PPG-BASED HEART RATE ESTIMATION USING WIENER FILTER, PHASE VOCODER AND VITERBI DECODING. Andriy Temko

Transcription

1 G-BASED HEART RATE ESTIMATION USING WIENER FILTER, HASE VOODER AND VITERBI DEODING Andriy Temko Irish ener for Feal and Neonaal Translaional Research, Universiy ollege ork, Ireland ABSTRAT Accurae HR esimaion from he phooplehysmographic (G) signal during inensive physical exercises is ackled in his paper. Wiener filers are designed o aenuae he influence of moion arifacs. The phase vocoder is used o improve he iniial DFT-based frequency esimaion. Addiionally, Vierbi decoding is used as a novel posprocessing sep o find he pah hrough ime-frequency saespace plane. The sysem performance is assessed on a publically available daase of 3 G recordings. The resuling algorihm is designed for scenarios ha do no require online HR monioring (swimming, offline finess saisics). The resulan sysem wih an error rae of.37 beas per minue ouperforms all oher sysems repored odae in lieraure and in conras o exising alernaives requires no parameer o une a he pos-processing sage and operaes a a much lower compuaional cos. The Malab implemenaion is provided online. Index Terms hooplehysmography, moion arifacs, specrum esimaion, Vierbi decoding. INTRODUTION Wearable devices such as wris-bands, smar-waches, are equipped wih a number of sensors and offer many useful finess racking feaures. hooplehysmography (G) based hear rae (HR) monioring has become a popular alernaive o radiional Elecrocardiography as i allows for HR monioring a he peripheral posiions such as earlobes, fingerips or wriss which is seen much more convenien []. G sensors which are embedded in hese wearable devices emi ligh o he skin and measure he changes of inensiy of he ligh which is refleced or ransmied hrough he skin. The periodiciy of hese measuremens in mos cases corresponds o he cardiac rhyhm, and hus, HR can be esimaed from he G signal [, ]. During physical exercise he G signal is corruped wih moion arifacs (MAs). MAs significanly affec he accuracy of HR esimaion in free living condiions hus prevening he sraigh-forward usage of G. A number of mehods have been proposed o remove or aenuae MAs in G signals using he simulaneously recorded acceleromeer signals. These mehods include adapive filering [3, 4, 5, 6], independen componen analysis [7], decomposiion models [8, 9, 0, ], specral subracion [, 3, 4], and Kalman filering [5]. Along wih de-noising rouines he accurae mehods uilize sophisicaed pos-processing of HR esimaes [, 6, 8, 0,, 4]. The pos-processing seps ofen include specral peak deecion, peak selecion, emporal peak racking, smoohing, ec. The pos-processing is usually composed of several heurisic if-hen rules and associaed hresholds. These hresholds are uned and esed on he same daa. However, when reporing he resuls, he effec of posprocessing is ofen overlooked. This work enhances he previously developed HR esimaion sysem [6] wih a hreshold-free pos-processing sep. Specifically, a ime-frequency specrogram is seen as a sae-space marix of emission probabiliies and he Vierbi decoding algorihm is used o find he mos probable pah hrough he G recording.. DATABASE AND METRIS The daase which is publically available (hp://zhilinzhang.com/spcup05/daa.hml) consiss of 3 5-min recordings of subjecs performing various physical exercises ranging from walking or running on a readmill (recordings -) o jump-ups or boxing (recordings 3-3). Each recording consiss of wo G and hree acceleromeer signals. The EG signal which was recorded simulaneously from he ches was used o provide he ground ruh HR in BM as described in deail in [, 8]. EG-based HRs were calculaed for every 8s window wih a s shif. The same window lengh and shif are suggesed for HR esimaion from G o have he same number of HR esimaes and rue HRs. All signals were sampled a 5 Hz. The convenional merics o measure he performance of developed HR esimaors are based on he Absolue Error (AE) of each esimae: This research was suppored by a Science Foundaion Ireland eners Award (/R/7) and Wellcome Trus Seed Award in Science (00704/Z/6). 07 IEEE. ersonal use of his maerial is permied. However, permission o reprin/republish his maerial for adverising or promoional purposes or for creaing new collecive works for resale or redisribuion o servers or liss, or o reuse any copyrighed componen of his work in oher works mus be obained from he IEEE.

2 G Acceleromeer re-processing DFT Wiener Filer hase Vocoder Vierbi Decoding Fig.. The flowchar of he developed HR esimaion sysem (WFV+VD). AE i = BM es ( i) BM ( i) rue () 3. HR ESTIMATOR DESIGN where BM es(i) and BM rue(i) denoe he esimaed and he rue HR value in he i-h ime window in BM, respecively. To summarize he performance for a whole recording, Average Absolue Error (avae) and Sandard Deviaion of he Absolue Error (sdae) are repored: N avae = AE i N i= () N i N i = ( ) sdae = AE avae where N is he oal number of esimaes (number of windows). These merics are compued for each of he 3 recordings and he average performance across subjecs is repored. (3) The flowchar of he developed sysem (WFV+VD) is shown in Fig.. The G and acceleromeer signals are segmened o 8s windows wih s shif, filered wih a 4h order Buerworh band-pass filer (0.4-4Hz) and downsampled from 5 o 5 Hz as shown in Fig. (a). The G signals are hen normalized o zero mean and uni variance and averaged. The signals are hen subjeced o he DFT wih he number of bins se o 04. The conen ha corresponds o he HR beween 60 BM and 80 BM is kep as shown in Fig. (b). Wiener filering [7] is applied o aenuae he effec of MA in he G signal. The frequency-domain Wiener filer is given as: W ( f ) = XX XX ( f ) ( f ) + ( f ) (4) (b) (a) (c) (d) Fig.. Signal ransformaion in he developed HR esimaion sysem. lo (a) shows wo G and hree acceleromeer signals afer filering; (b) shows he specral envelope and is maximum afer he DFT is applied o he G, (c) shows he processed specral envelope and is maximum afer MAs were aenuaed wih Wiener filering; (d) shows he maximum of he specral envelop before and afer he phase vocoder.

3 The noise specrum,, is esimaed from he acceleromeer signals. The clean G specrum, XX, can be esimaed as (f) (f) or recursively from previous filer oupus. Depending on how he power specrum of he clean G signal is esimaed, (, k) w wo Wiener filers are implemened: (, k) = ( i, k) w (, k) = i = + i= i= ( i, k) w ( i, k) ( i, k) w ( i, k) + (, k) (5) (6) (a) where w(,k) is he weigh of he k-h frequency bin a ime,. The power specrum of he observed signal is averaged over he pas specral envelopes ( =, =3). If =0, hen he Wiener filer in Eq. 5 performs a simple version of specral subracion. The oupus of boh Wiener filers are normalized by heir sandard deviaion and averaged o represen he final specral envelope of he cleaned G signal. The dominan frequency (he frequency wih he highes magniude) is convered o he HR esimae in BM as shown in Fig. (c). The minimum frequency ha can be esimaed (he Rayleigh frequency) is limied by he size of he window of he analyzed daa (8s) and equals o /8*60 = 7.5 BM. Apar from zero-padding which is used o inerpolae he specral envelope o oher frequencies by decreasing he frequency spacing beween neighboring DFT bins, he frequency esimae is improved by means of he phase vocoder echnique [8 0]. hase changes beween wo consecuive frames encode he deviaion of he rue frequency from he bin frequency. Thus he phases from he chosen peak in he magniude specrum from he curren and previous frames can be used o refine he iniial frequency esimaion: / (7) where θ, θ are he wo phases from he curren and previous frames, respecively;, are he ime samps of he wo frames, here - is a windows shif and is equal o s, n is an ineger. The values of ϕ new are compued for several n using Eq. 7, and he value ha is closes o he iniial frequency esimaion is chosen. In his manner he dominan frequency peak is adjused accordingly as shown in Fig. (d). The novel sep proposed in his work performs posprocessing in a probabilisic framework using Vierbi decoding []. The specrogram of a cleaned G recording (afer Weiner filering) is considered as a N-by-T sae-space map of emission probabiliies (likelihoods), B, for N saes (discree values of HR as deermined by he size of DFT) and (b) Fig. 3. (a) Time-frequency sae-space plane of DFT magniudes considered as log emission probabiliies, wih superimposed ground ruh HRs in whie. The oupu of Vierbi decoding is shown in black. (b) a marix of esimaed log ransiion probabiliies. Bes viewed in colour. T observaions (ime windows), where B j is a magniude value of he j h DFT bin for he h ime window. An example of emission probabiliy marix is shown in Fig. 3(a) for rec.. The N-by-N marix of ransiion probabiliies, A, where A ij represens he probabiliy of changing from he i h HR o he j h HR, is esimaed from he ground ruh by couning he ransiions using he leave-one-recording-ou procedure. In his manner, he ground ruh of he esing recording is never used bu he ground ruhs of all oher recordings are used o esimae he ransiion probabiliy marix. An example of a log ransiion probabiliy marix is visualized in Fig. 3(b). I can be seen ha he variance of he ransiion probabiliies increases wih he increase of HR. The Vierbi algorihm is hen applied o recursively esimae he mos likely pah (he pah wih he highes cumulaive log probabiliy) hrough he ime dimension,, using emission and ransiion probabiliy marices, B, A: argmax! " #$ % &, (8) where! max! "#$ % &) %, * * +,and * * /, and! # ), * # * /

4 The prior probabiliies, π i, are approximaed as diag(a). Afer he recursion is compued he sae sequence is backracked as: # 0 argmax! 0 #, (9) # = 3 # 3,=+,+,, The sae sequence is convered o HR esimaes which are hen smoohed wih a cenral moving average filer. The Vierbi decoding effecively performs pos-processing in a hreshold-free probabilisic manner. 4. RESULTS AND DISUSSION Table I deails he performance of he sysem. On he daabase of 3 recordings, he sysem resuls in an avae of.3 BM wih sdae of.77 BM. Table I also shows he performance of he sysem if a cerain block from Fig. is removed. This gives an indicaion of he conribuion of each sysem consiuen owards he final performance. I can be seen ha wihou Wiener filering (W/o WF in Table I), he performance degrades from.3 o 5.7 BM. This resul represens a HR esimaion sysem ha does no address MAs and also shows he effec of MAs in he daabase. Using only WF resuls in an avae of.43 BM while using only WF resuls in an avae of.46 BM, o compare wih he avae of.3 BM using boh filers combined. A refinemen inroduced by he phase vocoder reduces he error from.47 o.3 BM (W/o V in Table I). Finally, he sysem performance wihou Vierbi posprocessing (W/o VD) resuls in an avae of 5.86 BM. I can be seen ha pos-processing of HR esimaions has a significan effec on he performance, similar in size o he conribuion of signal de-noising. The pos-processing seps in approaches which were previously evaluaed on he same daase usually rely on a number of heurisic rules and hresholds [, 8, 6, 0,, 4]. These rules and hreshold values are uned and esed on he same daa and he bes possible resuls are usually repored. In his manner, he number of rules (degrees of freedom) is direcly linked o an improved performance bu i comes a he cos of an increased risk of poor generalizaion on he unseen daa. I is worh emphasizing ha in his work he proposed pos-processing requires no hresholds and is performed in he wellesablished probabilisic framework. Table II provides a comparison wih oher HR esimaion algorihms. Many developed sysems repor resuls only on an easier par of he daase (he firs G recordings) [6, 0, ]. These Gs are capured during running on a readmill. The recordings are less corruped wih irregular MAs. Only a few echniques are evaluaed on a more difficul par of he daase (he las 0 recordings), in addiion o he firs. This is replicaed here for comparaive purposes (ha is he WFV+VD is evaluaed on recordings excluding rec. 3). These sysems include: a hree-sage mehod which TABLE I. ERFORMANE OF HR ESTIMATION SYSTEM WFV+VD ON 3 G REORDINGS WFV+VD W/o WF W/o V W/o VD avae All sdae TABLE II. OMARISON OF HR ESTIMATION SYSTEMS ON G REORDINGS TROIKA JOSS SpaMa Specrap WFV+VD avae is based on signal decomposiion, sparsiy-based highresoluion specrum esimaion, and specral peak racking and verificaion (TROIKA, []); a mehod which joinly esimaes he specrum of G and acceleromeer signals using a common sparsiy consrain on he specral coefficiens (JOSS, [8]); a ime-varying specral filering algorihm for reconsrucion of moion arifac (SpaMa, [3]), a HR esimaion algorihm based on asymmeric leas squares specrum subracion and Bayesian decision heory (Specrap, [4]). As i can be seen from Table II, he WFV+VD sysem ouperforms every mehod on he daabase. I is worh menioning ha he firs hree mehods perform online processing, whereas Specrap is he only mehod ha performs offline processing. Vierbi decoding in his work requires he specrogram of he whole recording o be available beforehand. The proposed algorihm akes under 0s o process he whole G daase of 3 recordings (Malab Inel ore E700.5GHz). This ime compares favorably wih oher echniques published. I is repored ha o process he firs G recordings TROIKA [] and IMAT [6] akes several hours, JOSS [8] akes 300s, EEMD [0] akes 00s. The presened sysem wih is superior accuracy and a comparaively low compuaional cos can be used for HR monioring for swimmers or calculaion of HR summary saisics. Boh asks require quick processing bu do no require on-he-fly HR esimaion. For he purpose of reproducibiliy he Malab implemenaion along wih he main resuls is available online (hps://gihub.com/andem000/g). 5. ONLUSIONS This work proposed an alernaive hreshold-free sep o posprocess HR esimaes which were derived from G. I was shown ha HR esimae pos-processing and moion arefac rejecion had a commensurable effec on he performance. Vierbi decoding was applied o specrogram o find he pah hrough ime-frequency sae-space plane of HR esimaes. Evaluaed on a publicly available daase he sysem resuled in an error of.37 BM which ouperformed alernaives repored o-dae. The novel pos-processing requires no parameer o une and resulan sysem operaes a a much lower compuaional cos.

5 6. REFERENES [] J. Allen, hooplehysmography and is applicaion in clinical physiological measuremen, hys Meas, v. 8, pp. -39, 007. [] Z. Zhang, Z. i, B. Liu, TROIKA: A General Framework for Hear Rae Monioring Using Wris-Type hooplehysmographic Signals During Inensive hysical Exercise, IEEE Trans Biomed Eng, v. 6, pp. 5-53, 05. [3] R. Yousefi, M. Nourani, S. Osadabbas, and I. anahi, A moion-oleran adapive algorihm for wearable phooplehysmographic biosensors, IEEE J Biomed Healh, v. 8, pp , 04. [4] M. Ram, K. V. Madhav, E. H. Krishna, N. R. Komalla, and K. A. Reddy, A novel approach for moion arifac reducion in G signals based on AS-LMS adapive filer, IEEE Trans Insrum Meas, v. 6, pp , 0. [5] H. an, D. Temel, G. AlRegib, HearBEAT: Hear bea esimaion hrough adapive racking, in roc. IEEE EMB, 06. [6] M. Mashhadi, E. Asadi, M. Eskandari, S. Kiani, F. Marvasi, Hear Rae Tracking using Wris-Type hooplehysmographic (G) Signals during hysical Exercise wih Simulaneous Acceleromery, IEEE Signal rocessing Leers, v. 3, 06. [7] B. Kim, S. Yoo, Moion arifac reducion in phooplehysmography using independen componen analysis, IEEE Trans Biomed Eng, v. 53, pp , 006. [8] Z. Zhang, hooplehysmography-based Hear Rae Monioring in hysical Aciviies via Join Sparse Specrum Reconsrucion, IEEE Trans Biomed Eng, v.6, pp , 05. [9] X. Sun,. Yang, Y. Li, Z. Gao, and Y.-T. Zhang, Robus hear bea deecion from phooplehysmography inerlaced wih moion arifacs based on empirical mode decomposiion, in roc. IEEE BHI, pp , 0. [0] E. Khan, F. Al Hossain, S. Uddin, S. Alam, M. Hasan, A Robus Hear Rae Monioring Scheme Using hooplehysmographic Signals orruped by Inense Moion Arifacs, IEEE Trans Biomed Eng. v.63, pp , 06. [] J. Xiong, L. ai, D. Jiang, H. Song, X. He, Specral Marix Decomposiion-Based Moion Arifacs Removal in Muli- hannel G Sensor Signals, IEEE Access, 06. [] H. Fukushima, H. Kawanaka, M. Bhuiyan, and K. Oguri, Esimaing hear rae using wris-ype phooplehysmography and acceleraion sensor while running, in roc. IEEE EMB, pp , 0. [3] S. Salehizadeh, D. Dao, J. Bolkhovsky,. ho, Y. Mendelson, K. hon, A Novel Time-Varying Specral Filering Algorihm for Reconsrucion of Moion Arifac orruped Hear Rae Signals During Inense hysical Aciviies Using a Wearable hooplehysmogram Sensor, Sensors, 6(), 06. [4] B. Sun, Z. Zhang, hooplehysmography-based hear rae monioring using asymmeric leas squares specrum subracion and bayesian decision heory, IEEE Sensors J., v. 5, pp , 05. [5] B. Lee, J. Han, H. Baek, J. Shin, K. ark, and W. Yi, Improved eliminaion of moion arifacs from a phooplehysmographic signal using a kalman smooher wih simulaneous acceleromery, hysiol Meas, vol. 3, no., pp , 00. [6] A. Temko, Esimaion of Hear Rae from hooplehysmography during hysical Exercise using Wiener Filering and he hase Vocoder, in roc. IEEE EMB, Aug. 05. [7] R. Brown,. Hwang. Inroducion o Random Signals and Applied Kalman Filering (3 ed.). New York: John Wiley & Sons, 996. [8] J. Flanagan, R. Golden, hase Vocoder, Bell Sysem Technical Journal, , 966. [9] T. Duoi, F. Marquès. Applied Signal rocessing A MATLAB-Based roof of oncep. Springer, 009. [0] A. Temko, W. Marnane, G. Boylan, G. Lighbody, linical Implemenaion of a Neonaal Seizure Deecion Algorihm, Decis Suppor Sys, v.70, pp , 05. [] L. Rabiner, A uorial on hidden Markov models and seleced applicaions in speech recogniion, roc. of he IEEE, v. 77, pp , 989.