Filtering and Wavelet Regression Methods with Application to Exercise ECG

Sammanfattning: The analysis of the recorded electrical activity of the heart during an exercise test is a valuable method for investigating a patient's circulatory and respiratory system. But the disturbances that occurr during a test often make it difficult to interpret the signal in order to detect changes evoked by the increased workload and related to for instance coronary artery diseases. Suppression of disturbances are therefore necessary and in the first part of the thesis this is performed by estimation via a Kalman filtering based method where models with components from time series analysis are constructed both for the profile related to the electrical activity of the heart and the disturbances in the exercise ECG signal. The estimated models are evaluated on real datasets. The second part of this thesis introduces two new methods for signal representation and nonparametric regression. The advantages of these methods are that they are fast, adaptive and essentially automatic. As shown by examples can for instance ECG signals be effectively 'denoised'. The first method is based on a multiple wavelet extension of the standard Haar wavelet. This method basically uses a class of Haar wavelet matrices with maximum number of vanishing moments, the Chebyshev system of orthogonal polynomials. When used with the Stationary Wavelet Transform (SWT), also described in the thesis, they performed well in a simulation study when compared to the classic dyadic wavelet bases. Finally a robust nonparametric, wavelet inspired regression method is proposed. It is based on recursive subtractions by robust location estimators. A paramatric bootstrap method is proposed in order to estimate a signal contaminated with outliers. Robustness and performance of this method are studied in a simulation.