Mathematical Modeling And Scientific Computing Approaches For Advanced Ecg Signal Analysis

Dr. Mohammed Zabeeulla A N; Dr. Rajeev Ranjan; Nagaraju K.R.; Shashikala B S; Dr. J. Kavitha; Sanjeev Kumar; K.S. Niraja

doi:10.29284/4rmevq12

Authors

Dr. Mohammed Zabeeulla A N Associate Professor, CSIT, JAIN(Deemed-to-be University)ORCID ID: 0000-0002-4445-9089
Dr. Rajeev Ranjan Associate Professor, Humanities and Basic Science, Vasantdada Patil Pratishthan's College of Engineering and visual arts, Sion, pin-400022, Mumbai, Maharashtra
Nagaraju K.R. Associate Professor, Department of Mathematics, Government Engineering College, Mosalehosahalli, Hassan, Karnataka, India
Shashikala B S Associate Professor, Department of Mathematics, K. R Pete Krishna Government Engineering College, K. R. Pete-571426 Mandya (D)Karnataka, India
Dr. J. Kavitha Associate Professor, Computer Science and Engineering Koneru Lakshmaiah Education Foundation, Bowrampet, Hyderabad-500043 ORCID ID: 0000-0003-0290-337X
Sanjeev Kumar Assistant Professor, Department of Mathematics, Chandigarh University Gharuan, Mohali-140413, Punjab, India
K.S. Niraja Assistant Professor, C.S.E, Gokaraju Lailavathi Engineering College ORCID ID: 0000000209695342

DOI:

https://doi.org/10.29284/4rmevq12

Keywords:

ECG signal analysis, mathematical modeling, scientific computing, signal reconstruction, regularization-based optimization

Abstract

Electrocardiogram (ECG) signal analysis is fundamental to the diagnosis and monitoring of cardiovascular conditions; however, ECG recordings are frequently corrupted by noise arising from acquisition systems and patient movement. This work presents a mathematically grounded and computationally efficient framework for advanced ECG signal analysis based on regularized optimization and scientific computing principles. The proposed approach formulates ECG signal reconstruction as a well-posed optimization problem that balances fidelity to noisy observations with smoothness constraints reflecting underlying physiological signal characteristics. To ensure numerical stability and reproducibility, the model is implemented using finite-difference discretization and solved via efficient linear system solvers. The framework is evaluated using publicly available ECG heartbeat datasets derived from the MIT-BIH Arrhythmia Database. Controlled Gaussian noise is introduced to assess robustness under noisy conditions. Comprehensive experimental analysis, including exploratory data analysis, feature characterization, and dimensionality reduction, is conducted to investigate signal structure and variability. Qualitative results demonstrate effective noise suppression while preserving essential waveform features. Quantitative evaluation using signal-to-noise ratio and root mean square error shows consistent improvements across individual signals and batch-level experiments, confirming the stability and reliability of the proposed method. The results highlight the effectiveness of mathematically principled and scientifically computable approaches for interpretable and robust ECG signal analysis, providing a solid foundation for further extensions and integration with advanced biomedical signal processing techniques.

References

1. Jia, Y., Pei, H., Liang, J., Zhou, Y., Yang, Y., Cui, Y. and Xiang, M., 2024. Preprocessing and Denoising Techniques for Electrocardiography and Magnetocardiography: A Review. Bioengineering, 11(11), p.1109.

2. Arsene, C., 2019. Complex deep learning models for denoising of human heart ecg signals. arXiv preprint arXiv:1908.10417.

3. Tutuko, B., Darmawahyuni, A., Nurmaini, S., Tondas, A.E., Naufal Rachmatullah, M., Teguh, S.B.P., Firdaus, F., Sapitri, A.I. and Passarella, R., 2022. DAE-ConvBiLSTM: End-to-end learning single-lead electrocardiogram signal for heart abnormalities detection. PloS one, 17(12), p.e0277932.

4. Zhang, M. and Wei, G., 2020. An integrated EMD adaptive threshold denoising method for reduction of noise in ECG. Plos one, 15(7), p.e0235330.

5. Fotiadou, E., Melaet, R. and Vullings, R., 2022. Deep unfolding for multi-measurement vector convolutional sparse coding to denoise unobtrusive electrocardiography signals. Frontiers in Signal Processing, 2, p.981453.

6. Zhu, D., Chhabra, V.K. and Khalili, M.M., 2024. ECG Signal Denoising Using Multi-scale Patch Embedding and Transformers. arXiv preprint arXiv:2407.11065.

7. Malik, S.A., Parah, S.A., Aljuaid, H. and Malik, B.A., 2023. An iterative filtering based ECG denoising using lifting wavelet transform technique. Electronics, 12(2), p.387.

8. Mao, J., Li, Z., Li, S. and Li, J., 2023. A novel ECG signal denoising algorithm based on sparrow search algorithm for optimal variational modal decomposition. Entropy, 25(5), p.775.

9. Shan, L., Li, Y., Jiang, H., Zhou, P., Niu, J., Liu, R., Wei, Y., Peng, J., Yu, H., Sha, X. and Chang, S., 2022. Abnormal ECG detection based on an adversarial autoencoder. Frontiers in Physiology, 13, p.961724

10. Lin, H., Liu, R. and Liu, Z., 2023. ECG signal denoising method based on disentangled autoencoder. Electronics, 12(7), p.1606.

11. Chen, Y., Ma, B., Hao, H. and Li, L., 2021. Removal of electrocardiogram artifacts from local field potentials recorded by sensing-enabled neurostimulator. Frontiers in Neuroscience, 15, p.637274.

12. Samann, F. and Schanze, T., 2022, September. Multiple parallel hidden layers autoencoder for denoising ECG signal. In Current Directions in Biomedical Engineering (Vol. 8, No. 2, pp. 161-164). De Gruyter.

13. Antczak, K., 2020. A generative adversarial approach to ECG synthesis and denoising. arXiv preprint arXiv:2009.02700.

14. Mvuh, F.L., Ebode Ko’a, C.O.V. and Bodo, B., 2024. Multichannel high noise level ECG denoising based on adversarial deep learning. Scientific Reports, 14(1), p.801.

15. Fazeli, S., 2018. ECG heartbeat categorization dataset. Kaggle. Available at: https://www.kaggle.com/datasets/shayanfazeli/heartbeat

16. Bing, P., Liu, W., Zhai, Z., Li, J., Guo, Z., Xiang, Y., He, B. and Zhu, L., 2024. A novel approach for denoising electrocardiogram signals to detect cardiovascular diseases using an efficient hybrid scheme. Frontiers in Cardiovascular Medicine, 11, p.1277123.

17. Wang, J., Pei, S., Yang, Y. and Wang, H., 2024. Convolutional transformer-driven robust electrocardiogram signal denoising framework with adaptive parametric ReLU. Math. Biosci. Eng, 21(3), pp.4286-4308.

18. Shaheen, A., Ye, L., Karunaratne, C. and Seppänen, T., 2025. Fully-Gated Denoising Auto-Encoder for Artifact Reduction in ECG Signals. Sensors (Basel, Switzerland), 25(3), p.801.

19. Yang, W., Cao, B. and Wu, J., 2025. ECGDeDRDNet: A deep learning-based method for Electrocardiogram noise removal using a double recurrent dense network. arXiv preprint arXiv:2505.05477.

20. Raggi, M. and Mesin, L., 2025. Denoising the ECG from the emg using stationary wavelet transform and template matching. Electronics, 14(17), p.3474.

21. Nejad, M.P.S., Hicks, D., Valentine, M. and Chon, K.H., 2025. Lightweight Deep Autoencoder for ECG Denoising with Morphology Preservation and Near Real-Time Hardware Deployment. arXiv preprint arXiv:2511.12478.

22. Jabeur, T.B., Bashier, E., Sandhu, Q., Bwalya, K.J. and Joshua, A., 2024. Noise and artifacts elimination in ECG signals using wavelet, variational mode decomposition and nonlocal means algorithm. arXiv preprint arXiv:2406.01023.