ECG Sparsity Evaluation on a Multiwavelet Basis

Kromka, Jozef; Jusková, Antónia; Šaliga, Ján

doi:10.2478/aei-2023-0018

Abstract

In this paper, an evaluation of the multiwavelet basis’ capability to represent the ECG signal sparsely was performed. The paper includes the mathematical formulation of sparsity, a brief introduction to the multiwavelet transform, as well as details about the simulation setup used for evaluation. Throughout the paper, various multiwavelets were investigated. The reported results show that the BAT and DB multiwavelets performed well, thus they could be used in the ECG signal sparsification. The investigation also focused on the ECG signals displaying deformations associated with illnesses. Preliminary results suggest that multiwavelets may prove beneficial for diverse processing of ECG signals.

References

N. TOWNDEND, D. KAZAKIEWICZ, L. F. WRIGHT, A. TIMMIS, R. HUCULECI, A. TORBICA, C. P. GALE, S. ACHENBACH, F. WEIDINGER, and P. VARDAS, “Epidemiology of cardiovascular disease in europe,” Nature Reviews Cardiology, vol. 19, no. 2, pp. 133–143, 2022.
Search in Google Scholar Back to article
O. KOVÁČ, J. KROMKA, J. ŠALIGA, and A. JUSKOVÁ, “Multiwavelet-based ecg compressed sensing,” Measurement, vol. 220, p. 113393, 2023.
Search in Google Scholar Back to article
L. De VITO, E. PICARIELLO, F. PICARIELLO, S. RAQUANO, and I. TUDOSA, “A prototype of a wearable health device for mobile telemonitoring applications,” in 2022 IEEE International Symposium on Medical Measurements and Applications (MeMeA). IEEE, 2022, pp. 1–6.
Search in Google Scholar Back to article
M. R. MOHEBBIAN and K. A. WAHID, “Ecg compression using optimized b-spline,” Multimedia Tools and Applications, pp. 1–13, 2023.
Search in Google Scholar Back to article
H. S. PAL, A. KUMAR, A. VISHWAKARMA, and L. BALYAN, “A hybrid 2d ecg compression algorithm using dct and embedded zero tree wavelet,” in 2022 IEEE 6th Conference on Information and Communication Technology (CICT). IEEE, 2022, pp. 1–5.
Search in Google Scholar Back to article
L. ZHENG, Z. WANG, J. LIANG, S. LUO, and S. TIAN, “Effective compression and classification of ecg arrhythmia by singular value decomposition,” Biomedical Engineering Advances, vol. 2, p. 100013, 2021.
Search in Google Scholar Back to article
J. MALIK, E. Z. SOLIMAN, and H.-T. WU, “An adaptive qrs detection algorithm for ultra-long-term ecg recordings,” Journal of Electrocardiology, vol. 60, pp. 165–171, 2020.
Search in Google Scholar Back to article
S. L. BRUNTON and J. N. KUTZ, Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022.
Search in Google Scholar Back to article
S. M. KHORASANI, G. A. HODTANI, and M. M. KAKHKI, “Investigation and comparison of ecg signal sparsity and features variations due to preprocessing steps,” Biomedical Signal Processing and Control, vol. 49, pp. 87–95, 2019.
Search in Google Scholar Back to article
U. SATIJA, B. RAMKUMAR, and M. SABARI-MALI Manikandan, “Noise-aware dictionary-learning-based sparse representation framework for detection and removal of single and combined noises from ecg signal,” Healthcare technology letters, vol. 4, no. 1, pp. 2–12, 2017.
Search in Google Scholar Back to article
Y. HUANG, G. YANG, K. WANG, H. LIU, and Y. YIN, “Learning joint and specific patterns: A unified sparse representation for off-the-person ecg bio-metric recognition,” IEEE Transactions on Information Forensics and Security, vol. 16, pp. 147–160, 2020.
Search in Google Scholar Back to article
G. GROSSI, R. LANZAROTTI, and J. LIN, “High-rate compression of ecg signals by an accuracy-driven sparsity model relying on natural basis,” Digital Signal Processing, vol. 45, pp. 96–106, 2015.
Search in Google Scholar Back to article
S. FOUCART and H. RAUHUT, Sparse Solutions of Underdetermined Systems. New York, NY: Springer New York, 2013, pp. 41–59. [Online]. Available: https://doi.org/10.1007/978-0-8176-4948-7_2
Search in Google Scholar Back to article
R. D. DRIVER, Cardinality. New York, NY: Springer New York, 1984, pp. 212–220. [Online]. Available: https://doi.org/10.1007/978-1-4612-1108-2_13
Search in Google Scholar Back to article
K. SAYOOD, “Data compression,” in Encyclopedia of Information Systems, H. Bidgoli, Ed. New York: Elsevier, 2003, pp. 423–444. [Online]. Available: https://www.sciencedirect.com/science/article/pii/B0122272404000290
Search in Google Scholar Back to article
E. MAHMOUDIAN, H. AMINDAVAR, and S. M. AHADI, “New sparsity measure based on energy distribution,” Displays, vol. 80, p. 102542, 2023. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0141938223001750
Search in Google Scholar Back to article
D. L. DONOHO, “Compressed sensing,” IEEE Transactions on information theory, vol. 52, no. 4, pp. 1289–1306, 2006.
Search in Google Scholar Back to article
F. KEINERT, Wavelets and multiwavelets. CRC Press, 2003.
Search in Google Scholar Back to article
J. LEBRUN and M. VETTERLI, “High-order balanced multiwavelets: theory, factorization, and design,” IEEE Transactions on Signal Processing, vol. 49, no. 9, pp. 1918–1930, 2001.
Search in Google Scholar Back to article
C. K. CHUI and J.-A. LIAN, “A study of orthonormal multi-wavelets,” Applied Numerical Mathematics, vol. 20, no. 3, pp. 273–298, 1996.
Search in Google Scholar Back to article
G. C. DONOVAN, J. S. GERONIMO, D. P. HARDIN, and P. R. MASSOPUST, “Construction of orthogonal wavelets using fractal interpolation functions,” SIAM Journal on Mathematical Analysis, vol. 27, no. 4, pp. 1158–1192, 1996.
Search in Google Scholar Back to article
L. SHEN, H. H. TAN, and J. Y. THAM, “Symmetric– antisymmetric orthonormal multiwavelets and related scalar wavelets,” Applied and Computational Harmonic Analysis, vol. 8, no. 3, pp. 258–279, 2000.
Search in Google Scholar Back to article
K.-W. CHEUNG and L.-M. PO, “Integer multi-wavelet transform for lossless image coding,” in Proceedings of 2001 International Symposium on Intelligent Multimedia, Video and Speech Processing. ISIMP 2001 (IEEE Cat. No. 01EX489). IEEE, 2001, pp. 117–120.
Search in Google Scholar Back to article
J. KROMKA, O. Kováč, and J. ŠALIGA, “Multi-wavelet toolbox for matlab,” in 2022 32nd International Conference Radioelektronika (RADIOELEKTRONIKA), 2022, pp. 01–05.
Search in Google Scholar Back to article
A. KALYAKULINA, I. YUSIPOV, V. MOSKALENKO, A. NIKOLSKIY, K. KOSONOGOV, N. ZOLOTYKH, and M. IVANCHENKO, “Lobachevsky university electrocardiography database,” Type: Dataset. Available online: https://physionet.org/content/ludb/1.0.0/ (accessed on 10 July 2021), 2020.
Search in Google Scholar Back to article
A. I. KALYAKULINA, I. I. YUSIPOV, V. A. MOSKALENKO, A. V. NIKOLSKIY, K. A. KOSONOGOV, G. V. OSIPOV, N. Y. ZOLOTYKH, and M. V. IVANCHENKO, “Ludb: a new open-access validation tool for electrocardiogram delineation algorithms,” IEEE access, vol. 8, pp. 186 181–186 190, 2020.
Search in Google Scholar Back to article
A. L. GOLDBERGER, L. A. AMARAL, L. GLASS, J. M. HAUSDORFF, P. C. IVANOV, R. G. MARK, J. E. MIETUS, G. B. MOODY, C.-K. PENG, and H. E. STANLEY, “Physiobank, physiotoolkit, and physionet: components of a new research resource for complex physiologic signals,” circulation, vol. 101, no. 23, pp. e215–e220, 2000.
Search in Google Scholar Back to article

ECG Sparsity Evaluation on a Multiwavelet Basis

Abstract

Paradigm

My account