An Adaptive Filter Based on Wavelet Packet Decomposition in Motor Imagery Classification

Transcription

1 An Adaptve Flter Based on Wavelet Paket Deomposton n Motor Imagery Classfaton J. Payat, R. Mt, T. Chusak, and N. Sugno Abstrat Bran-Computer Interfae (BCI) s a system that translates bran waves nto eletral sgnal. In a sublass of suh nterfae, motor magery, Eletroenephalograph (EEG) sgnal related to sensormotor areas les on an 8-30 Hz range. Unfortunately, an ndvdual produes mportant patterns for lassfaton n dfferent frequeny omponents. Hene, we desgn an adaptve flter that automatally selets nformatve bands of eah subjet. The adaptve flter s based on band seleton usng a dsrmnatve value omputed by energy of wavelet oeffents. The seleted bands are used n wavelet flter as the adaptve flter. Subsequently, varane of the fltered sgnal maxmzed by Common Spatal Pattern (CSP) s extrated as features. Then, Bayes deson theory traned by these features s appled for pattern lassfaton. The proposed method shows mprovement n lassfaton auray over usng stat flterng. Keywords BCIs, Motor Imagery, EEG, WPT, Wavelet Flter, CSP, Bayes Deson Theory. B I. INTRODUCTION RAIN-Computer Interfae systems provde an alternatve hannel to ommunate between a human bran and omputers. The hannel allows an ndvdual to translate bran states nto nstrutons. There are many applatons for the system suh as a omputer ursor, omputer graph, and a robot lmb. In the translaton, the sgnal proessng tehnque namely pattern reognton plays a key role n the systems. For example, researhers utlze BCI systems n order to treat patents who annot move ther lmb by turnng patent s thnkng nto ommands to ontrol a robot arm. Durng rehabltaton, paralyts an magne movng ther lmb wthout any musle atvty. Bran waves respondng to ths magnaton are alled Motor Imagery (MI). In hand motor magery, the related EEG sgnal an be reorded from sensormotor areas, and It s well known that when patents exeute hand motor magery tasks, ampltudes of MU rhythm tend to be suppressed alled Event Related Desynhronzaton (ERD) [1]. ERD wll our n MU (8-12 Hz) and Beta (18-25 Hz) rhythms. To enhane the nformatve pattern from the sgnal, ntally, researhers used flter banks [2]. The sgnal was deomposed nto several bands, and then the deomposed sgnals were extrated features to tran a learnng mahne. Subsequently, another group of researhers desgned an adaptve flter [3] to selet approprate bands for an ndvdual. However, although, the sgnal was fltered wth proper bands, t s neessary to analyze frequeny doman and tme doman smultaneously. In order to evaluate the EEG sgnal, tmefrequeny analyss has been provded for motor magery tasks. Though Wavelet Transform (WT), whh s one of the useful tme-frequeny transforms, has been wdely used n EEG sgnal analyss [1], Wavelet Paket Transform (WPT), whh s a developed verson of WT, provdes more frequeny resolutons than the orgnal one [4]. In ths paper, we fous on desgnng an adaptve flter based on WPT alled Wavelet Flter [5]. The wavelet flter follows the perfet reonstruton of the wavelet transform. Frst, orgnal sgnal s deomposed nto subbands by the deomposton. The subbands are ranked by a dsrmnatve value. Ths value an be determned by a funton alled a ost funton. We seleted the hghest-valued bands as proper bands for eah subjet. Then, only bands whh are seleted by the prevous proess are reonstruted usng WPT. The reonstruted sgnal s the band-pass fltered sgnal. Ths paper s organzed as follow: n the seond seton, we onsder motor mager data, frequeny flterng, band seleton, wavelet flter, Common Spatal Pattern (CSP) and Bayes lassfer. The thrd seton presents results of the proposed method. Conlusons are gven n the fourth seton. A. Data Desrpton II. MATERIAL AND METHODS BCI ompetton 2008 data set provded by Graz Unversty of tehnology [6] s used to test our algorthm. The data set was reorded from subjets asked to exeute four motor magery tasks namely left hand, rght hand, both feet, and tongue. The reordng deve uses twenty-two Ag-AgCl eletrodes, and The EEG sgnals were reorded monopolarly wth the eletrode at left mastod servng as referene and rght mastod as ground. The sgnals were sampled at 250 Hz and were fltered by a Hz band-pass flter wth a 50 Hz noth flter. Eletrode plaement orresponds to the nternatonal system. Intally, the subjets were sttng on a omfortable har and lookng at a omputer sreen. At the begnnng of a tral (t=0s), a fxaton ross appeared for 2s. Subsequently, a task nstruton appeared on the sreen for lettng the subjets prepare for exeuton. At t=3s, the subjets were asked to exeute the nstruton that stll appeared on the sreen untl the nstruton dsappeared at t=6s. There was a short break untl the fxaton ross appeared agan. The paradgm s llustrated n Fg 1.

2 Fg. 1 Tmng sheme of the paradgm [6] In ths researh, the data set s hanged referene from monopolar to laplaan. The hangng s performed by subtratng mean of ts four nearest neghborng eletrodes from the hannel of nterest. Besdes, two eletrodes seleted n ths paper for lassfyng left and rght hand motor magery are C 3 and C 4 eletrode postons. B. Frequeny Flterng EEG sgnal has stll had all nformaton omponents both sgnfant and undesrable. Sne a type of EEG sgnal s grouped by a frequeny range. For example, EEG sgnal used n motor magery task s related to MU and Beta rhythms. It s mportant to remove rrelevant frequeny omponents by usng a band-pass flter. The FIR flter s desgned by Kaser wndow method, and An 8-30 Hz band s used beause the fltered sgnal must ontan both MU and Beta bands. C. Band Seleton In band seleton, we ntend to selet the most nformatve frequeny bands for eah person. The bands are seleted by a dsrmnatve value. The value an be determned by usng energy of wavelet oeffents between left hand and rght hand patterns. Even though Wavelet Deomposton (WD) s a powerful tool to analyse non-statonary sgnals, Wavelet Paket Deomposton (WPD) provdes more frequeny resolutons. WPD deomposes both approxmaton and detals nstead of only approxmaton lke n WD. The 2 level deomposed subbands an be represented by a bnary tree shown n Fg 2. A node of the bnary tree s labeled by S( j, k ). j s the depth of the node n the tree, and k s the number of nodes at the same depth. For nstane, S (0, 0) represents orgnal sgnal. Beause the paket deomposton produes 2 level subbands, t s redundant as well as tme onsumng. We an redue dmensons of the deomposton by fndng an optmum tree (the best-bass paradgm). Loal Dsrmnant Bases (LDB) algorthm has been used n the reduton. LDB wll fnd the optmum tree wth the bottom-up searh [7]. As an objetve of the algorthm s to fnd an effent bass, there s no any nformaton loss after ths proess. For nstane, Fg 3 shows an orgnal paket tree ompares wth a redued tree obtaned by LDB. The bands n the tree are sorted by the dsrmnatve value beause hgh dsrmnatve values mean hghly dfferent patterns between the two lasses. A funton that omputes the values s alled a ost funton. Therefore, we onsder the ost funton based Fg. 2 Struture of a three-level wavelet paket tree on energy of wavelet oeffents and Euldean Dstane followng Equaton (1-3) [8]. Let s denote ( W ),, x as the deomposton oeffents of sgnal x at the subband S( j, k ), where l s the ndex of the loaton of the deomposton oeffents. Let N be the number of sgnals C belongng to lass. ( e ) ( j, k) s the normalzed energy vetor of lass, D s Euldean Dstane, and H ( S( j, k )) s the dsrmnatve value of the subband. = j k l C 1 C ( ) ( m ) H ( S ( j, k )) D( e ( j, k ), e ( j, k )) = 1 m = + 1 (1) ( ) ( ) ( ) n0 j e ( j, k) = [ e ( j, k,0);..; e ( j, k,2 1)] (2) NC 2 ( W ( ) 1 j, k, l ( x )) = ( j, k, l) = N 2 C x = 1 (3) e As a onsequene, the hghest-valued bands are seleted as approprate bands. For example, eah hannel (C 3 and C 4 ) s seleted the best band shown n Fg 4. D. Wavelet Flter Ownng to the perfet reonstruton property of the wavelet transform, t s able to mplement a band-pass flter. The flter s omputed by deomposng and reonstrutng only nformatve bands. Frst, orgnal sgnal s deomposed by WPT. Then, we selet the bands by usng the prevous proess and remove other bands by settng all values n the deomposed subbands to zeros. Subsequently, the reonstruted sgnal s the band-pass fltered sgnal. Fg. 3 An optmum tree obtaned from LBD

3 transformed egenvetor matrx. Therefore, the egenvetor wth the largest egenvalue n S l has the smallest egenvalue n S r. Fg. 4 The hghest-valued bands of eah hannel E. Common Spatal Pattern (CSP) It s well known that raw EEG sgnal has a poor spatal resoluton beause of volume onduton. Thus, the sgnal of nterest an only be observed after approprate sgnal proessng. The most useful approah s Common Spatal Pattern (CSP) tehnque [9]. Ths approah albrates the system spef for eah user. Besdes, CSP tehnque maxmzes varane of the fltered sgnal under one ondton (lassfy left and rght hand motor magery), whle mnmzng t for other ondtons. In CSP analyss, EEG data are represented as an N T matrx E, where N s a number of hannels and T s a number of task samples. Frst, the normalzed ovarane s obtaned by Equaton 4, where the trae funton s summaton of the dagonal matrx. EE C = trae ( EE ) In ths paper, we wll lassfy between left hand (l ) and rght hand ( r ) motor magery tasks. Thus, C l s alulated by averagng over the trals of the left hand task group, and C r s alulated smlarly. C, whh s the spatal ovarane, an fnd egenvalues and egenvetors followng Equaton 6. U s the matrx of the egenvetors and λ s the dagonal matrx of the egenvalues. Before next proessng, the egenvetors n matrx U are sorted n desendng order of the egenvalues n matrx λ. (4) CC = Cl + Cr (5) CC = U Cλ CU C (6) To deorrelate relatonshp among varables, the whtenng transformaton has been used. P = 1 λ C U C Subsequently, durng deorrelaton n Equaton 8-9, C r are transformed to S l and (7) C l and S r by usng matrx P n Equaton 7 resultng n the shared egenvetor matrx. Equaton 10 shows the shared egenvalues of eah lass, where I s the dentty matrx. λ and λ are the egenvalue matrx l of eah lass after the whtenng transformng, and B s the r Sl = PCl P, Sr = PCr P (8) Sl = Bλ l, Sr = Bλ r (9) λl + λr = I (10) To onstrut the projeton matrx as Equaton 11, frst and last m egenvetor of matrx B are hosen, where W s the transformaton that uses for the later data. W Z P WE = (11) = (12) When the sgnal matrx E multples the transformaton W, Z s the CSP sgnal matrx followng Equaton 12. Beause the transformaton maxmzes varane of the sgnal, features representng the sgnal should be the varane omputed from Equaton 13, where p s a number of hannels of nterest. Funton var s varane of the sgnal. F. Classfer f p = log var( Z p) var( Z) 2m = 1 (13) Bayes Deson Theory has been proposed as a lassfer whh s about to probablst terms [10]. The soluton of Bayes theory s to maxmze the posteror probabltes P( ω x). However, P( ω x) annot be dretly alulated, but Bayes formula allows us to alulate P( ω x) from the pror probabltes P( x ω ) and the probablty of eah lass P( ω ) gven as equaton 14. The feature probablty P( x ) an be gnored beause t must be equal every omparson. Features that represent the sgnal eah lass are alulated the posteror probablty by equaton 15. P( x ω ) P( ω ) P( ω x) = P( x) (14) If the features belongng to whh lass have the probablty hgher than that of the other one, the sgnal represented by these features wll be deded as ths lass. g ( x) = ln P( x ω ) + ln P( ω ) (15) g( x) = g1( x) g2 ( x) (16)

4 As a result, one of the most onvenent ways to lassfy patterns s to use the deson funton n Equaton 16. The deson rule s able to lassfy a two-lass data by dedng as lass 1 when g( x ) > 0 ; otherwse dedng as lass 2. G. Proedure TABLE I CLASSIFICATION ACCURACY OF THE PROPOSED METHOD DEPENDING ON VARIOUS MOTHER WAVELETS AND THE NUMBER OF THE SELECTED BANDS db1 db2 db3 db4 30 bands % % % % 20 bands % % % % 10 bands % % % % 5 bands % % % % 1 bands % % % % IV. CONCLUSIONS Ths paper has presented a method for seletng the proper bands of eah ndvdual. The proposed method s an adaptve wavelet flter based on band seleton by a dsrmnatve value. The wavelet flter an be mplemented wth the perfet reonstruton of the wavelet transform by deomposng orgnal sgnal and then reonstrutng only the seleted band. The reonstruted sgnal orrespondng the band-pass fltered sgnal s already enhaned nformatve patterns spef for eah user. As a result, the proposed method an mprove the auray from the prevous method usng stat flters. Besdes, we are able to know nformatve band of eah subjet. Fg. 5 Flow hart of the proposed method To follow the flow hart n Fgure 5, the data set s equally separated nto 2 sets: tranng set and tested set. The tranng set s fltered by Kaser 8-30 Hz band-pass flter to remove rrelevant frequeny omponents. Next, the fltered sgnal s deomposed nto bnary-tree subbands, and the subbands are sorted by the dsrmnatve value. The hghest-valued bands are seleted as approprate bands n order to use n the adaptve flter desgnaton. The adaptve flter s used for both tranng set and tested set. After adaptve flterng, the fltered sgnal s extrated features. The learnng mahne s traned by these features by Bayes deson theory. The theory models probablst equatons to lassfy the patterns. For the tested set, t s fltered by the wavelet flter. Then, the fltered sgnal s extrated the features. Fnally, Bayes equaton s appled to lassfy the test set. III. RESULTS BCI ompetton 2008 provdes motor magery tasks produed by several subjets. Ths experment hoose an arbtrary subjet to test the proposed method. Classfaton auray n the Table I shows varous mother wavelets and the number of the seleted band have an mpat on lassfaton. As you see n the table, Daubehes4 mother wavelet and only the hghest-valued band produes the best auray. The best band of C3 and C4 are approxmately Hz and Hz respetvely. The prevous method that derves from the Kaser 8-30 Hz band-pass flterng wthout the wavelet flterng produes 65.07% auray, whle the proposed method an aheve 68.82% auray. ACKNOWLEDGMENT Ths researh s fnanally supported by Thaland Advaned Insttute of Sene and Tehnology (TAIST), Natonal Sene and Tehnology Development Ageny (NSTDA), Tokyo Insttute of Tehnology and Kasetsart Unversty (KU). Authors would to thank NTC Teleommunaton Researh Laboratory at Department of Eletral Engneerng, Kasetsart Unversty for Matlab program. REFERENCES [1] Maan M. Shaker, EEG Waves Classfer usng Wavelet Transform and Fourer Transform, Internatonal Journal of Bologal and Lfe Senes 1: [2] Ka Keng Ang, Zheng Yang Chn, Hahong Zhang, Cunta Guan, Flter Bank Common Spatal Pattern (FBCSP) n Bran-Computer Interfae, Internatonal Jont Conferene on Neural Network, [3] Kavtha P. Thomas, Cunta Guan, Chew Tong Lau, A. P. Vnod, Ka Keng Ang, A New Dsrmnatve Common Spatal Pattern Method for Motor Imagery Bran-Computer Interfaes, IEEE Transaton on Bomadal, Vol. 56, No. 11, November [4] Ye Nng, Me Zhan, Sun Yuge, Wang Xu, Researh of Feature Extraton of BCI Based on Common Spatal Pattern and Wavelet Paket Deomposton, Chnese Control and Deson Conferene, [5] Chen XaoNan, Xu Zhyuan, Suo Jdong, Bandpass Flter Desgn Based on Wavelet Paket, College of Informaton Sene and Tehnology, Dalan Martme Unversty, Dalan, Chna. [6] R. Leeb, C. Brunner, G. R. Müller-Putz, A. Shlögl, G. Pfurtsheller, BCI Competton Graz data set B, Graz Unversty of Tehnology, Austra. [7] Naok Sato, Ronald R. Cofman, Loal Drmnant Bases and Ther Applatons, Journal of Mathematal Imagng and Vson, 5, , [8] Yang Bang-hua, Yan Guo-zheng, Yan Rong-guo, Wu Tng, Adaptve subjet-bases feature extraton n bran-omputer nterfaes usng wavelet paket best bass deomposton, Medal Engneerng and Physs 29, 2007, [9] Herbert Ramoser, Johannes Müller-Gerkng, Gert Pfurtsheller, Optmal Spatal Flterng of Sngle Tral EEG Durng Imagned Hand

5 Movement, IEEE Transaton on Rehabltaton Engneerng, Vol. 8, No. 4, Deember [10] Jen Kohlmorgen, Benjarmn Blankertz, Bayes Classfaton of Sngle- Tral Event-Related Potentals n EGG, Fraunhofer FIRST.IDA Kekuléstr. 7, D Berln, Germany.