Research and Simulation of FECG Signal Blind Separation Algorithm Based on Gradient Method

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1 Research Joural of Appled Sceces, Egeerg ad Techology 4(6): , 202 ISSN: Maxwell Scetfc Orgazato, 202 Submtted: March 23, 202 Accepted: Aprl 20, 202 Publshed: August 5, 202 Research ad Smulato of FECG Sgal Bld Separato Algorthm Based o Gradet Method Yu Che ad Cheg Zhao Zhegzhou Isttute of Aeroautcal Idustry Maagemet, Hea, Zhegzhou, 45005, Cha Abstract: Idepedet Compoet Aalyss (ICA) s a ew developed sgal separato ad dgtal aalyss techology recet years. ICA has wdely used because t does ot eed to kow the sgal pror formato, whch has became the hot spot sgal processg feld research. I ths study, we frstly troduce the prcple, meag ad bld source separato algorthm based o the gradet. By usg the tradtoal atural gradet algorthm ad Equ-varat Adaptve Source Separato va Idepedet (EASI) bld separato algorthm, mxg ECG sgals wth oses had bee separated effectvely to the Materal Electrocardograph (MECG) sgal, Fetal Electrocardograph (FECG) sgal ad ose sgal. The algorthm separato test showed that EASI algorthm ca better separate the fetal ECG sgal ad because the gradet algorthm s a kd of ole algorthm, whch ca be used for clcal fetal ECG sgal of the real-tme detecto wth mportat practcal value ad research sgfcace. Keywords: Bld sgal separato, EASI algorthm, FECG, gradet algorthm, MECG INTRODUCTION FECG s a objectve dcators reflectg the fetal heart actvty, whch ca determe the fetal heart rate, judge whether the fetal s dstress, multple brths, fucto parameter aalyss of heart ad to prevet the eoatal dsease (L et al., 2002). At preset, the FECG acqusto method bascally have two kds, the fetal scalp electrode ad materal abdomal sk electrode. Fetal scalp electrode method wll ot oly damage to the fetal ad caot be used pregacy. Materal abdomal sk electrode has the advatage of ts coveet, ovasve ad ca be used pregacy, so, the medcal workers ad pregat wome have the deeply welcome (Ahmad et al., 2008). Because FECG sgal s very weak ad mxed wth strog backgroud ose, such as MECG (Zhewe ad Chagshu, 2007), power frequecy terferece ad basele drft ad so o, FECG accurate extracto ad aalyss s more dffcult. So, lookg for a effectve sgal separato method of FECG has mportat theoretcal sgfcace ad clcal applcato value. ICA s a recetly developed ew sgal separato techology (Yag et al., 20), whch s frst proposed by Jutte ad Herault (99) the H-J algorthm s put forward based o the eural etwork techology. Jutte ad Herault (99) I 994, Commo frst put forward the ICA cocept (Como, 994), the basc deas s solated the orgal sgal form the multple source sgal lear mxed. Besdes assumptos source sgal s depedet of the statstcs, wthout ay other pror kowledge. ICA s developed wth bld sgal separato problem, so t s also kow as the Bld Source Separato (BSS). ICA techology has developed ad applcated the felds of commucatos, mage processg, physologcal medcal sgal processg, speech sgal processg, feature extracto, etc., Cchock ad Amar (2002) ad Barros ad Cchock (200). Amog the BSS algorthm, the gradet algorthm s a kd of classc ucostraed optmzato algorthm, the prcple s smple, easy to realze, wth equ-varat characters, whch ca realze the ole calculato ad has bee wdely used BSS. We ad Che (202) Ths study maly troduced the EASI algorthm based o the gradet model ad through the FECG separato smulato expermet, we ca accurately get the FECG from the bld mxed sgals. METHODOLOGY Mmum mutual formato crtero: If we suggest m umbers of source sgal ad sesor, there s a basc relatos betwee the measuremet sgal ad source sgal, whch s show as formula (). L ad Zhag (2006): x(t) = AS(t)+(t) () The observato sgal s X(t): X(t) = [x (t), x 2 (t),., x m (t)] T (2) X (t) s stataeous lear mxed sgal by the umbers of source sgal of S(t) = [S (t), S 2 (t),, S (t)] T, S(t) s source sgal matrx ad =, 2,...,, whch s Correspodg Author: Yu Che, Zhegzhou Isttute of Aeroautcal Idustry Maagemet, Hea, Zhegzhou, 45005, Cha 2707

2 Res. J. Appl. Sc. Eg. Techol., 4(6): , 202 umbers of mutually depedet radom sgals. Mxg matrx A = a ad =, 2,..., m, j =, 2,...,. I formula (), (t) s ose jammg sgal mxg the source sgal, source sgal separato problem s to estmate the system matrx W, whch makes the Y (t) passg through the X (t) s the estmato value of the source sgal. That s the formula (3) as bellow: Y(t) = WX(t). S(t) (3) The Mmum Mutual Iformato (MMI) (Wu ad Ya, 20) s to fd a accurate eural etwork weght value of matrx W, whch makes each compoet of output Y(t) to have the mmze depedeces, eve to zero ad acheves the purpose of separato true. We ca use etropy to express the depedeces betwee sgals. The depedece s expressed by the Kullback- Lebler degree betwee the jot probablty desty fucto p (Y, W) ad the product of the edge probablty desty fucto py ( ): pyw (, ) IW ( ) = pyw (, )log dy... dy py ( ) Amog the formula (4), duet to the characters of the Kullback-Lebler degree, mutual formato s oegatve, t s that, I(W) $0. Whe ad oly whe each compoets s mutual depedece, the mutual formato of Y(t) s equal to zero. That s pyw (, ) = p( y). (4) I (W) takes the mmal whe the compoet of Y(t) depedece each other. Ths s sutable for the measuremet of depedece formato. For the estmates sgal Y(t) to the bld separato problem, the mutual formato s as formula (5): pyw (, ) IW ( ) = pyw (, )log dy py ( ) = pyw (, )log pywdy (, ) py ( )log py ( ) dy (5) Accordg to the dfferetal etropy value defto of the cotuous radom varable: Hx ( ) = px ( )log pxdx ( ) (6) We ca get the formula (7) betwee put sgal ad output sgal etropy by y = Wx: H(y) = H(x) + log W (7) Therefore, we ca express the formula (5) as the mutual formato etropy, whch s show as formula (8): IW ( ) = HYW ( ; ) + Hy ( ; W) (8) The mutual formato I(W)$0 ad Perre Commo proved the mutual formato amot sa comparso fucto of ICA. That s I(W) = 0, f W = 7PA G. Whe the every compoet of Y(t) = WX(t) = 7PA G X(t) s depedet, I(W) equals to zero. Ad Y(t) = WX(t) = 7PS (t). S(t), here, 7 s ay reversble dagoal matrx, P s ay substtuto matrx. Bss algorthm based o gradet method: Because the bld separato problem s complex ad havg o uversal aalyss soluto, ear te years, researchers had doe some smple hypothess ad put forward may good approxmato soluto based o the source sgal s statstcal propertes. The exstg gradet separato algorthm clude the mprovemet Ifomax algorthm, atural gradet algorthm, equ-varat adaptve source separato va depedet algorthm ad verse terato algorthm, etc. Bell ad Sejowsk (995) put forward a kd of sgle feed forward eural etwork algorthm. Its characterstc s mxed by the W soluto, the each compoet y of output y respectvely uses a reversble drab olear fucto g (y ) to treated ad after gvg a approprate g (y ), through adjustg the W to make comprehesve formato etropy H (g (y)) of g (y) largest. Usg the radom gradet descet optmzato algorthm ad adoptg the stataeous or radom gradet stead of the real gradet, the radomzed gradet algorthm ca be gotte as formula (9): )W = :[W -T -g(y)x T ] (9) Amog formula, : s step legth, g(y) s gve olear fucto, g(y) s each compoet of vector y executg gve scalar fucto g(y). Ifomax algorthm ca effectvely separate more super gaussa source sgal. The dsadvatage of ths algorthm s that the covergece speed s slow ad volves the verse of the separato matrx W, oce the codto umber of W becomes poor, the algorthm ca expad. If rght multplcato W T W of the radomzed gradet, we ca get the atural gradet, the atural gradet algorthm s show as formula (0). )W = :[I - g(y)y T ]W (0) 2708

Res. J. Appl. Sc. Eg. Techol., 4(6): 2707-27, 202 8 6 4 2 0-2 -4-6 0 200 400 600 800 000 (a) Mxg observato source sgal 8 6 4 2 0-2 -4-6 -8 0 200 400 600 800 000 (b) MECG sgal Fg.

: Source sgal The atural gradet algorthm ca't guaratee orthogoalty of separatg matrx W teratve processes, Cardoso, etc put forward a kd of the equal chagg adaptve depedet separato algorthm.

3 Res. J. Appl. Sc. Eg. Techol., 4(6): , (a) Mxg observato source sgal (b) MECG sgal Fg. 2: Separato sgals by usg atural gradet algorthm Fg. : Source sgal The atural gradet algorthm ca't guaratee orthogoalty of separatg matrx W teratve processes, Cardoso, etc put forward a kd of the equal chagg adaptve depedet separato algorthm. The ma characterstc of EASI algorthm s to use relatve gradet stead of radomzed gradet ad mx the umeral algorthm ad separato algorthm together, whch decomposes the separato matrx W to the product of orthogoal matrx ad albo matrx. EASI algorthm s show as formula (): )W = :[I yy T - g(y)y T + yg(y) T ]W () Algorthm applcato the FECG separato: I order to prove the accuracy separatg the FECG, we obta the actual measuremet sgal from the mother s belly, the processg of sgal collecto, may ose such as work frequecy terface, MECG, etc., wll mx, the mx observato sgal s show as Fg. a. MECG s show as Fg. b. BSS SIMULATION We suggest the observato sgal cotag the fetal ECG, motheral ECG ad the ose sgal, etc. The atural gradet algorthm ad EASI algorthm were carred out the mxed sgal BSS ad the results by usg atural gradet separato algorthm ad EASI algorthm to separate the source sgals are show as Fg. 2. Fg. 3: Separato sgals by usg EASI algorthm Fgure 2 s the result by usg the atural gradet algorthm, (a) s ose sgal, (b) s FECG, (c) s MECG. The Arrow Fg. 2 descrbes the sgular pot that ca ot be separated out of the MECG. From the separato result we ca see, MECG stll has FECG by usg the atural gradet algorthm ad we use crcle to pot out. From the Fg. 2b ad c we ca see, separatg the FECG from the mxg sgal, part of ose ca ot be separated from the mxg source sgal. Adoptg EASI algorthm to separate the mxg source sgal, the result s show as Fg. 3. Amog the Fg. 3a s the ose sgal, b s FECG ad c s MECG. From the separato result we ca see, we ca completely separate the MECG, FECG ad the ose sgal by usg EASI algorthm. Comparg BSS algorthm: From the materal ECG sgals we ca measure the posto of each heart beatg ad we compare the atural algorthm ad EASI algorthm, the results are show as Table. 2709

4 Table : Materal heart-beat posto compare betwee the separated sgal ad source sgal Source sgal Natural gradet EASI algorthm MECG value (tme) algorthm (tme) (tme) Res. J. Appl. Sc. Eg. Techol., 4(6): , 202 Table 2: Fetal heart-beat posto compare betwee separated sgal ad source sgal Natural gradet EASI algorthm FECG value (samplg pot) (samplg pot)! 8 8 2! ! ! ! ! ! ! ! ! Fg. 5: Frequecy spectrum by usg the EASI algorthm sgular frequecy pot the MECG. The frequecy eergy dagram EASI separato algorthm s show as Fg. 5. I Fg. 5a s the frequecy spectrum of the ose sgal, b s the frequecy spectrum of the FECG, c s the frequecy spectrum of the MECG. From the Fg. 5 we ca see, the sgular frequecy pot s ot obvously the Fg. 4c, whch s more smooth ad proves that the fetal ECG ca ot be separated by the atural gradet algorthm. Ad the expermet results proves the EASI algorthm ca separate the mxed sgal better tha the atural gradet algorthm. CONCLUSION Fg. 4: Frequecy spectrum by usg the atural gradet algorthm From the separato result, comparg the separato MECG by the atural algorthm ad EASI algorthm wth the actual MECG. The heart beatg posto of separato sgal by usg the atural gradet algorthm ad EASI algorthm are show as Table 2. From Table 2 ca see the FECG separato result s basc same ad the two kds of the separato algorthm verfed the separato effcecy each other. The frequecy eergy dagram atural gradet separato algorthm, whch s show as Fg. 4. I Fg. 4a s the frequecy spectrum of the ose sgal, b s the frequecy spectrum of the FECG, c s the frequecy spectrum of the MECG. We ca fd the Ths study detaled study the bd sgal separato algorthm, through usg the atural gradet algorthm ad EASI algorthm, we ca get FECG from the bld mxed ECG. The smulato result realzes the mxed sgal separato effectvely. I addto, through comparg the two algorthm, we ca fd the EASI algorthm s better tha the atural gradet algorthm. The gradet algorthm ca realze ole bld separato, whch ca be appled to the clcal fetal dsease motorg ad ole protecto. REFERENCES Ahmad, M., M. Ayat, K. Assaleh ad H. Al-Nashash, Fetal ECG sgal ehacemet usg polyomal classfers ad wavelet deosg. Iteratoal Coferece o Bomedcal Egeerg, Caro, pp: -4. Barros, A.K. ad A. Cchock, 200. Extracto of specfc sgals wth temporal structure. Neural Comput., 3(9):

5 Res. J. Appl. Sc. Eg. Techol., 4(6): , 202 Bell, A.J. ad T.Y. Sejowsk, 995. A formato maxmzato approch to bld separato ad bld decovoluto. Neural computato, 7: Cchock, A. ad S. Amar, Adaptve Bld Sgal ad Image Processg. Joh Wley ad Sos Ltd., Eglad. Como, P., 994. Idepedet compoet aalyss, a ew cocept. Sgal Proc., 36: Jutte, C. ad J. Herault, 99. Bld separato of source, Part I: A adaptve algorthm based o eurommetc archtecture. Sgal Proc., 24(): -0. L, G. ad J. Zhag, Adaptve step-sze EASI algorthm based o separatgmatrx. Shp Sc. Tech., 28(5): L, X., B. Hu ad X. Lg, The extracto of FECG based o BSS. Chese J. Bomed. Eg., 0(5): We, X. ad Y. Che, 202. Research of bld source separato o the speech sgal based o atural gradet method. Iform. Tech. J., 3: Wu, Z. ad S. Ya, 20. Study o mechacal ose separato based o techque of bld source. J. Zhejag U. Sc. Tech., 5(4): Yag, S.P., Wu X. P ad Zhag L. 20. Fetal ECG extractg system based o ICA. Comput. Syst. Appl. 20, (9): Zhewe, S., Chagshu, Z., Sem-bld source extracto for fetal electrocardogram extracto by combg o-gaussaty ad tme-correlato, Neurocomputg, 70, (7-9):

Nonlinear Blind Source Separation Using Hybrid Neural Networks*

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