in this application because they are designed for deterministic signals that are corrupted with impulsive noise. For stochastic signals the PSD is defined as the ...
Proceedings of the 26th Annual International Conference of the IEEE EMBS San Francisco, CA, USA • September 1-5, 2004
Impulse Rejection Filter for Artifact Removal in Spectral Analysis of Biomedical Signals J. M c N a m e s 1, T. Thong 2, M. A b o y 1 1Biomedical Signal Processing Laboratory, Electrical and Computer Engineering, Portland State University, Portland, OR, USA 2Biomedical Engineering, OGI School of Science and Engineering, Oregon Health & Science University, Portland, OR, USA Abstractm Biomedical signals are frequently corrupted with artifact that occurs rarely, but is impulsive and large amplitude when it does occur. Because the artifact spans a broad frequency range that overlaps with the signal spectrum, linear filters cannot remove it. Because it is large in amplitude, it dominates characterizations of the signals based on second-order statistics such as correlation and spectral analysis. In this study we assess the ability of impulse rejection filters to remove the effect of synthetic PVCs in interbeat interval series from patients with a normal sinus rhythm. The simulation results demonstrate that the PVCs severely corrupt the estimated heart rate power spectral density (PSD), impulse rejection filters are effective at removing this effect, and the filter performance is robust to the choice of user-specified parameters. Keywordsm Electrocardiogram (ECG), artifact, impulse noise, interbeat intervals (IBI), heart rate variability (HRV), outlier removal, impulse rejecting filter.
I. INTRODUCTION
RTIFACT is a ubiquitous problem that confounds the traditional methods of biomedical signal processing. Movement artifact is especially problematic because biomedical sensors are sensitive to subject movement and can cause largeamplitude short-duration excursions in the signals. These characteristics then dominate many characterizations of the process based on second-order statistics such as correlation and spectral analysis. Premature ventricular contractions (PVCs) in interbeat interval (IBI) and instantaneous heart rate (IHR) series is one example of this type of artifact. Fig. 1(a) shows an example of three PVCs that occur in a 5 min period. Because these events are much larger amplitude than the fluctuations in the normal sinus rhythm of the IBI time series, these events comprise the majority of the signal variation and severely distort most heart rate variability (HRV) metrics [1]. This is illustrated by the estimated power spectral density (PSD) of the original IHR series shown in Fig. 1(c) compared to the same series with the PVCs removed shown in Figs. 1(b) and 1(d). In this paper, we consider the problem of how to estimate the PSD of stochastic signals that are contaminated with occasional artifact that is of short duration and large amplitude. An obvious approach to this problem is to simply apply one of the robust transforms that have been developed recently [2], [3]. Unfortunately these transforms can not be directly applied in this application because they are designed for deterministic signals that are corrupted with impulsive noise. For stochastic signals the PSD is defined as the Fourier transform of the
A
This work was supported in part by the Thrasher Research Fund.
0-7803-8439-3/04/$20.00©2004 IEEE
autocorrelation sequence, OO
-
(1)
where rx(6) = E { x ( n ) x ( n - 6)}. In practice the autocorrelation is unknown and must be estimated from an observed record. Since the impulsive artifact affects standard estimators of the autocorrelation at many lags 6, robust estimates of the Fourier transform of the autocorrelation sequence do not reduce the impact of this artifact. In this paper we report the results of a study designed to assess the effectiveness of impulse rejection filters for reducing the impact of artifact on the estimated PSD of IHR series. These nonlinear filters are based on two simple steps: 1) at each sample decide whether the signal is corrupted with artifact; 2) if it is corrupted, reject the artifact and replace it with an interpolated value, otherwise leave it unaltered [4], [5]. We assess the performance of these filters by adding artificial PVCs to IHR series from people with normal sinus rhythms in a series of Monte Carlo simulations.
II. METHODOLOGY
A. Statistical Model Mathematically, we propose to model biomedical signals with occasional artifact as
x(n) = s ( n ) + u(n)
(2)
where s ( n ) i s the signal of interest, u(n) models the impulsive artifact, and x(n) is the observed signal. In most biomedical applications, we argue that artifact rarely occurs and has a large amplitude when it does occur. Others have modelled impulsive noise as a white noise process with a continuous, heavy-tailed marginal distribution (e.g. Laplacian noise) [2], [3]. We suggest that impulsive artifact is more accurately modelled as a white noise process with a mixed distribution where there is a high probability that the noise is zero. The cumulative distribution function of such a process could be expressed as F(u) -
(1 - p ) u ( u ) + p
f(c~) dc~
(3)
O
