhoo R X (X=L,R,TorB): 1) Distne ftor: the istne etween the missing pixel p n the region templte R X. 2) Similrity ftor: the miniml MAD (MMAD) lulte y templte mthing to fin the preition vlue for p. 3) Sttus ftor: the sttus of the region, ll pixels re either originlly goo or lrey reovere. Here we further give the etile explntion of these ftors Distne Ftor Mny interpoltion-se sptil EC methos, suh s those in [3 5], show tht the loser Tle 2 PSNR (B) omprison in isolte error sitution. Imge BI [2] BNM [12] Wng s [6] Sun s [18] Prk s [14] Go s [9] Sirikm s [10] ours Len Pepper Zel Foremn Tle 3 PSNR (B) omprison in onseutive error sitution. Imge BI [2] BNM [12] Wng s [6] Sun s [18] Prk s [14] Hsi s [15] Go s [9] Sirikm s [10] Ghrvi s [11] ours Len Pepper Zel Foremn

5 J Sign Proess Syst (2010) 60: Figure 6 Comprison etween BI, BNM n the propose metho for Len in isolte error sitution, () the error imge () the BI s result () the Figure 7 omprison etween BI, BNM n the propose metho for Pepper in isolte error sitution, () the error imge () the BI s result () the

6 296 J Sign Proess Syst (2010) 60: neighor region is to missing pixel p, the more ontriution it mkes towrs the reonstrution of p. Let represent the istne etween the pixel p n the speifi neighor region R X, then we opt the simple iliner interpoltion ie to set the istne ftor f : f ðr X ; m; nþ ¼M þ 1 ðm; nþ ð5þ Similrity Ftor The similrity etween the templte region n its est mth is expete to e lose to the one etween the preition n the missing pixel. Thus the MMAD vlue n e use to mesure the qulity of the ultimte reovery results. Generlly speking, preition otine with smller MMAD vlue shoul ontriute more to the reonstrution of missing pixel. In orer to quntittively evlute the effet of MMAD on reonstrution of the missing pixel p, we perform extensive experiments to ount the proportion of the orret (extly the sme s the originl ones in imge) preitions mong ll the preitions hving the sme MMAD vlue. The vlues of MMAD re normlize y the mximum vlue to hve the rnge [0, 1]. To only regr the effet of MMAD, the istne ftor n the sttus ftor re kept fixe uring the tests. Finlly, the similrity ftor is formulte s truntion funtion of the normlize MMAD urves s elow: 8 1=2; >< NMAD 1 T f s ðr X ; m; nþ ¼ s NMAD < Ts ð6þ >: 0 ; otherwise where prmeter T s is etermine empirilly. Figure 4 shows the vlues estimte y (6) in the se of =1, the rel ifferene vlues etween the preition n the missing pixel is lso provie for omprison purpose. It n e foun tht Eq.(6) well represents the proximity of the reonstrution to the missing pixel. Sttus Ftor The neighorhoo with ifferent vli sttus shoul hve ifferent impts on the pixel in missing lok. A preition otine from n unorrupte neighorhoo shoul mke ominnt ontriution to the reovery of the missing pixel. In ontrst, the preition generte y onele region shoul ount for little. Aoringly we set the sttus ftor f s elow: f ðr X ; m; nþ ¼ 8 < 1; goo region : 1=T ; onele region where T is preefine onstnt. ð7þ Figure 8 omprison etween BI, BNM n the propose metho for Zel in isolte error sitution, () the error imge () the BI s result () the

7 J Sign Proess Syst (2010) 60: Figure 9 omprison etween BI, BNM n the propose metho for Foremn in isolte error sitution, () the error imge () the BI s result () the Now, we n integrte the ovementione three ftors into weight funtion of the preitions in the ontext of ifferent neighorhoos for p. Let w(r X,m,n) enote the weight vlue of the preition p(r X,m,n) from neighor region R X, then we hve wr ð X ; m; n Þ ¼ f ðr X ; m; nþf s ðr X ; m; nþf ðr X ; m; nþ ð8þ n the reonstrute vlue of the missing pixel p(m,n) is: r 1 ðm; nþ ¼ X X ¼L:R;T;B wr ð X ; m; nþpr ð X ; m; nþ! þ 1 X wr ð X ; m; nþ Pm; ð nþ ð9þ X ¼L:R;T; B where r 1 (m, n) represents the reovery vlue for pixel p(m,n). pm; ð nþ is the verge vlue of the ville pixels in 3x3 sliing winow entere t pixel p, whih is introue to llevite the ill effets of the outliers mong the preitions. As reviewe in setion 2.1, BNM nnot hieve goo results in the omplex re in n imge, ut it works well in the plin re. Therefore, we further integrte the norml BNM results into the propose metho to improve its performne in the plin re in n imge. Speifilly, the reovery proeure is expne s follows: 1) Fining the est mthing lok of the orrupte lok through templte mthing y the BNM metho. As shown in Fig. 1, neighorhoo B is use s templte. 2) Clulting the intensity vrition of the pixels within templte B. 3) Otining the ultimte reovery vlue r(m,n) s: rm; ð n Þ ¼ r 1ðm; nþs þ r 2 ðm; nþt s f s ðb; m; nþ s þ T s f s ðb; m; nþ ð10þ where r 1 (m,n) is the reovery vlue previously otine, n r 2 (m,n) is the reovery vlue for p otine y the BNM. f s (B,m,n) is the similrity ftor isusse efore with the MMAD etween the region lok B n its est mth. T σ is the prmeter to just the BNM s ontriution to the finl results. 2.4 Conseutive Blok Loss Sitution In the previous isussion, we ssume tht the four neighor regions of orrupte lok re ll ville, whih n e lle the isolte lok loss. But in prtie, loks re

8 298 J Sign Proess Syst (2010) 60: Figure 10 omprison etween BI, BNM n the propose metho for Len in onseutive error sitution, () the error imge () the BI s result () the Figure 11 omprison etween BI, BNM n the propose metho for Pepper in onseutive error sitution, () the error imge () the BI s result () the

9 J Sign Proess Syst (2010) 60: Figure 12 omprison etween BI, BNM n the propose metho for Zel in onseutive error sitution, () the error imge () the BI s result () the Figure 13 omprison etween BI, BNM n the propose metho for Foremn in onseutive error sitution, () the error imge () the BI s result () the

10 300 J Sign Proess Syst (2010) 60: Tle 4 PSNR (B) omprison in rnom error sitution for Len. Error Pttern BI[2] BNM[12] ours 5% % % orrupte onseutively more often. In this sitution, sine some neighoring regions of missing lok my e unville, we n only use ville neighorhoos to reover the lost informtion. Then we moify Eq. (9) to: r 1 ðm; nþ ¼ X R X RV þ wr ð X ; m; n 1 X R X RV ÞPR ð X ; m; nþ wr ð X ; m; nþ! Pm; ð nþ ð11þ where RV is the vli neighorhoo set. Another prolem to e solve in this sitution is the onele orer of the lost loks. In [8], the uthor resses this prolem in the ontext of imge inpinting n inites tht ifferent reovery orer woul result in quite ifferent results. The missing pixels towrs whih there re more geometri isophote flowing n more vli neighor pixels shoul e inpinte firstly. The isophote flow is efine s the ege informtion in the imge with the iretion perpeniulr to the whole ounry rossing through the missing pixel. Here we re motivte to exploit priority onstrint to reover given orrupte lok, where two ftors re onsiere: 1) the volume size of isophote flowing towrs the lok; 2) the ville neighor informtion roun the lok. In orer to lulte the isophote of lost lok in imge, we estlish set W p ompose of ville neighor pixels, whose istne to the nerest ounry of the lok is one pixel wie, s shown in Fig. 5. Then the isophote strength of the MB n e ompute s elow: I s ¼ mxðege strengthði; jþþ; ði; jþ 2 4 p ð12þ Where ege strengthði; jþis lulte y Soel opertor (13) long the iretion perpeniulr to the lok s ounry nerest to the pixel t (i,j), s illustrte in Fig sole x A; sole y A ð13þ The vilility of neighor informtion (enote s CR x ) roun the lost lok oul e onfirme y the pixel sttus. Figure 14 omprison etween BI, BNM n the propose metho for Len in 10% rnom error sitution, () the error imge () the BI s result () the

11 J Sign Proess Syst (2010) 60: Figure 15 omprison etween BI, BNM n the propose metho for Len in 20% rnom error sitution, () the error imge () the BI s result () the Hene, we estimte the onfiene i; ð jþ of these informtion pixel y pixel. The umultion of the onfiene is use to set the priority vlue PR x of eh neighor: 8 < i; ð jþ ¼ : 0; ði; jþ is lost 1; ði; jþ is goo 1=T ; ði; jþ is onele CR x ¼ X ði;jþr x ði; jþ PR x ¼ I s CR x ð14þ ð15þ ð16þ The lok with the highest priority vlue is selete to onel urrent missing lok. It shoul e notie tht the priority vlues of the remining missing loks shoul e upte fter finishing oneling the selete one. 3 Experimentl Results Stte-of-the-rt sptil error onelment methos [2, 6, 9 12, 14, 15, 18] re provie for omprison purpose, mong whih two methos re esigne speilly for the onseutive lok loss sitution n hieve etter results. Themethoproposein[6] is performe in DCT omin. The methos isusse in [14] n[18] respetively use NUBRS n POCS tehnique. The pprohes in [9 11] fous on improving interpoltion methos. Exept the experimentl results re offere se on our implementtion sttion, ll the results re ite from the originl ppers. We hoose severl stnr imges, inluing Len, Pepper, n Zel with the size of 512x512 n the foremn vieo sequene with the size of 352x288. In our experiments, lok size is fixe t 16x16, the serh rnge W is 48x32, n the neighor region size equls to 1x16 for ll the test imges. The threshol vlue in similrity ftor (T s ) is set to 20 y mny experiments, n the justing prmeter T σ equl to I s of Eq. (12) to mke it ptive with imge. As for the prmeter of sttus ftor (T ), we try ifferent vlues for severl test imges in onseutive error ptterns (25% lok-loss rtio) to eie its proper vlue. Tle 1 shows optiml prmeter is little flutunt with ifferent imges, ut ifferenes re negligile. Thus, T tkes fixe vlue 2. Firstly two kins of ifferent lok-loss situtions re investigte. One kin of imges re pture uner the se of isolte lok losses with the lok-loss rtio of 10%, while the other one is pture uner the se of onseutive lok losses with the lok-loss rtio of 25%. Tle 2 shows the omprison results in the se of isolte lok losses, while Tle 3 shows the results of onseutive lok losses. Moreover, the visul

12 302 J Sign Proess Syst (2010) 60: qulity omprisons etween BI, BNM n the propose metho re illustrte from Figs. 6, 7, 8, 9, 10, 11, 12 n 13. In terms of PSNR, our onelment result is higher or omprle with stte-of-the-rt methos ([9, 10]) for Len n foremn in the isolte lok loss se. As for Pepper n Zel imge, we notie these two imges hve ovious illumintion vrition whih mke the similrity ftor n the justing prmeter (ompute y Soel opertor) impreise, thus result in egrtion of reovery qulity. However, the sujetive pereption of our metho presente in Fig. 7() n Fig. 8() prove to e stisftory. In the onseutive error sitution, our metho outperforms others in most test imges exept Zel, in whih Ghrvi s metho[11] is 0.35 higher thn us. This exeption n e overlooke in ontext of error onelment. As for visul qulity omprison, the propose metho n reover the ege informtion well n protet the none-ege re well from the isturne of wrong eges. In prtie, errors often hppen to one imge in rnom wy. To simulte suh ses, we further set three ifferent rnom ptterns inste of the regulr ptterns with the lokloss rtio of 5%, 10% n 20% respetively. Tle 4 shows the PSNR omprison results for Len n orresponing sujetive improvements n e notie in Figs. 14 n 15, espeilly in the re of omplex texture strutures like eyes. 4 Conlusions We hve propose n ptive pixel interpoltion tehnique for sptil error onelment in the lok se oing system. For missing pixel in orrupte lok, we otin set of preition vlues erive from four neighorhoos of the lok n then the missing pixel n e reovere through ptive interpoltion, lying ifferent importne on these preition vlues. More importntly, it enles the reovery of the onseutive loks loss, whih is the most often t loss pttern in prtie. Aknowlegements This work ws supporte in prt y Ntionl Nturl Siene Fountion of Chin ( , , ), n Reserh Fun for the Dotorl Progrm of Higher Eution of Chin ( ). Referenes 1. Wng, Y., & Zhu, Q. (1998). Error ontrol n onelment for vieo ommunition: review. Pro IEEE, 86(5), oi: / Aign, S., & Fzel, K. (1995). Temporl n sptil error onelment tehniques for hierrhil mpeg-2 vieo oe. In Pro. IEEE int. onf. ommunition, ICC, June 3, Kwok, W., & Sun, H. (1993). Multi-iretionl interpoltion for sptil error onelment. IEEE Trnstions on Consumer Eletronis, 39(3), oi: / Slm, P., Shroff, N. B., Coyle, E. J., & Delp, E. J. (1995). Error onelment tehniques for enoe vieo strems. In Pro. Int. Conf. Imge Proessing, Ot. 1, Suh, J. W., & Ho, Y. S. (1997). Error onelment se on iretionl interpoltion. IEEE Trnstions on Consumer Eletronis, 43(3), oi: / Wng, Y., & Zhu, Q. (1991). Signl loss reovery in DCT-se imge n vieo oes, In Pro. SPIE Conf. Visul Communition n Imge Proessing, Nov 1605, Prk, J. W., Kim, J. W., & Lee, S. U. (1997). DCT oeffiients reovery-se error onelment tehnique n its pplition to the MPEG-2 it strem error. IEEE Trnstions on Ciruits n Systems for Vieo Tehnology, 7(10), oi: / Criminisi, A., Perez, P., & Toym, K. (2004). Region filling n ojet removl y exemplr-se imge inpinting. IEEE Trnstions on Imge Proessing, 13(9), oi: / TIP Go,Y.,Wng,J.,Liu,Y.Q.,Yng,X.K.,&Wng,J.(2007).Sptil error onelment tehnique using verge points, In Pro. IEEE int. onf. Aoustis, Speeh n Signl Proessing, ICASSP, April. 1, Sirikm, A., & Kumwilikk, W. (2007). New sptil error onelment using ynmi texture estimtion n geometri interpoltion, In Pro. IEEE int. onf. Multimei n Expo, ICME, July. (pp ). 11. Ghrvi, H., & Go, S. (2008). Sptil interpoltion lgorithm for error onelment, In Pro. IEEE int. onf. Aoustis, Speeh n Signl Proessing, ICASSP, Mrh April Wng, Z., Yu, Y., & Zhng, D. (1998). Best neighorhoo mthing: An informtion loss restortion tehnique for lokse imge oing systems. IEEE Trnstions on Imge Proessing, 7(6), oi: / Li, X., & Orhr, M. (2002). Novel sequentil error-onelment tehniques using orienttion ptive interpoltion. IEEE Trnstions on Ciruits n Systems for Vieo Tehnology, 12(10), oi: /tcsvt Prk, J. W., & Lee, S. U. (1999). Reovery of orrupte imge t se on the NURBS interpoltion. IEEE Trnstions on Ciruits n Systems for Vieo Tehnology, 9(10), oi: / Hsi, S. C. (2004). An ege-oriente sptil interpoltion for onseutive lok error onelment. IEEE Signl Proessing Letters, 11(6), oi: /lsp Zhng, R. F., Zhou, Y. H., & Hung, X. D. (2004). Contentptive sptil error onelment for vieo ommunition. IEEE Trnstions on Consumer Eletronis, 50(1), oi: /tce Agrfiotis, D., Bull, D., & Cngrjh, C. N. (2006). Enhne error onelment with moe seletion. IEEE Trnstions on Ciruits n Systems for Vieo Tehnology, 16(8), oi: /tcsvt Sun, H., & Kwok, W. (1995). Conelment of mge lok trnsform oe imges using projetion onto onvex set. IEEE Trnstions on Imge Proess., 4(4), oi: / Kumwilisk, W., & Hrtung, F. (2004). An intrfrme error onelment: nonliner pttern lignment n iretionl interpoltion, In Pro. IEEE int. onf. Imge Proessing, ICIP, Ot.2,

13 J Sign Proess Syst (2010) 60: Li Song reeive the B.S. n M.S. egrees in eletroni engineering from Nnjin University of siene n tehnology in 1997 n 2000, n the PhD egree from Shnghi Jio tong University, Shnghi, P.R. Chin, in He is urrently leturer in the Institute of Imge Communition n Informtion Proessing, Deprtment of Eletroni Engineer, Shnghi Jiotong University, Shnghi, Chin. He hs pulishe over 30 reserh ppers n file 15 ptents. His reserh interests re in the res of signl proessing, imge n vieo oing, omputer vision, n mhine lerning. Xin M reeive the B.S. egrees in eletroni engineering from Shnghi Jiotong University in His reserh interests inlue imge ommunition n informtion proessing.