A review of time–frequency matched filter design with application to seizure detection in multichannel newborn EEG

doi:10.1016/j.dsp.2014.02.007

Digital Signal Processing

Volume 28, May 2014, Pages 28-38

https://doi.org/10.1016/j.dsp.2014.02.007 Get rights and content

Abstract

This paper presents a novel design of a time–frequency (t–f) matched filter as a solution to the problem of detecting a non-stationary signal in the presence of additive noise, for application to the detection of newborn seizure using multichannel EEG signals. The solution reduces to two possible t–f approaches that use a general formulation of t–f matched filters (TFMFs) based on the Wigner–Ville and cross Wigner–Ville distributions, and a third new approach based on the signal ambiguity domain representation; referred to as Radon-ambiguity detector. This contribution defines a general design formulation and then implements it for newborn seizure detection using multichannel EEG signals. Finally, the performance of different TFMFs is evaluated for different t–f kernels in terms of classification accuracy using real newborn EEG signals.

Experimental results show that the detection method which uses TFMFs based on the cross Wigner–Ville distribution outperforms other approaches including the existing TFMF-based ones. The results also show that TFMFs which use high-resolution kernels such as the modified B-distribution, achieve higher detection accuracies compared to the ones which use other reduced-interference t–f kernels.

Introduction

In a wide range of applications such as radar, speech and biomedical signal processing, there is a need to detect the presence of a particular signal embedded in noise [1]. In the case when the signal-to-detect is completely known and the noise is additive white Gaussian, the conventional time-domain matched filter is known to be the optimal detector [2]. However, in cases that require detecting non-stationary signals that exhibit certain unknown parameters such as unknown time and/or frequency shifts, those detectors may no longer be optimal [1]. For such scenarios, detectors based on time–frequency matched filters (TFMFs) were shown to be superior [1], [2], [3], [4], [5], [6]. In such cases, the signals are correlated in the time–frequency (t–f) domain and the kernel of the time–frequency distribution (TFD) is designed to take into account the unknown parameters of the signal-to-detect. An additional property is that t–f smoothing resulting from the introduction of kernels can also attenuate noise components with large lag or Doppler value [7].

An example of non-stationary signals is the electroencephalogram (EEG) signals measured from the scalp which describe brain functions. As EEG signals can be collected noninvasively and in real time, they provide a strong medical motivation to develop new advanced digital signal processing methods for analyzing them [8], [9], [10], [11], [12], [13]. Previous studies showed that such newborn EEG seizures can be modeled as piecewise linear frequency modulated (LFM) signals and proposed TFMFs for newborn EEG seizure detection [2], [14].

The work presented in this paper focuses on the processing of EEG signals for detection of seizures in newborns using an adapted advanced design of TFMFs. This paper considers solutions arising from the classical problem of detecting a non-stationary signal in the presence of noise using TFMFs and discusses the general design formulation of filters based on the Wigner–Ville and cross Wigner–Ville distributions (WVD and XWVD). The paper shows that all the existing TFMFs can be considered as special cases of the general formulation, then applies the idea to the problem of detecting seizures in multichannel newborn EEGs, and compares with other methods.

A variety of methods have already been applied for automatic seizure detection using EEG signals. This includes the use of time-domain statistics [15], spectral features [16], autoregressive modeling [17], and linear prediction error energy [18]. Other methods deploy a combination of time with frequency features [19], [20], non-linear features [21], [22], FFT coefficients [23], wavelet transform [24], coefficients of the discrete wavelet transform (DWT) of the EEG signals [25], combination of DWT coefficients and chaotic measures [26], matching pursuit [27], and energy distribution of the EEG signals in t–f plane [28]. A comparison of the performance of different feature sets in classifying EEG signals can be found in [29]. In addition, 2 new t–f based classification algorithms were proposed in [30], [31] which use phase synchrony and t–f signal and image related features.

In essence, this paper exploits the natural idea that as EEG signals exhibit non-stationary behavior, t–f methods are naturally more suitable for seizure analysis, detection and classification [2], [14], [32], [7, Section 15.5]. Then, taking into account the development of detection methods using TFMF-based methods [2], [3], [6], this paper extends previous studies by bringing all existing seizure detection methods based on TFMFs under one general formulation which can then be adapted to a wider range of circumstances. This then leads to the design of methods based on this general formulation of TFMFs and their evaluation in terms of the improvement in detection accuracy using multichannel newborn EEG. The methodology presented in this paper can be extended and applied to other important areas such as t–f based watermarking [33].

The rest of the paper is organized as follows. Section 2 reviews relevant background for signal detection, TFDs and t–f matched filtering. The general formulation of TFMFs based on the WVD and XWVD are presented in Section 3. Time–frequency matched filtering methods for newborn seizure detection are formulated in Section 4. Section 5 presents novel multichannel newborn seizure detectors based on t–f matched filtering and describes the results of evaluating the performance of the proposed methods for different TFDs. A brief description of how to use the methodology presented in the paper for newborn EEG classification is provided in Section 6. Section 7 concludes.

Section snippets

EEG abnormality, classical detection problem and matched filter

One of the main issues affecting newborn health is the possibility of brain disfunction caused by a number of factors. Such disfunction is reflected by abnormalities appearing in the EEG which need to be detected. Following the classical detection problem, the measured signal $x (t)$ of duration T is processed to detect the presence of a known signal corresponding to an EEG abnormality. The two hypotheses on $x (t)$ are: $H_{0} : x (t) = n (t), signal absent,$ $H_{1} : x (t) = s (t; Θ) + n (t), signal present,$ where $n (t)$

Formulation

An intuitive approach to generalize (10) is to replace the WVD $W (t, f)$ with the more general TFD representation $ρ (t, f; γ_{0})$ , defined by a particular t–f kernel $γ_{0}$ , i.e. $η_{TF} = \iint_{(T)} ρ_{x} (t, f; γ_{0}) ρ_{s} (t, f; γ_{0}) d t d f .$ Using the properties of the FT in (11a) and (11b), one can rewrite $η_{TF}$ in the ambiguity domain as: $η_{TF} = \iint A_{x} (ν, τ) A_{s}^{⁎} (ν, τ) {| g_{0} (ν, τ) |}^{2} d ν d τ$ where $g_{0} (ν, τ) = F_{τ \to ν} {{F^{- 1}}_{f \to τ} {γ_{0} (t, f)}}$ . The test statistic $η_{TF}$ in (14) reduces to the test statistic of QMF only if the Doppler-lag kernel of the TFD is uni-modular, i.e.

Rationale

Previous studies have shown that newborn EEG signals are non-stationary and multi-component signals [2], [14], and that newborn EEG seizures can be modeled as piecewise LFM signals with harmonics, where the number of LFM pieces depends on the duration of the EEG seizure epoch [2]. The background patterns, on the other hand, usually exhibit irregular activities with no clear consistent behavior [3]. These observations about EEG patterns correlate well with clinical information reported in [41].

Template set

The problem considered is to detect the presence of seizures in multichannel newborn EEG signals using a t–f matched filtering approach. Central to the success of this approach is choosing a suitable template set. The selected template set contains seizure-like events which, based on previous t–f analysis studies, are modeled by piecewise LFM signals. Defining the templates to best represent the range of seizure types is the main challenge here, given that too many templates lead to

Extension to TFMF-based classification of newborn EEG abnormalities

The methodology depicted in Fig. 2 and described in Section 5.2 can also be used for on-line classification of newborn EEG signals, e.g. into seizure and non-seizure segments. For this application, based on the results presented in the previous section, one may use an XWVD-based TFMF with an MBD kernel. Therefore for the kth channel of the multichannel EEG, the test statistic $μ_{2}^{(k)}$ given in (32b) with γ being the MBD kernel, is calculated. The only parameter which needs to be found is the

Conclusion

This paper presents a general design approach for t–f matched filtering of newborn EEG abnormalities. This proposed general design of TFMFs offers a framework for their application in detecting non-stationary signals that exhibit certain unknown parameters, such as detecting seizure in multichannel newborn EEG and other real-life applications.

The results of a performance evaluation in terms of AUC scores show that TFMF-based detectors offer an improvement of up to 13% in AUC score compared with

Acknowledgements

The authors thank Prof. Paul Colditz and his colleagues at the University of Queensland, Centre for Clinical Research, Brisbane, Australia, for providing the newborn data used in this paper. They also acknowledge the technical discussions with Dr. J.M. O' Toole from the Neonatal Research Group, University College Cork, Ireland, and the technical assistance provided by Amir Omidvarnia from the University of Queensland, Centre for Clinical Research, Brisbane, Australia, in simulations.

This

Boualem Boashash (IEEE Fellow 99) is a Scholar and Senior Academic with experience in 5 leading Universities in France and Australia. He has published over 500 technical publications, including over 100 journal publications covering Engineering, Applied Mathematics and Bio-medicine. He pioneered the field of Time–Frequency Signal Processing.

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Ghasem Azemi received his PhD in Signal Processing from Queensland University of Technology, Brisbane, Australia in 2004. He then joined Razi University, Kermanshah, Iran. Since 2010, he is with The University of Queensland, Brisbane, Australia as a Research Fellow. His research interests are Biomedical and Time–Frequency Signal Processing.

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A review of time–frequency matched filter design with application to seizure detection in multichannel newborn EEG

Abstract

Introduction

Section snippets

EEG abnormality, classical detection problem and matched filter

Formulation

Rationale

Template set

Extension to TFMF-based classification of newborn EEG abnormalities

Conclusion

Acknowledgements

Med. Eng. Phys.

Digit. Signal Process.

Digit. Signal Process.

Clin. Neurophysiol.

Clin. Neurophysiol.

Comput. Biol. Med.

Expert Syst. Appl.

Clin. Neurophysiol.

Expert Syst. Appl.

Comput. Methods Programs Biomed.

Appl. Math. Comput.

Clin. Neurophysiol.

Expert Syst. Appl.

Clin. Neurophysiol.

Digit. Signal Process.

J. Franklin Inst.

Clin. Neurophysiol.

Clin. Neurophysiol.

Pattern Recognit. Lett.

Optimal time–frequency detectors

Time–frequency detection of slowly varying periodic signals with harmonics: Methods and performance evaluation

EURASIP J. Adv. Signal Process.

Time–frequency processing of nonstationary signals: Advanced TFD design to aid diagnosis with highlights from medical applications

IEEE Signal Process. Mag.

Time–frequency based detection using discrete-time discrete-frequency Wigner distributions

IEEE Trans. Signal Process.

Design of a time–frequency domain matched filter for detection of non-stationary signals