RADIOELECTRONIC AND COMPUTER SYSTEMS

The research subject of the article is the methods of locally adaptive filtering of non-stationary (from the point of view of its variance) noise in long-term electrocardiogram (ECG) signals. The goal is to develop locally adaptive algorithms for filtering noise with different a priori unknown levels of variance in real-time for ECG signals recorded with a standard sampling rate of 500 Hz. The tasks to be solved are: to investigate the effectiveness of the developed adaptive ECG filtering algorithms using numerical statistical estimates of processing quality in a wide range of additive Gaussian noise variance variation, to investigate the suppression of real non-stationary electromyographic (EMG) noise, and to analyze the application for normal and pathological ECG signals. The methods are integral and local indicators of the filter quality according to the criteria of the mean square error and the signal-to-noise ratio was obtained using numerical simulation (via Monte Carlo analysis). The following results were obtained: an adaptive method for real-time suppression of non-stationary noise in the ECG is proposed, the one-pass and the two-pass algorithms, and the algorithm with selective depending on the preliminary estimates of noise levels re-filtering have been developed on the method basis. Statistical estimates of the filters' efficiency and analysis of their outputs show a high degree of suppression of the noise with different levels of variance in the ECGs. The distortions absence while processing QRS-complex and high efficiency of suppression of Gaussian and real EMG noise with varying variance are demonstrated. The analysis of the output signals and plots of the local adaptation parameters and the adaptable parameters of the proposed algorithms confirms the high efficiency of filtering. The developed algorithms have been successfully tested for normal and pathological ECG signals. Conclusions. The scientific novelty of the results is the development of a locally adaptive method with noise and signal-dependent filter parameters switching and of the adaptive algorithms based on this method for non-stationary noise reduction in the ECG in real-time. This method does not require time for filter parameters adaptation and a priori information about the noise variance, and it has a high-speed performance in real-time mode.

real-time adaptive filtering of the electrocardiogram signal; non-stationary electromyographic noise; statistical estimates of efficiency

Bolezni serdechno-sosudistoi sistemy: Vnutrennie bolezni. Kniga 5. [Diseases of the cardiovascular system: Internal diseases. Book 5]. Editors: E. Braunwald, K. J. Isselbacher, R. Q. Petersdorf, et al. Moscow, Meditsina Publ., 1995. 448 p.

Dabrovski, A., Dabrovski, B., Piotrovich R. Sutochnoe monitorirovanie EKG [Holter ECG monitoring]. Moscow, Medpraktika Publ., 2000. 208 p.

Martin, T., Jovanov, E., Raskovic, D. Issues in wearable computing for medical monitoring applications: a case study of a wearable ECG monitoring device. Digest of Papers. Fourth International Symposium on Wearable Computers, Atlanta, GA, USA, 2000, pp. 43-49. DOI: 10.1109/ISWC.2000.888463.

De Luca, C. J. Physiology and mathematics of myoelectric signals. IEEE Transactions on Biomedical Engineering, 1979, vol. 26, no. 6, pp. 313-325. DOI: 10.1109/TBME.1979.326534.

Kligfield, P., Gettes, L. S., Bailey, J. J., et al. Recommendations for the standardization and interpretation of the electrocardiogram: Part I: The electrocardiogram and its technology. A scientific statement from the American Heart Association Electrocardiography and Arrhythmias Committee, Council on Clinical Cardiology; the American College of Cardiology Foundation; and the Heart Rhythm Society endorsed by the International Society for Computerized Electrocardiology. Journal of American College of Cardiology Foundation, 2007, vol. 49, pp. 1109-1127. DOI: 10.1016/j.hrthm.2007.01.027

Dotsinsky, I., Christov, I., Daskalov, I. Assessment of metrological characteristics of digital electrocardiographs. Journal of Clinical Engineering, 1996, vol. 21, pp. 156-160.

Rangayyan, R. M. Analiz biomeditsinskikh sig-nalov. Prakticheskiy podkhod [Biomedical signal analysis. A case-Study Approach]. Moscow, FIZMATLIT Publ., 2010. 440 p.

Willigenburg, N. W., Daffertshofer, A., Kingma, I., van Dieën, J. H. Removing ECG contamination from EMG recordings: A comparison of ICA-based and other filtering procedures. Journal of Electromyography and Kinesiology, 2012, vol. 22, pp. 485-493. DOI: 10.1016/j.jelekin.2012.01.001.

Kalra, A., Lowe, A., Al-Jumaily, A. Critical review of electrocardiography measurement systems and technology. Measurement Science and Technology, 2018, vol. 30, no. 1. DOI: 10.1088/1361-6501/aaf2b7.

Öktem, R., Yaroslavsky, L., Egiazarian, K. Signal and image denoising in transform domain and wavelet shrinkage: A comparative study. In Proc. of EUSIPCO'98, 9th European Signal Processing Conference, Rhodes, Greece, 1998, pp. 1-4.

Öktem, H., Nikolaev, N., Gotchev, A., Egiazarian, K. ECG denoising approach aimed at detail preservation. Biosignal' 2000: Proc. of the Int. Conference, 2000, pp. 26-29.

Nikolaev, N., Gotchev, A., ECG signal denoising using wavelet domain Wiener filtering. EUSIPCO'2000: Proc. of the European Signal Processing Conference, 2000, pp. 51-54.

Nikolaev, N., Gotchev, A., Egiazarian, K., et. al. Suppression of electromyogram interference on the electrocardiogram by transform domain denoising. Medical and Biological Engineering and Computing, 2001, vol. 39, pp. 649-655. DOI: 10.1007/BF02345437.

Gotchev, A. Spline and Wavelet Based Techniques for Signal and Image Processing: Thesis for the degree of Doctor of Technology: 5th September, Tampere (Finland). Tampere University of Technology, 2003. 171 p.

Gotchev, A., Christov, I., Egiazarian, K. Denoising of electrocardiogram from electromyogram artifacts by combined transform-domain and dynamic approximation method. ICASSP'2002: Proc. of the IEEE Int. Conference on Acoustics, Speech and Signal Processing, 2002, pp. 3872-3875.

Christov, I., Gotchev, A., Bortolan, G., Neycheva, T., Raikova, R., Schmid, R. Separation of the electromyographic from the electrocardiographic signals and vice versa. A topical review of the Dynamic procedure. Int. J. Bioaotomation, 2020, vol. 24, no. 3, pp. 289-317. DOI: 10.7546/ijba.2020.24.3.000744.

Christov, I. I., Daskalov, I. K. Filtering of electromyogram artifacts from the electrocardiogram. Medical Engineering and Physics, 1999, vol. 21, pp. 731-736. DOI: 10.1016/S1350-4533(99)00098-3.

Bortolan, G., Christov, I., Simova, I., Dotsinsky, I. Noise processing in exercise ECG stress test for the analysis and the clinical characterization of QRS and T wave alternans. Biomedical Signal Processing and Control, 2015, vol. 18, pp. 378-385. DOI: 10.1016/J.BSPC.2015.02.003.

Christov, I., Neycheva, T., Schmid, R., Stoyanov, T., Abächerli, R. Pseudo real-time low-pass filter in ECG, self-adjustable to the frequency spectra of the waves. Medical and Biological Engineering and Computing, 2017, vol. 55, no. 9, pp. 1579-1588. DOI: 10.1007/s11517-017-1625-y.

Christov, I., Neycheva, T., Schmid, R. Fine tuning of the dynamic low-pass filter for electromyographic noise suppression in electrocardiograms. Computing in Cardiology, 2017, vol. 44, pp. 1-4. DOI: 10.22489/CINC.2017.088-007.

Christov, I., Raikova, R., Angelova, S. Separation of electrocardiographic from electromyographic signals using dynamic filtration. Medical Engineering and Physics, 2018, vol. 57, pp. 1-10. DOI: 10.1016/j.medengphy.2018.04.007.

Bortolan, G., Christov, I. Dynamic filtration of high-frequency noise in ECG signal. Computing in Cardiology, 2014, vol. 41, pp. 1089-1092.

Savitzky, A., Golay, M. Smoothing and differentiation of data by simplified least squares procedure. Analytical Chemistry, 1964, vol. 36, pp. 1627-1639. DOI: 10.1021/ac60214a047.

Dotsinsky, I. A., Mihov, G. S. Tremor suppression in ECG. BioMedical Engineering OnLine, 2008, vol. 7, no. 29, pp. 1-10. DOI: 10.1186/1475-925X-7-29.

Dotsinsky, I. A., Mihov, G. S. Simple approach for tremor suppression in electrocardiograms. Int. J. Bioaotomation, 2010, vol. 14, no. 2, pp. 129-138.

Tulyakova, N. O., Trofimchuk, A. N., Strizhak, A. E. Adaptivnyi metod s shumo- i signal'no-zavisimym pereklyucheniem fil'trov dlya podavleniya nestatsionarnogo shuma v signale elektrokardiogrammy v real'nom vremeni [Adaptive method with noise- and signal-dependent switching of filters for suppression of non-stationary noise in an electrocardiogram signal in real time]. Radiotekhnika: All-Ukr. Sci. Interdep. Mag, Kharkiv, 2018, no. 194, pp. 79-96.

Tulyakova, N. O., Trofymchuk, O. M. Adaptyvni alhorytmy fil'-tratsiyi elektrokardiohramy v real'nomu chasi z bahatorivnevoyu otsinkoyu shumu [Adaptive algorithms for real-time filtering of electrocardiogram with multilevel noise estimation]. Radiotekhnika: All-Ukr. Sci. Interdep. Mag, Kharkiv, 2020, no. 201, pp. 201-214. DOI: 10.30837/rt.2020.2.201.20.

Kalluri, S., Arce, G. R. Adaptive weighted myriad filter algorithms for robust signal processing in -stable noise environments. IEEE Transactions on Signal Processing, 1998, vol. 46, no. 2, pp. 322-334. DOI: 10.1109/78.655418.

Gonzalez, J. G., Arce, G. R. Optimality of the myriad filter in practical impulsive-noise environment. IEEE Transactions on Signal Processing, 2001, vol. 49, no. 2, pp. 438-441. DOI: 10.1109/78.902126.

Gonzalez, J. G., Arce, G. R. Statistically-Efficient Filtering in Impulsive Environments: Weighted Myriad Filters. EURASIP J. on Applied Signal Processing, 2002, vol. 1, no. 1, pp. 4-20.

Pander, T. Impulsive noise filtering in biomedical signals with application of new myriad filter. Biosignal'2010: Proc. of the Int. Conference, 2010, vol. 20, pp. 94-101.

Tulyakova, N. O. Lokal'no-adaptivnaya miri-adnaya fil'tratsiya signala elektrokardiogrammy [Locally-adaptive myriad filtering of electrocardiogram signal]. Radiotekhnika: All-Ukr. Sci. Interdep. Mag, Kharkiv, 2015, no. 180, pp. 152-162.

Tulyakova, N. O., Trofimchuk, A. N., Strizhak, A. E. Algoritmy fil'tratsii elektrokardiogrammy s dinamicheski izmenyaemym razmerom okna [Algorithms of ECG filtering with dynamically variable window size]. Radioelektronni i komp'uterni sistemi – Radioelectronic and computer systems, 2016, no. 2 (76), pp. 4-14.

Tulyakova, N. O., Trofimchuk, A. N., Strizhak, A. E. Adaptivnye miriadnye fil'try dlya obrabotki signalov elektrokardiogrammy, registriruemykh s vysokoi chastotoi diskretizatsii [Adaptive myriad filters for processing signals of electrocardiogram registered with high sampling frequency]. Radioelektronni i komp'uterni sistemi – Radioelectronic and computer systems, 2016, no. 4 (78), pp. 97-107.

Tulyakova, N. Locally-adaptive myriad filters for processing ECG signals in real time. Int. J. Bioaotomation, 2017, vol. 21, no. 1, pp. 5-18.

Tulyakova, N., Trofimchuk, A., Strizhak, A. Adaptive algorithms for elimination of electromyographic noise in the electrocardiogram signal. Telecommunications and Radio Engineering, 2018, vol. 77, no. 6, pp. 549-561. DOI: 10.1615/TelecomRadEng.v77.i6.70.

Tulyakova, N. O., Trofimchuk, A. N., Strizhak, A. E. Algoritmy miriadnoy fil'tratsii [Algorithms of myriad filtering]. Radioelektronni i komp'uterni sistemi – Radioelectronic and computer systems, 2014, no. 4(68), pp. 76-83.

Tulyakova, N., Neycheva, T., Trofymchuk, O., Stryzhak, O. Locally-adaptive myriad filtration of one-dimensional complex signal. Int. J. Bioaotomation, 2018, vol. 22, no. 3, pp. 273-294. DOI: 10.7546/IJBA.2018.22.3.275-296.

Tulyakova, N. O., Trofimchuk, A. N., Strizhak, A. E. Modifitsirovannye lokal'no-adaptivnye miriadnye fil'try [Modified locally-adaptive myriad filters]. Radiotekhnika: All-Ukr. Sci. Interdep. Mag, Kharkiv, 2019, no. 196, pp. 77-88. DOI: 10.30837/rt.2019.1.196.10.

Davies, L., Gather, U. The identification of multiple outliers. J. American Statistical Association, 1993, no. 88, pp. 782-801. doi: 10.1080/01621459.1993.10476339

Pearson, R. K., Neuvo, Y., Astola, J., Gabbouj, M. The class of generalized Hampel filters. EUSIPCO'2015: Proc. of the 23rd European Signal Processing Conference, Nice, 2015, pp. 2501-2505. DOI: 10.1109/EUSIPCO.2015.7362835.

Astola, J. Fundamentals of Nonlinear Digital Filtering. USA, CRC Press LLC Publ., 1997. 276 p.

Pitas, I., Venetsanopoulos, A. N. Nonlinear digital filters: principles and application. USA: Kluwer Academiс Publisher, 1990. 324 p. DOI: 10.1007/978-1-4757-6017-0.

Melnik, V. P., Lukin, V. V., Zelensky, A. A., Astola, J. T., Kuosmanen, P. Local activity indicators: analysis and application to hard-switching adaptive filtering of images. J. Optical Engineering, 2001, vol. 40, no. 8, pp. 1441-1455. DOI: 10.1117/1.1385815.

Lukin, V. V. Analiz povedeniya pokazatelei lokal'noi aktivnosti dlya nelineinykh adaptivnykh fil'trov [Analysis of local activity indicator behaviour for nonlinear adaptive filters]. Radiofizika i elektronika : sb. nauchn. tr. NAN Ukrainy. In-t radiofiziki i elektroniki im. A. Ya. Usikova, 1998, vol. 3, no. 2, pp. 80-89.

Lukin, V. V. Tseli, metody i algoritmy lo-kal'no-adaptivnoi ustoichivoi fil'tratsii radio-lokatsionnykh izobrazhenii [Goals, methods, and algorithms of locally-adaptive robust filtering of radar images]. Kosmicheskaya nauka i tekhnologiya – Space science and technology, 1998, vol. 2, no. 3, pp. 39-50.

Lukin, V. V., Zelensky, A. A., Tulyakova, N. O., Melnik, V. P. Adaptive method for 1-D signal processing based on nonlinear filter bank and Z-parameter. NSIP`99: Proc. of the IEEE/EURASIP Workshop on Nonlinear Signal and Image Processing, 1999, vol. 1, pp. 287-291.

Lukin, V. V., Tulyakova, N. O., Doroshchuk, M. O. Analiz svoistv algoritmov nelineinoi fil'tratsii odnomernykh informatsionnykh signalov [Property analysis of algorithms of nonlinear filtering of onedimensional information signals]. Aviacijno-kosmicna tehnika i tehnologia – Aerospace technic and technology, 1999, vol. 12, pp. 109-113.

Zywietz, Chr. CTS-ECG Test Atlas. Center for Computer Electrocardiography. Biosignal Processing. Medical School. European conformance testing services for computerized electrocardiography. Hannover, Germany, 1999.