Fetal Electrocardiogram Extraction Using Let Techniques

Transcription

1 Journal of Computer Scence 8 (9): , 202 ISS Scence Publcatons Fetal Electrocardogram Extracton Usng Let echnques Hemajoth, S. and 2 K. Helen Prabha Department of ECE, St. Peter s Unversty, Chenna, Inda 2 Department of ECE, RMD Engneerng College, Chenna, Inda Abstract: Fetal Electrocardogram Extracton (FECG) dentfes the congental heart problems at the earler stage. he major problem n the non nvasve procedure s the extracton of FECG from Maternal ECG (MECG) and many nterferences. he proposed methods () Combnaton of Adaptve euro Fuzzy Inference (AFIS) and Fractonal splne wavelet () Combnaton of Fractonal splne wavelet and AFIS () Combnaton of AFIS and SURE-LE and (v) Combnaton of SURE-LE and AFIS remove the unwanted noses present n the FECG more effectvely. hs new approach extracts FECG by removng the nosy Abdomnal ECG (AECG) and subsequently cancels the MECG. he pure thoracc ECG (ECG) or maternal ECG was used to remove nosy MECG present n the sgnal from abdomen sgnal and thereby the requred noseless FECG s extracted by means of the new approach. he excellence of the LE technques are evaluated usng Mean Square Error (MSE) and Peak Sgnal to ose Rato (PSR). he result of combnaton of AFIS and SURELE gves the best result and the closest match to the smulated FECG wth hgh PSR and low MSE among all the proposed methods. Keywords: Abdomnal Electrocardogram (AECG), Adaptve euro-fuzzy Inference System (AFIS), Fetal electrocardogram (FECG), Maternal Electro Cardogram (MECG), Mean Square Error (MSE), Peak Sgnal to ose Rato (PSR) IRODUCIO he fetal Electrocardogram (FECG) calculates fetal cardac frequency and n the predcton of fetal acdoss. Medcal treatment can be gven to the mother at the earler stages f any abnormaltes are found and thereby congental problems can be avoded. he ECG sgnals are taken by placng electrodes on the mother s thorax and abdomen. he ECG sgnals obtaned from maternal abdomen are a combnaton of fetal ECG, maternal ECG, noses lke electromyogram, power lne nterference, base lne wander and other random noses. For the extracton of FECG, estmaton from the abdomnal sgnal and separaton from the noses are essental. Related works: ovel method for fetal ECG extracton from a combnaton of FECG, MECG and noses s proposed n (Khamene and egahdarpour, 2000). he ECG taken from mother s thorax s orgnal thoracc ECG or maternal ECG and the sgnal taken from abdomen area has mother s ECG and fetal ECG. he mother s ECG sgnal porton present n the abdomnal sgnal s a nonlnear sgnal of mother s thoracc ECG. An effcent method of AFIS and wavelet s proposed n (Swarnalatha and Prasad, 200a; 200b) to get the requred fetal ECG from the sgnal n mother s abdomen. AFIS technque for fetal ECG extracton s correlaton and artfcal neural network s presented n (Hasan et al., 2009). Adaptve neuro-fuzzy method (AFIS) n (Vjla et al., 2006). FPGA mplementaton of Gamma flter for extractng FECG s presented n (HelenPrabha and atarajan, 2007), FECG extracton usng AFIS wth Gamma adaptatons n (HelenPrabha and Valarmathy, 2007), the noses and the mother s ECG (MECG) present n the dstorted form n the composte sgnal are removed by adaptve nose cancellaton property of Gamma AFIS (Vjla and Kanagasabapathy, 2005). Polynomal networks technque for the FECG extracton presented n (Assaleh and Al-ashash, 2005). Hybrdsaton of Sngular Value Decomposton (SVD) and AFIS s dscussed n (Al-Zaben and Al-Smad, 2006). MAERIALS AD MEHODS AFIS: Adaptve neuro fuzzy nference system was dscussed by Jang and Gulley (993). Adaptve ose Cancellaton (AC) usng AFIS technque s shown n Fg.. he unwanted noses can be removed by fndng the non-lnearty between the mother s ECG and the noses by AC technque. Here, x(k) gves the fetal ECG sgnal obtaned from the unwanted nosy sgnal. n(k) s the nose sgnal from presented n (Assaleh, 2007). Hybrd technque of mother s abdomen MECG. Correspondng Author: Hemajoth, S., Department of ECE, St. Peter s Unversty, Chenna, Inda 547

2 Fg. : Adaptve nose cancellng structure Fg. 2: Bell shape membershp functon he nose sgnal goes through unknown nonlnear dynamcs (f) and generates a dstorted nose d(k), whch s then added to x(k) to form the measurable output sgnal (abdomnal) y(k). he ntenton here s to dfferentate x(k) from the abdomnal sgnal y(k) whch has the mxture of wanted sgnal x(k) and d (k) and the unwanted nosy sgnal. AFIS s a multlayer feed forward network. hs archtecture has fve layers such as fuzzy layer, product layer, normalzed layer, de-fuzzy layer and total output layer. he fxed nodes are represented by crcle and the nodes represented by square are the parameters to be learnt. he system archtecture of AFIS s shown n Fg. 2. AFIS gves the advantages of the mxture of neural network and fuzzy logc (Helenprabha and atarajan, 2007). he am of mxng fuzzy and neural networks s to desgn an archtecture whch uses a fuzzy logc to show knowledge n a fantastc manner, n addton to the learnng nature of a neural network to maxmze ts parameters. he dsadvantages of both the black box behavor of neural networks and the problems of gettng approprate membershp values for fuzzy systems can be neglected. J. Computer Sc., 8 (9): , 202 tunng. hs s shown n Fg. 2. It s specfed by three parameters namely a, b and c represents the wdth, centre and slope of the curve. he bell shaped functons change whenever there a s change n the parameter value. Smoothness and concse notaton s the major plus pont of ths technque. FIS Structure and MF Parameter Adjustment: he very standard structure of a Fuzzy Inference System (FIS) maps nput characterstcs to nput membershp functons, nput membershp functon to rules, rules to a set of output characterstcs, output characterstcs to output membershp functons and the output membershp functon to a sngle-valued output or a decson assocated wth the output. In a conventonal FIS, the number of rules are determned by an expert who s same as the target system. If there s no expert, empercal selecton of membershp functon s gven to each nput. he FIS s appled to modelng systems whose rule structure s essentally predetermned by the user's nterpretaton of the characterstcs of the varables n the model. Here, the shape of the membershp functons depends on parameters and changng these parameters wll change the shape of the MF. Instead of just lookng at the data to choose the MF parameters, MF parameters can be chosen automatcally usng AFIS. Hybrd learnng algorthm s used n AFIS to tran the network parameters. It mxes the gradent method and the least square estmate to fnd the MF parameters. Gradent method s normally slow and become strucked n local mnma. So, hybrd rule s used to decrease the area of the search space n the gradent method and also reduces the convergence tme. As a result of multlayer AFIS archtecture, the parameters n the hdden layer s tuned by the gradent method learnng rule and the least squares method s used to fnd the parameters n the output layer. AFIS archtecture: For smplcty, assume that the fuzzy nference system has two nputs x and y and one output z. A frst-order (akag and Sugeno, 985) fuzzy model has the followng rules: Rule : If x s A and y s B, then f = px + qy + r Rule 2: If x s A2 and y s B2, then f2 = p2x + q2y + r2 Here, x s A and y s B and x s A2 and y s B2 are called as the premse secton (non lnear secton), whle f = px + qy + rand f2 = p2x + q2y + r2 are called as the consequent secton (lnear secton)..e., p, p2, q, q2, r, r2 are lnear parameters and A, A2, B, B2 are non lnear parameter. he correspondng equvalent AFIS Membershp functon n AFIS: A Membershp Functon (MF) s a curve whch explans how each and every pont n the nput space s mapped to a membershp value (or degree of membershp) between 0 and (Helenprabha and atarajan, 2007). Here, generalzed bell type MF s used for the FIS parameters archtecture s shown n Fg. 3 (Jang and Gulley, 993). 548

3 J. Computer Sc., 8 (9): , 202 Each node represents the frng strength of the rule. w, w 2 are the weght functons of the next layer. Layer 3: It s the normalzed layer. Every node n ths layer s a fxed node labeled orm. Its functon s to normalze the weght functon wth the followng condton, where O 3, denotes the Layer 3 output as shown n Eq. 4: O w = w = w + w 3, 2 (4) Fg. 3: AFIS archtecture AFIS s a multlayer feed forward network. he system archtecture conssts of fve layers namely, fuzzy layer, product layer, normalzed layer, de-fuzzy layer and total output layer. he fxed nodes are represented by crcle and the nodes represented by square are the parameters to be learnt. he forthcomng secton gves a clear detal about the lnk between the nput and output of each layer n AFIS. Layer : It s the fuzzy layer. Every node n ths layer s an adaptve node wth a node functon. O l, s the output of the th node of the layer l whch s shown n Eq. : O = µ (x)for =,2,or l, A O = µ (y)for = 3,4 l, B 2 () x (or y) s the nput node and A (or B-2) s a lngustc label assocated wth ths node. herefore O, s the membershp grade of a fuzzy set (A, A2, B, B2). In ths work, bell shaped Membershp Functons (MF) are chosen and t s shown n Eq. 2: µ A(x) = x c + a 2b (2) where, a, b and c s are the premse parameter set to be learnt. Layer 2: It s the product layer that conssts of two nodes labeled as Π. he output s the product (X) of all the ncomng sgnals whch s shown n Eq. 3: O2, = w = ( µ A (x))x( µ B (y)) =,2 (3) Outputs are called normalzed frng strengths. Layer 4: It s the defuzzy layer. Every node n ths layer s an adaptve node. he defuzzy relatonshp between the nput and output of ths layer can be defned below, where O4, denotes the layer 4 output as shown n Eq. 5: O4, = w f = w (p x + q y + r ) (5) where, w s the normalzed frng strength from layer 3. p, q, r denote the lnear parameters whch are also called consequent parameters of the node. Layer 5: It s the total output layer, whose node s labeled as sum, whch computes the overall output as the summaton of all ncomng sgnals. he result can be wrtten as follows where as O 5, denotes the layer 5 output as shown n Eq. 6: w f Overalloutput = O5, = wf = =, 2 w (6) he mxture of gradent descent method and least square method traned the AFIS. Each epoch of hybrd learnng conssts of forward pass and backward pass. Least-square method s used to fnd the consequent parameters on the layer 4 durng forward pass. Gradent descent method upgrades the premse parameters and propagates the error backward durng the reverse pass (Jang and Gulley, 993). he evalfs command determnes the output of the FIS system for gven nput. Here, the reference sgnal MECG and the desred abdomnal sgnals are gven as a tranng par for AFIS. Wavelet transform: he wavelet transform s a tmescale representaton technque, whch explans a sgnal by means of correlaton wth translaton and dlaton of a functon called as mother wavelet. he Dscrete 549

4 J. Computer Sc., 8 (9): , 202 Wavelet ransform (DW) s defned by splttng f(t) n to smaller non overlappng parts f (t), takng a fnte number of scales and down samplng the dscrete wavelet coeffcents samples to M, the number of samples of f (t): DW (s,t, ) = CW (s, τ ) j k j k the tme frame ndcaton t can be removed for gettng the clear dea. Whle takng the multframe processng θ nto our account: R R R, the mean square error of wavelet sub-band j of frame t can be expressed wthout bas by: = θ + θ 2 ( (y n,p n ) et y n) 2et R (y n,p n) et Ret n = he wavelet denosng method conssts of applyng DW to the orgnal sgnal, thresholdng the detal and approxmaton coeffcents and nversng the threshold coeffcents to obtan the tme doman denosed data (Paraschv-Ionescu et al., 2002). he performance of the wavelet denosng depends upon the type of wavelet transform, type of the wavelet, thresholdng rule and the number of decomposton levels. Surelet Denosng: he proposed new methodology to sgnal denosng, reles on the mage-doman mnmzaton of an estmate of the mean squared error- Sten's Unbased Rsk Estmate (SURE). he denosng methods are explaned as a lnear combnaton of denosng processes and Lnear Expanson of hresholds (LE). Accordng to the SURE and LE prncples, denosng algorthm s partcularly meant for solvng a lnear system of equatons whch s effcent and fast. By takng threshold over the undecmated Haar wavelet coeffcents, good results are obtaned whch clearly explans a SURELE algorthm s more effcent. SURE s nothng but an statstcal estmate of the Mean Squared Error (MSE) between an orgnal unknown sgnal and a nosy sgnal. hs method reles upon the served data and never expects prevous assumpton on the nose-free sgnal. he only statstcal assumpton s done on the nose. Denotng by ˆv, an estmate of the nose-free vdeo v, the global MSE s expressed as: MSE = e j (vn ˆ vn)(vn ˆ vn) et t = n= MSE Here, p n denotes any random varables statstcally ndependent of y n and corresponds to the gradent operator wth respect to the frst varable of the functon, y n. Lnear Expanson of hresholds (LE): he thresholdng functon s expressed by a lnear combnaton of thresholdng functons, whch was coned LE, that s: θ (y n,p n) θ2(y n,p n ). θ (y n,p n) = a a 2...a k. a. θ (y,p ) K n n θ(y n,p n ) where, a and θ are both K vectors. Each θ k : R R - R s an arbtrary vector-valued thresholdng. he optmal-n the mnmum-sense-parameters of (5) are the soluton of a lnear system of equatons: a opt = M C Where: M = θ(y n,p n) θ(y n,p n ) n= C = θ (y,p ) ( θ (y,p ) R)e n= ( n n n n n t ) t he steps for the SURELE denosng are as j J j j j j = e (xˆ x )(xˆ x ) e follows: t n n n n t t = j= n= j j MSE Step : Obtan the nosy abdomnal sgnal t Step 2: Set the number of teratons. where, e ˆt x j n = θ j t (y j n, p j n) s the nth pxel of the jth Step 3: Compute the standard devaton of the nose. wavelet subband of the denosed frame t. It s obtaned Step 4: Compute the Surelet transform of the sgnal. by thresholdng the nth pxel of the jth wavelet subband Step 5: Denose the sgnal usng the calculated of the nosy frame t, takng nto account (some of) ts Parameters. neghborng frames. he subband superscrpt j and Step 6: Reconstruct to obtan the denosed sgnal. 550

5 FECG extracton usng SURELE and AFIS: In ths process, the ECG taken from mother s abdomen s pre-processed at frst by surelet transform and the output s passed through AFIS. he other nput to AFIS s the sgnal from the thorax area. he requred FECG s the result from the AFIS. FECG Extracton Usng AFIS and SURELE: In ths process, the sgnal mother s abdomen and from the thorax area s frst passed through AFIS to get the estmated ECG sgnal and the output s processed by SURELE transform to get the extracted FECG. Fractonal Splne Wavelets: Fractonal splne wavelets are also called as splnelet. he Schoenberg's famly of polynomal splnes wth unform knots are extended to all fractonal degrees. hese splnes, whch nvolve lnear combnatons of the one sded power functons x + xα = { }α max 0, are α-holder contnuous for α 0. We construct the correspondng B-splnes by takng fractonal fnte dfferences and provde an explct characterzaton n both tme and frequency domans. he name Fractonal splnes ndcates that t should have an approxmaton n fractonal order, a property whch have not been encountered before approxmaton theory. Absolutely, the error of approxmaton decays lke f Pf Oa a = (α+) as a 0. he asymptotc development of the L2-error s provded and quanttatve error bounds are gven to substantate ths ssue. he Strang-Fx theory s not satsfed by the fractonal splnes for non-nteger α whch gves the equvalence between the reproducton of polynomals of degree n and the order of approxmaton whch s gven by one degree more (L = n+). Partcularly, the fractonal splnes wll reproduce polynomals of degree n wth n- <α n whle the order of approxmaton s α+. he vald multresoluton analyses of L2 for α> 2 s generated by fractonal B-splnes. But, for α<<-2, the factor (+z) s not present n the refnement flters H(Z) whch s essental for the buldng up of real wavelet bases. But, the flters have the correct fadng property: H(e jπ ) = 0, whch assures the segregaton of unty condton (everywhere, excludng the knots). he multresoluton analyss of L2 s satsfed by the above mentoned functons and so t can be used to construct new wavelet bases famles wth a parameter n a contnuously-varyng mode. he steps for the Fractonal splne wavelet denosng are as follows: Step : Obtan the nosy abdomnal sgnal. Step 2: Decompose the sgnal nto low frequency and hgh Frequency bands usng splnelet transform. J. Computer Sc., 8 (9): , 202 Step 3: Analyze the bands to dentfy the hgh frequency nose. Step 4: Remove the nose by replacng those bands wth null bands. Step 5: Reconstruct to get the noseless sgnal. FECG Extracton Usng Splnelet and AFIS: In ths method, the abdomnal ECG s frst pre-processed by Fractonal splne wavelet transform and the output s passed through AFIS. he other nput to AFIS s the thoracc sgnal. he output of AFIS s the extracted fetal ECG. FECG Extracton Usng AFIS and Splnelet: In ths method, the abdomnal ECG and thoracc ECG s frst passed through AFIS to get the estmated thoracc sgnal and the output s processed by Fractonal splne wavelet transform to get the extracted FECG. MSE = PSR = e RESULS he requred FECG sgnal was obtaned by the methods gven below: AFIS SURELE and AFIS AFIS and SURELE Fractonal splne wavelet and AFIS AFIS and Fractonal splne wavelet Analyss of Method I: Smulated maternal ECG, Fetal ECG, Abdomnal sgnal s used to extract orgnal FECG. Fgure 4 shows the sgnal from mother s abdomen, estmated sgnal from thorax area and the wanted FECG by AFIS method. In ths process, there s an oscllatory phenomena can be seen n the poston of maternal ECG n the acqured sgnal. he calculated MSE and PSR values are as MSE = 7.658e-04 PSR = Analyss of Method II: he smulated abdomnal sgnal s denosed usng SURELE transform technque and the denosed sgnal s fed nto AFIS for FECG extracton. he output are depcted n Fg. 5. he calculated MSE and PSR values are as

6 J. Computer Sc., 8 (9): , 202 Fg. 4: FECG extracton usng AFIS Fg. 7: FECG extracton usng Splnelet and AFIS Fg. 5: FECG extracton usng SURELE and AFIS Fg. 8. FECG extracton usng AFIS and Splnelet Analyss of Method III: SURELE post-processng s done by denosng the extracted FECG usng the AFIS. he results are shown n Fg. 6. Upon comparson, the SURELE post-processng provdes more accurate fetal ECG extracton. he calculated MSE and PSR values are as MSE = 2.542e-04 PSR = Fg. 6: FECG extracton usng AFIS and SURELE Analyss of Method IV: In ths process, the fractonal splne transform s used to remove the random nose n the sgnal taken from mother s abdomen and the requred fetal ECG s obtaned by AFIS as shown n Fg

7 J. Computer Sc., 8 (9): , 202 able : Performance evaluaton results Method MSE PSR Surelet pre-processng E-04 Surelet post-processng E-04 Splnelet pre-processng E-04 Splnelet post-processng E-04 he calculated MSE and PSR values are as MSE = 3.663e-004 PSR = Analyss of method V: In ths method, the sgnal from mother s abdomen s s estmated by AFIS and fractonal splne wavelet transform s used to extract FECG as shown n Fg. 8. he calculated MSE and PSR values are as MSE = 2.679e-004 PSR = DISCUSSIO he analyss of new mehodologes are partcularly towards the effcency of the requred fetal ECG. he mportant parameters used for mantanng the effcency of the fetal ECG are Peak Sgnal to ose Rato (PSR) and mean square error (MSE). he results of performance evaluaton for all the above mentoned methods are shown n the able. Upon comparson, Post-processng usng SURELE acheved the best results and can be concluded as the better of the fve methods. COCLUSIO In ths study, we have projected a new approach of hybrd algorthm of AFIS and LE to obtan fetal ECG from mother s abdomen wth hgh PSR. ECG from the mother s abdomnal area and from the thoracc area s used for obtanng the wanted fetal ECG sgnal. he proposed methods are evaluated usng MSE and PSR. Whle comparng the results, AFIS followed by SURELE post-processng produces hgh PSR whch shows that ths method produces good qualty FECG sgnal. Further optmzaton can be performed for the better estmaton of the wanted fetal ECG. he results wll be used for hardware mplementatons. REFERECES Assaleh, K. and H. Al-ashash, A novel technque for the extracton of fetal ECG usng polynomal networks. IEEE rans. Bomed. Eng., 52: DOI: 0.09/BME Assaleh, K., Extracton of fetal electrocardogram usng adaptve neuro-fuzzy nference systems. IEEE rans. Bomed. Eng., 54: PMID: Hasan, M.A., M.I. Ibrahmy and M.B.I. Reaz, An effcent method for fetal electrocardogram extracton from the abdomnal electrocardogram sgnal. J. Appled Sc., 5: Helenprabha, K. and A.M. atarajan, FPGA mplementaton of gamma flter for extractng fetal electrocardogram. IEE J. Res., 53: HelenPrabha, K. and S. Valarmathy, Fetal electrocardogram usng anfs wth gamma adaptatons. Int. J. HI ran. ECC, 2: Jang, J.S.R., 993. AFIS: adaptve-network-based fuzzy nference system. IEEE rans. Syst. Man Cybern, 23: DOI: 0.09/ Khamene, A. and S. egahdarpour, A new method for the extracton of fetal ECG from the composte abdomnal sgnal. IEEE rans. Bomedcal Eng., 47: DOI: 0.09/ Paraschv-Ionescu, A., C. Jutten, K. Amnan, B. ajaf and P. Robert, Source separaton n strong nosy mxtures: A study of wavelet denosng preprocessng. IEEE Int. Conf. Acoustcs Speech Sgnal Process., 2: Swarnalatha, R. and D.V. Prasad, 200a. A novel technque for extracton of FECG usng mult stage adaptve flterng. J. Appled Sc., 0: Swarnalatha, R. and D.V. Prasad, 200b. Maternal ECG cancellaton n abdomnal sgnal usng AFIS and wavelets. J. Appled Sc., 0: DOI: /jas akag,. and M. Sugeno, 985. Fuzzy dentfcaton of systems and ts applcatons to modelng and control. IEEE rans. Syst. Man Cybermetcs, 5: Vjla, C.K.S. and P. Kanagasabapathy, Adaptve neuro fuzzy Inference System for extracton of fecg. IEEE IDICO. DOI: 0.09/IDCO Vjla, S.C.K., M.E.P. Kanagasabapathy and S. Johnson, Fetal ECG extracton usng softcomputng technque. J. Appled Sc., 6: Al-Zaben, A. and A. Al-Smad, Extracton of foetal ECG by combnaton of sngular value decomposton and neuro-fuzzy nference system. Phys. Med. Bol., 5: PMID: