Multiscale PCA based Quality Controlled Denoising of Multichannel ECG Signals

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1 Multscale PCA based Qualty Controlled enosng of Multchannel ECG Sgnals L. N. Sharma, S. anadapat, and A. Mahanta Abstract Multscale Prncpal Component Analyss (MSPCA) s appled for qualty controlled denosng of Multchannel Electrocardogram (MECG) sgnals. Wavelet transform of MECG sgnals dssemnates clncal nformaton content nto dfferent wavelet subbands or scales. Collectng wavelet coeffcents of all ECG channels at a wavelet scale multvarate data matrces are formed. Prncpal Component Analyss (PCA) s performed on these matrces for sgnal denosng. The desred qualty of processed sgnals s acheved by selectng the prncpal components (PC) based on energy features n selected wavelet subband matrces. To control the qualty of denosed sgnals, the number of PC selecton s based on cumulatve percentage of total varaton of varances. The choce of multscale matrces and selecton of egenvalues preserve the desred energy n the processed sgnals. Quanttatve performance s measured usng nput and output Sgnal-to-Nose Rato (SNR). Sgnal dstorton metrcs are evaluated usng Percentage Root Mean Square fference (PR) and Wavelet Energy based agnostc storton (WE) measures. SNR mprovement of. db has been found wth better denosng effect usng database of CSE Multlead Measurement Lbrary. Index Terms enosng, ECG, MSPCA, PCA, PR, WE. I. INTROUCTION Pathologcal nformaton n physologcal sgnals s most mportant and essental for a physcan. The dagnostc nformaton n the sgnals should not be dsturbed by sgnal processng methods, rrespectve of ts nature whether t s normal or pathology. Electrocardogram sgnals may carry mportant pathologcal nformaton. Clncally, standard -lead ECG recorded n dfferent leads: I, II, III, avr, avl, avf, V, V, V, V4, V5 and V6, are n practce world-wde. The heart potental dstrbuton, recorded n dfferent leads, gves vtal cardac nformaton. The clncally essental dagnostc nformaton present n the sgnals must be preserved durng sgnal denosng process. Ths requres a qualty control measure. Sgnal processng by Prncpal Components Analyss (PCA) [], [], [] s extensvely used as a classcal multvarate sgnal processng tool. PCA has been appled n dfferent felds of scence and engneerng to better utlze ts ablty [4], [5], [6]. For bomedcal sgnals lke ECG, a robust extenson of classcal PCA by analyzng shorter sgnal segments s suggested [7]. It may be used n data reducton, beat detecton, classfcaton, sgnal separaton and feature extracton [8], [9]. Manuscrpt receved January 5, 0; revsed February 7, 0 The authors are wth the epartment of Electroncs and Electrcal Engneerng, Indan Insttute of Technology Guwahat, Inda. (e-mal: lns@tg.ernet.n.; e-mal: samaren@tg.ernet.n; E-mal: anlm@tg.ernet.n.) In ths artcle, t s suggested to apply Multscale PCA to multchannel ECG sgnals, for qualty controlled denosng. PCA s appled at wavelet scales after formng multvarate data matrces. The qualty controlled denosng s a two steps process, (a) selecton of multvarate matrces at wavelet scale for PCA based dmenson reducton and (b) the choce of number of Prncpal Component (PC) at each wavelet matrces. The selecton of effectve PCs s normally based on the cumulatve percentage of total varaton shown by egenvalues. For conventonal PCA, t s taken 70% to 99% []. The dagnostc qualty of denosed sgnal s qualtatvely compared wth the orgnal sgnal. The quanttatve dstorton measures lke PR and WE are evaluated [0], [], []. The enhanced multchannel sgnals contan all the clncal components wth requred 'PQRST' morphologes of ECG sgnals whle reducng the nose. II. METHO Multscale Wavelet decomposton of, L levels, for each channel sgnal from multchannel ECG data set results n L+ subbands. ue to the nature of multresoluton decomposton, these subbands contan dfferent dagnostc components [0]. agnostc nformaton les n hgher order subbands [0], []. Hgh frequency nformaton and nose appears n lower order subbands. In Fg., energy contrbuton effcency (ECE) [0], [], [] of wavelet subbands for multchannel ECG sgnals are shown. The multchannel ECG data s taken from CSE Multlead Measurement Lbrary database. For sx level wavelet decomposton the approxmaton subband s denoted as ca6 and detals subbands are denoted as c6, c5, c4, c, c and c. Fg.. ECE of wavelet subbands for multchannel ECG sgnals Most of the sgnals energy s reman n ca6, c6, c5 and c4 subbands. The dagnostc components and ts clncal mportant s hgher. The lower order subbands are less 07

2 sgnfcant n terms of dagnostc mportant. If subband matrces are formed arrangng wavelet coeffcents of the same scales of all the channels of multchannel ECG data set, we may apply PCA selectvely to avod losng PQRST morphologes of orgnal data set. th Wavelet transform (WT) gves k wavelet coeffcent at th. level as w, k. Thus, we fnd an approxmaton subband at level L and detal subbands at level, where =,,...L. Wavelet coeffcents are equal n numbers at a partcular wavelet scale provded a same transformaton crteron s appled wth same mother wavelet. There s n number of ECG channels. So, wavelet coeffcents obtaned by WT of MECG sgnals can be arranged n L+ subband matrces. In these multscale matrces rows represent wavelet coeffcents and columns represent ECG leads or channels. So, ths forms multvarate data matrx at a wavelet scale. At approxmaton level, the matrx s denoted as A L and at detals, matrces are wrtten as. PCA analyss by covarance method s appled n these multscale matrces. To fnd the Prncpal Components (PCs) followng operaton are requred Fndng out the covarance matrces for AL and Egen-decomposton of covarance matrces Fndng out the egen-vector and egenvalues Arrangng egenvectors and egenvalues n descendng order Selecton of egenvalues to decde number of PC Let, egenvalues for A are wrtten as L λ λ, λ,..., λ n A A A A L L L L = () λ λ, λ,..., λ = () n where L, s wavelet decomposton level,, s the wavelet scale and n s the number of ECG channels. Ths gves the number of egenvalues and hence the number of prncpal components. For dmenson reducton or denosng, the selecton of egenvalues whch decdes the prncpal components s an mportant step. The number of PC selected for PCA based processng decdes the denosng effect. There may be the loss of sgnal and t may affect the sgnal qualty. Hgher number of PC selected for processng captures more sgnal energy. Based on analyss of energy contrbuton effcency of wavelet subbands (Fg.) of multchannel ECG sgnals and egenvalues due to egen-decomposton, qualty controlled denosng s proposed as ) Select wavelet matrces from A L based on ECE values. ) Select the number of PC based on cumulatve percentage of total varaton of varances. The frst operaton results n mnmum loss of dagnostc components. In the second operaton, cumulatve energy may be vared between 60% to 99% to acheve qualty denosng. Matrces at dfferent wavelet scale do have dfferent parts of PQRST morphologes whch are due to wavelet decomposton. These clncal components carry dagnostc nformaton n the sgnal. To retan clncal nformaton n the denosed sgnal, multscale matrces should be handled carefully. It s seen that only few numbers of hgher order multscale matrces can be processed wth reduced set of PCs. For lower order matrces all the PCs are kept for further processng. If hgher order wavelet subband matrces are treated wth lower number of PCs, we may loss the dagnostc Components. For denosng operaton, selected prncpal components plays mportant role. There are many method suggested n lterature. Most common method s to compare the cumulatve percentage of total varaton [] shown by selected egenvalues. If m numbers of egenvalues are consdered from total n numbers of egenvalues for denosng, then cumulatve percentage of total varaton can be expresses as Fg.. Scree plots for, an d. In panel (a) scree plots before addton of nose and n (b) scree plots after addton of zero mean, unty varance Gaussan nose TABLE I: NUMBER OF PC FOR, Number of PC varyng wth T for, T T m λ = = 00 n λ = th where λ s the egenvalue and T s the threshold set whch gves cumulatve percentage of total varaton explaned by number of PCs selected. The denosed sgnal qualty depends on the energy captured by egenvalues. Qualty of the sgnal may be controlled f T s selected sutably. Ths mnmzes the loss of dagnostc components wth optmzed denosng. In present work, the value of T s made varable from 60% to 99% as per requred qualty of sgnal wth proper denosng effect. () 08

3 Fg..Orgnal sgnals wth addton of gaussan nose, (a) lead-ii (nput SNR=.), (f) lead-iii (nput SNR=9.7) and (k) lead-v4 (nput SNR=.0). the correspondng qualty controlled denosed sgnals for T= 60%, 80%, 95% and 99% are shown n panels (b), (c), (d), (e); (g), (h), (), () and (l), (m), (n), (o); respectvely. CSE multlead measurement lbrary, data set-m0-040 s used. TABLE II: INPUT AN OUTPUT SNR (IN B), CSE ATABASE, ATASET-M0-040 SNRs (n db) at defferent leads Lead I II III avr avl avf V V V V4 V5 V6 Input SNR Output SNR SNR Improvement TABLE III: ISTORTION MEASURES: CSE MULTILEA MEASUREMENT LIBRARY ATABASE, ATA SET-M0-040 storton metrcs for proposed method Metrc I II III avr avl avf V V V V4 V5 V6 PR(T= PR(T= PR(T= PR(T= WE(T= WE(T= WE(T= WE(T= Fg. 4. Orgnal sgnals wth Gaussan nose at lead-avr (I/P SNR=9.95), lead-avf(i/p SNR=5.97) & lead-v(i/p SNR=.88) and respectve qualty controlled denosed sgnal for T= 60%, 80%, 90% and 99% usng proposed MSPCA based denosng method. In (a) lead-avr sgnal wth denosed sgnals, (b) lead-avf sgnal wth denosed sgnals and (c) lead-v sgnal wth denosed sgnals. CSE multlead measurement lbrary, data set-m0-04 s used 09

4 III. RESULTS AN ISCUSSION Multchannel ECG sgnals are extracted from standard clncal data base, CSE Multlead Measurement Lbrary [4]. ata set of CSE multlead measurement lbrary s used. The data set has 5 orgnal ECG data sets wth almost equal numbers of normal and varous pathologcal cases. The samplng frequency s 500 Hz. It has 0 bts resoluton wth maxmal 5 mv quantzaton. Multvarate data matrx, S, s formed takng 4096 samples from each channel. Ths gves S as [4096 ] matrx. Sgnals extracted from data set-m0-040, are subected to mean removal and ampltude Normalzaton. Sx level wavelet decomposton s performed on each channel sgnals. The choce of decomposton level, L, whch satsfy the frequency range of the man features of an ECG, s based on samplng frequency, F s, [0], []. aubeches 9/7 borthogonal wavelet s used for wavelet transform of each channel sgnal. Ths wavelet s commonly used by dfferent authors [0,,, ] for ts lnear phase and symmetry and better performance for ECG sgnal. Across wavelet subbands at each scale the number of coeffcents are equal. From subbands of same level, consderng all the ECG channels, multvarate matrces are formed. At approxmaton, A L matrx and at detals,, matrces are constructed. L s the level of decomposton and =,,,...,L. Based on relatve subband energy n terms of ECE values, the mportant of multscale matrces are decded to retan clncal nformaton. To avod loosng clncal fdelty of multchannel sgnals, three subband matrces,, are selected for denosng operaton wth reduced number of prncpal components. Fg. shows scree plots for, matrces wth and wthout addton of whte Gaussan nose. In Fg. (a), scree plots for three multscale matrces, before addton of Gaussan nose are shown. After addton of zero mean and unty varance Gaussan nose, scree plots for same set of matrces are shown n Fg. (b). Comparng both the fgures, changes n ampltude of egenvalues wth prncpal components are notced. After addton of nose, the sgnfcant numbers of prncpal components requred for larger varaton of varances are ncreased. Accordngly, PCA may be performed wth selected set of PCs to reduce nose content. Hence, denosng effect can be controlled by varyng the numbers of PCs n these matrces. The cumulatve percentage of total varaton of varances decded by threshold, T, for, are vared from 60% to 99% to control the denosng performance. Number of prncpal components selected for denosng of multchannel sgnals, wth varyng T n dfferent subband matrces, are recorded n Tab.. For more denosng effect, less numbers of PCs are selected. So, a lower percentage varaton of, T, the loss s hgher. Smlarly, for hgher percentage of varaton, hgher numbers of PCs are selected. Ths gves less denosng effect and lower loss n sgnal. CSE database, ataset-m In Fg.(a) orgnal lead-ii sgnal (nose added) wth correspondng denosed sgnals n Fg. (b), (c), (d) and (e) at T=60%, 80%, 95% and 99% are shown. Smlarly, for sgnals of lead-iii and lead-v4 results are shown n Fg. (f), (g), (h), (), () and Fg. (k), (l), (m), (n) and (o) respectvely. The denosng effect s better at T=60% and s lesser at T=99%. Ths shows the denosng may be controlled by varyng threshold, T. It s essental to preserve clncal components of MECG sgnals durng denosng process. The proposed multvarate denosng based on MSPCA helps retan dagnostc components of the sgnals of lead-i, II, III, avr, avl, avf, V, V, V5 and V6. The ECG sgnals of dfferent leads are subected to addtve Gaussan nose to process wth proposed denosng method. To quantfy the denosng effect of the proposed method, the nput and output SNR (n db) are measured at T=60% and shown n Tab.. All the channels show sgnfcant mprovements n SNR (n db). Hgher SNR ndcates mprovement n sgnal qualty. Hgher SNR mprovements are observed for the sgnals at lead-avr, lead-v6 and lead-v4 wth. db,. db and 0.0 db respectvely. Lowest SNR mprovement of 5.5 s observed for lead-iii. Hgher SNR value at the nput tself may be the reason for low mprovement. In Fg. 4, another data set, M0-04 s from CSE Multlead Measurement Lbrary s tested at threshold T=60%, 80%, 90% and 99% of cumulatve varance and varances. Results for avr, avf and V are produced. Input SNRs for lead-avr, avf and V are 9.95, 5.97 and.88 respectvely. The output SNRs are found 9.7, and 40.4 respectvely for above leads. The controlled denosng of above sgnal show all the clncal nformaton present n the fltered sgnals. Ths shows the ablty of proposed method to clean the sgnal wth dfferent SNR values wth dfferent data sets. It s requred to evaluate the sgnal dstorton due to denosng process. For physologcal sgnals, a few exstng error measures are consdered n ths work. The sgnal dstorton metrc, Percentage Root Mean Square fference (PR) and Wavelet Energy based agnostc storton measure (WE) [0], [], [] are evaluated. In Table III, PR and WE are evaluated at T=60%, 80%, 95% and 99% for ata set-m The lowest PR at T=60%, 80%, 95% and 99% are 7.4 (avf), 5.87 (avf),.97 (avf) and 4. (V) respectvely. The lower WE values at T=60%, 80%, 90% and 99% are.4 (avf),.7 (avf),.7 (avr) and.6 (avr) respectvely. These value falls under excellent category sgnals []. Ths shows the proposed qualty control denosng method preserve all the dagnostc components wth requred fdelty n PQRST morphologes. IV. CONCLUSION In ths paper, qualty controlled denosng method usng multscale PCA s ntroduced. The proposed method explots the property of wavelet transform and PCA. The method s evaluated usng multchannel ECG sgnals from CSE multlead measurement lbrary data sets. The cumulatve percentage of total varaton of varances gven by egenvalues decdes the energy retan n the processed sgnal. Hgher the threshold value, T, selected lower s the sgnal loss and less denosng effect. In contrary, lower the 0

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