| Abstract [eng] |
This dissertation presents a novel approach for the analysis of electrocardiogram (ECG) signals using advanced matrix-based algorithms for the detection and monitoring of cardiac diseases. The research addresses the challenge of analysing complex, non-linear, and non-stationary biomedical time series by proposing algorithms based on Perfect Matrices of Lagrange Differences (PMLD), Hankel matrices, and the Secondary Matrix Framework (SMF). The dissertation introduces innovative methods for extracting subtle variations in ECG parameters such as RR, JT, QRS, AP, and DP intervals. These methods are validated through statistical techniques and compared with existing algorithms such as Singular Value Decomposition (SVD) and Permutation Entropy (PE). A particular focus is placed on early detection of cardiovascular conditions like atrial fibrillation and complexity collapse phenomena. The study uses real-world ECG data obtained during stress tests and ambulatory monitoring, with data preprocessing and algorithm development conducted in MATLAB. The proposed indicators and classification models enhance the sensitivity to individual cardiac signal characteristics and support clinical decision-making. This work demonstrates the potential of matrix-based techniques for accurate and scalable ECG signal analysis in modern cardiology. |
