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Filtering and Wavelet Regression Methods with Application to Exercise ECG

Peterson, Stefan LU (1996)
Abstract (Swedish)
Popular Abstract in Swedish

Signalen som registreras under ett arbets EKG prov kan innehålla viktig information rörande hjärtats kondition. De störningar som ofta uppträder i signalen kan dock försvåra en korrekt diagnos.



I avhandlingens första del används tidsserie modeller för att skatta profilen, den del av signalen som härrör från hjärtats elektriska aktivitet. Målet med dessa metoder är att dela upp signalen i huvudsakligen två komponenter, profil och störningar. Modellerna skattas på tre riktiga EKG signaler. I ett fall tycks signal uppdelningen fungera. Men för högre samplingsfrekvenser (500 Hz) får den skattade modellen dock problem med att separera signalen. De skattade modellerna utvärderas via... (More)
Popular Abstract in Swedish

Signalen som registreras under ett arbets EKG prov kan innehålla viktig information rörande hjärtats kondition. De störningar som ofta uppträder i signalen kan dock försvåra en korrekt diagnos.



I avhandlingens första del används tidsserie modeller för att skatta profilen, den del av signalen som härrör från hjärtats elektriska aktivitet. Målet med dessa metoder är att dela upp signalen i huvudsakligen två komponenter, profil och störningar. Modellerna skattas på tre riktiga EKG signaler. I ett fall tycks signal uppdelningen fungera. Men för högre samplingsfrekvenser (500 Hz) får den skattade modellen dock problem med att separera signalen. De skattade modellerna utvärderas via traditionella metoder från tidsserie området. En utvärdering i klinisk miljö återstår dock att göra.



I avhandlingens andra del presenteras wavelets, en teknik för att dela upp en signal eller funktion i komponenter där upplösningen i tids och frekvens planet varierar. Två metoder för att skatta kurvor eller signaler störda av brus utvecklas och studeras i simuleringar. Den första metoden är baserad på en utvidgning av Haar waveleten. Den andra metoden som till viss del är robust, dvs skattningen påverkas inte alltför mycket av enstaka stora avvikande värden, baseras på rekursiv subtraktion av medianen. Metoderna testas bland annat på simulerade EKG signaler. Fördelarna med dessa metoder är att de är snabba och adaptiva. Nackdelar är att de måste justeras för att ge skattningar med lägre varians, dvs jämnare skattningar. (Less)
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
opponent
  • Dr. Nason, Guy, Dep of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
organization
publishing date
type
Thesis
publication status
published
subject
keywords
aktuariematematik, programmering, operationsanalys, Statistik, actuarial mathematics, programming, operations research, Statistics, Model Selection, Robust Estimation, Haar Wavelets, Wavelets, Time Series Analysis, Exercise ECG, Kalman Filter
pages
170 pages
publisher
Department of Mathematical Statistics, Lund University
defense location
Sal B, Sölvegatan 18
defense date
1996-10-18 10:15
external identifiers
  • Other:ISRN: LUTFD2/TFMS-1009-SE
ISBN
91-628-2192-X
language
English
LU publication?
yes
id
f5bc93b1-7fc2-4de6-badb-7c090b5f81eb (old id 17542)
date added to LUP
2007-05-24 09:57:57
date last changed
2016-09-19 08:45:11
@misc{f5bc93b1-7fc2-4de6-badb-7c090b5f81eb,
  abstract     = {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.<br/><br>
<br/><br>
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.},
  author       = {Peterson, Stefan},
  isbn         = {91-628-2192-X},
  keyword      = {aktuariematematik,programmering,operationsanalys,Statistik,actuarial mathematics,programming,operations research,Statistics,Model Selection,Robust Estimation,Haar Wavelets,Wavelets,Time Series Analysis,Exercise ECG,Kalman Filter},
  language     = {eng},
  pages        = {170},
  publisher    = {ARRAY(0xa74da00)},
  title        = {Filtering and Wavelet Regression Methods with Application to Exercise ECG},
  year         = {1996},
}