A matching pursuit-based signal complexity measure for the analysis of newborn EEG

ORIGINAL ARTICLE

A matching pursuit-based signal complexity measurefor the analysis of newborn EEG

L. Rankine Æ M. Mesbah Æ B. Boashash

Received: 8 September 2006 / Accepted: 9 December 2006 / Published online: 13 January 2007� International Federation for Medical and Biological Engineering 2007

Abstract This paper presents a new relative measure

of signal complexity, referred to here as relative struc-

tural complexity (RSC), which is based on the matching

pursuit (MP) decomposition. By relative, we refer to

the fact that this new measure is highly dependent on

the decomposition dictionary used by MP. The struc-

tural part of the definition points to the fact that this

new measure is related to the structure, or composi-

tion, of the signal under analysis. After a formal defi-

nition, the proposed RSC measure is used in the

analysis of newborn electroencephalogram (EEG). To

do this, firstly, a time–frequency decomposition dic-

tionary is specifically designed to compactly represent

the newborn EEG seizure state using MP. We then

show, through the analysis of synthetic and real new-

born EEG data, that the relative structural complexity

measure can indicate changes in EEG structure as

it transitions between the two EEG states; namely

seizure and background (non-seizure).

Keywords Matching pursuit � Relative structural

complexity � Coherent dictionary � Time–frequency �Newborn EEG

1 Introduction

The electroencephalogram (EEG) is an important tool

in the study of the central nervous system (CNS),

particularly in the newborn where it provides high

prognostic and diagnostic capabilities [20]. In some

cases, the newborn EEG is the only indicator of CNS

pathologies, with electrographic seizure events being

the most significant indicator of CNS dysfunction [22].

The EEG of newborn patients suffering seizure

events can be broadly classified into two main states;

namely, background and seizure. The newborn EEG

background signal is a complex waveform which, in the

first instance, appears to be some form of noisy signal

[20]. In fact, it was recently shown that the newborn

EEG background can be modelled as a nonstationary

stochastic 1/fc process [27]. Newborn EEG seizure, on

the other hand, is generally characterized by periods of

rhythmic spiking or repetitive sharp waves [18], whose

patterns are highly variable, with complex and varied

morphology and cover a variety of frequencies. These

dynamical changes in structure and frequency infer

that the newborn EEG is highly nonstationary. Time–

frequency (TF) signal analysis techniques, which have

been shown to provide informative representations of

signal nonstationarities [5], are highly suitable for the

newborn EEG background and seizure states.

Quadratic time–frequency distributions (QTFDs),

such as the Wigner–Ville, Choi–Williams and Modified

B distributions [4], are very useful for the visualization

of nonstationary signals in the TF domain. A com-

prehensive analysis and characterization of the new-

born EEG using QTFDs was previously undertaken

by the present authors in [6–9, 27]. The TF analysis

revealed significant differences in the TF structure of

This work was supported by grants from the NHMRC and ARC.

L. Rankine (&) � M. Mesbah � B. BoashashPerinatal Research Centre, Royal Brisbane and Women’sHospital, Herston, QLD 4029, Australiae-mail: [email protected]

B. BoashashCollege of Engineering, University of Sharjah,University City, Sharjah, United Arab Emirates

123

Med Bio Eng Comput (2007) 45:251–260

DOI 10.1007/s11517-006-0143-0

newborn EEG background and seizure signals, with

significant changes in structure occurring as the new-

born EEG progresses from the background to seizure

state, and vice versa.

Although QTFDs have proved extremely useful in

the analysis of the nonstationary newborn EEG, they

are not designed for signal parameterization and usu-

ally require sophisticated image processing techniques

for feature extraction [23, 26, 32]. For this reason,

much attention has recently been directed to the use of

atomic decomposition techniques, such as the matching

pursuit (MP) algorithm [21], using overcomplete TF

dictionaries for TF representation and parameteriza-

tion [16].

An objective of atomic decomposition techniques is

to generate sparse (compact), yet highly informative,

signal representations [13], given a particular over-

complete dictionary. The development and theoretical

study of algorithms which attempt to find the sparsest

representation has been the focus of many researchers

recently [13–15, 17, 30, 31]. However, compact and

informative representations can also be achieved

through the use of a highly coherent TF dictionary [21].

In this paper, we aim to first develop a new relative

measure of signal complexity, referred to as relative

structural complexity (RSC), which is based on MP

decomposition using a coherent TF dictionary. Since

RSC is dependent on the use of a coherent dictionary,

the second aim is to develop a TF dictionary, which is

coherent with some particular newborn EEG signal

structures. Finally, we apply the RSC measure, using

the designed coherent dictionary, to the analysis of

newborn EEG, showing that RSC is an indicator of

structural change in the EEG as it transitions between

the background and seizure states.

2 Signal processing methods

2.1 Time–frequency signal analysis

In the following subsections, we give brief introductions

to the two TF methods mentioned in the introduction;

namely, QTFDs and MP atomic decomposition. It

was stated in the previous section that QTFDs are

extremely useful for visualization of nonstationary

signals in the TF domain but lack the compact repre-

sentation of atomic decomposition techniques such as

MP. Therefore, in this paper, QTFDs are used only for

visualization purposes while the MP atomic decompo-

sition technique is used in the development of the RSC

measure.

2.1.1 Quadratic time–frequency distributions

Quadratic TF distributions are commonly used

methods for obtaining joint TF representations of

nonstationary signals. The fundamental QTFD is the

Wigner–Ville distribution (WVD), from which all

other QTFDs can be obtained by a TF averaging or

smoothing [4].

The WVD of a continuous real signal, s(t), is defined

as

Wzðt; f Þ ¼Z1

�1

Kzðt; sÞe�j2pf s ds ð1Þ

where Kz(t,s) is the instantaneous autocorrelation

function (IAF) given by

Kzðt; sÞ ¼ zðt þ s2Þz�ðt � s

2Þ ð2Þ

and z(t) is the analytic associate of s(t)

ði:e:; zðtÞ ¼ sðtÞ þ jp

R1�1

sðsÞt�s dsÞ [5].

The WVD satisfies a number of desirable mathe-

matical properties. However, application of the WVD

is limited by interference terms, occurring as a result of

the bilinear transformation. These interferences occur

in the case of nonlinear frequency modulated signals

and multicomponent signals, (see [4] for details).

Quadratic time–frequency distributions, belonging

to a class referred to as reduced interference distribu-

tions (RIDs), were introduced in order to attenuate the

interference terms (crossterms), and hence, provide a

better signal representation. The RID used for TF

visualization in this paper is the modified B distribu-

tion, expressed as [3]

qzðt; f Þ ¼Z1

�1

Z1

�1

Gbðt � u; sÞKzðu; sÞe�j2pfs du ds ð3Þ

where

Gbðt; sÞ ¼cosh�2b tR1

�1 cosh�2b f dfð4Þ

is the smoothing time-lag kernel defining the modified

B distribution. This distribution was chosen as it has

been shown, using objective criteria, to provide high

TF resolution and excellent cross term suppression

simultaneously [11]. A discrete version of the modified

B distribution for digital implementation is presented

in [10].

252 Med Bio Eng Comput (2007) 45:251–260

123

2.1.2 Matching pursuit algorithm

Given a discrete signal of length N, s 2 RN ; we con-

sider the problem of representing s as a linear combi-

nation of elements from a large, overcomplete,

dictionary, U 2 RN�M; of M waveforms, where M > N.

The individual waveforms of U are referred to as

atoms, denoted by /i 2 RN ; i ¼ 0; 1; . . . ;M � 1: The

problem of representing s using the dictionary U can

be formulated simply as

s ¼X

i

ai/i ð5Þ

where ai are the atom coefficients. Methods for solving

this problem are referred to as atomic decomposition

techniques.

The MP algorithm is an iterative atomic decompo-

sition technique currently finding application in a

number of engineering areas. Using MP, a signal

s 2 RN can be represented using the overcomplete

dictionary U as follows.

s ¼XP�1

i¼0

ai/i þ RP ¼ sP þ RP ð6Þ

where RP ¼ s� sP is the signal residue and sP is the

signal approximation after the (P – 1)th iteration. The

signal approximation and the residual are updated

through the following iterative process:

Assume R0 = s. For k ¼ 1; . . . ;P;

Rk ¼ Rk�1 ��Rk�1;/k

i

�� /ki

sk ¼ sk�1 þ�Rk�1;/k

i

�� /ki

ð7Þ

where

i ¼ arg max1�i�M

�Rk�1;/k

i

�� ð8Þ

and h:; :i denotes the inner product. The dictionary

atoms are normalized such that ||/i||2 = 1. It can be

easily shown that the orthogonality of Rk + 1 and /ik in

each iteration ensures conservation of energy; that is

jjsjj22 ¼XP�1

i¼0

hRi;/ii�� 2þjjRPjj22 ð9Þ

2.2 Relative structural complexity measure

In many real signal processing applications, such as

machine condition monitoring and newborn EEG

seizure detection, the recorded signal undergoes a

change in structure, as the underlying process gener-

ating the signal undergoes some type of changes. An

analytical method for identifying changes in signal

structure is therefore highly desirable. The proposed

RSC measure, defined in this subsection, is a method

for analyzing changes in signal structure.

2.2.1 Definition of relative structural complexity

When using MP decomposition, we are usually inter-

ested in approximating a signal using the least number

of dictionary atoms while maintaining the most rele-

vant signal information embedded in the original sig-

nal. This is usually accomplished by stopping the MP

iterative process when a suitable criterion, referred to

as the stopping criterion, is met. In this paper, the level

of approximation accuracy, [i.e., signal to error ratio

(SER)], defined as

SERk ¼ 20 log10

jjsjj2jjRkjj2

� �dB ð10Þ

is used as the stopping criterion. The MP process is

stopped when SERk ‡ gD, where gD is the desired

approximation accuracy.

In [2], it was reported that the number of Gabor

atoms (modulated, scaled and translated Gaussian

functions), chosen in a MP approximation, was related

to the complexity1 of a signal. This was demonstrated

with synthetic signals exhibiting limit cycle and chaotic

behaviour constructed from the Duffing equation.

In [21], it was stated that ‘‘a matching pursuit

decomposition in a given dictionary defines a system of

interpretation for signals.’’ Signal components, which

are interpreted well with a given dictionary, are re-

ferred to as coherent structures, and these structures

are indicated by strong correlation with some dictio-

nary atoms. The more coherent a signal is with a dic-

tionary, the larger the correlations between dictionary

atoms and the signal residues [21]. From this, we infer

that the more coherent a signal is with a given dictio-

nary, the fewer MP iterations required to achieve the

desired level of approximation accuracy.

Considering the findings of [ 2, 21], it seems natural

to introduce a new MP-based complexity measure re-

ferred to as RSC, which gives a quantitative indication

of the complexity in interpreting a signal given a

decomposition dictionary.

1 The definition of complexity here is related to the complexity ofthe phase space representation (level of chaotic behaviour) ofthe signal, often used in nonlinear time series analysis [19].

Med Bio Eng Comput (2007) 45:251–260 253

123

Definition [RSC]: Given a decomposition dictionary

U 2 RN�M; we define the RSC of a signal s 2 R

N as the

minimum number of atoms needed by the MP

decomposition to approximate the signal to a desired

level of accuracy, as defined by (10).

As it can be seen from this definition, the RSC is

very dependent on both the chosen decomposition

dictionary and the desired accuracy of approximation.

This dependence justifies the word ‘‘relative’’ in our

definition. This complexity measure has the advanta-

geous ability to be adapted to the signal to be

approximated, given that some a priori information

about the signal is available.

2.2.2 Illustration of RSC using synthetic signals

To illustrate the idea of RSC, we designed the fol-

lowing experiment using synthetically generated sig-

nals. The experiment involved three different TF

dictionaries, which include:

1. Gabor dictionary—this dictionary consists of

translated, scaled and modulated versions of a

Gaussian window [21].

2. Wavelet Packet dictionary—this dictionary con-

sists of approximately Nlog2(N) waveforms [13]

and is simply a family of orthonormal wavelet

bases [21]. The dictionary used in this paper

was built from a Daubechies 10 quadrature mirror

filter.

3. Cosine Packet dictionary—this dictionary also

consists of approximately Nlog2(N) waveforms,

including the standard orthonormal Fourier basis

and a variety of rectangular windowed sinusoids of

various widths and locations [13] (n.b. this dictio-

nary is similar to the real Gabor dictionary).

In this experiment, a number of synthetic signals,

which have varying levels of coherency with the chosen

decomposition dictionary were created. To do this, two

different TF dictionaries were selected. One of the

dictionaries was chosen to be the decomposition dic-

tionary, UD: The second dictionary was used only in

the composition of the synthetic signals (i.e., not used

for signal decomposition), and is referred to as the

alternative dictionary, denoted by UA:

Synthetic signals of length N were constructed using

P randomly selected atoms of which P–L were selected

from UD and L from UA: The number of atoms, L,

from UA was increased from 0 to P, resulting in syn-

thetic signals with decreasing levels of coherency with

the decomposition dictionary UD:

In the case where L is small, we would expect

the signal to be highly coherent with UD and hence

produce a low RSC. For the case where L is close to P,

only a small proportion of UD atoms would be used to

construct the signal. For this signal, we would expect

low coherency with UD which translates to a large

RSC.

The plots shown in Fig. 1 are two examples of the

results obtained from this experiment. For the exam-

ples in Fig. 1, N = 512, P = 30, UD = Wavelet Packet

dictionary and gD = 13 dB were chosen. It can be seen

from Fig. 1 that two alternative dictionaries, namely

Cosine Packet dictionary and Gabor dictionary, were

used to illustrate RSC. This figure confirms our

expectation in that the RSC of the signal increases as

the number of alternative atoms, L, used in the con-

struction of the synthetic signals increases. This also

confirms that the coherency between the structures of a

signal and the decomposition dictionary, when using

MP, can be quantified by the RSC measure. This

finding suggests that a suitably chosen decomposition

dictionary will allow us to produce a compact signal

representation if information on signal structure is

available a priori. This result will be exploited in the

following subsection.

This experiment was repeated with P = 50 and 70,

and with UD : Cosine Packet dictionary and Gabor

dictionary with similar results as shown in Fig. 1.

A noteworthy remark related to Fig. 1 is that, the

Cosine Packet atoms are slightly more coherent with

the Wavelet Packet atoms than the Gabor atoms. This

is indicated by a slower rate of rise in the RSC measure

when using the Cosine Packet dictionary as the alter-

native compared to the Gabor dictionary.

0 5 10 15 20 25 3020

40

60

80

100

120

140

160

No. Alternative Atoms

Str

uctu

ral C

ompl

exity

ΦA: Cosine Packet

ΦA: Gabor

Fig. 1 Relative structural complexity (RSC) of synthetic signalswhen the decomposition dictionary is the Wavelet Packetdictionary and the alternative dictionaries are either the CosinePacket or Gabor dictionaries


123

2.2.3 Coherent newborn EEG time–frequency

dictionary design

Time–frequency analysis of both background and sei-

zure newborn EEG states was previously undertaken

by the present authors in [6–9]. They concluded that the

newborn EEG background state exhibits two significant

types of patterns in the TF domain. The first pattern is

related to the abnormal burst–suppression. In the time

domain, this pattern is characterized by a burst of high

voltage activity lasting 1–10 s followed by a period of

quiescence or inactivity [1]. An example of the TF

representation of a burst–suppression pattern, using the

modified B distribution, is shown in Fig. 2a. It can be

seen that the burst of high energy masks all other pat-

terns. The second class of pattern found in the TF

representation of the newborn EEG background is the

EEG activity lacking a clearly recognizable TF pattern

[6–9]. In this background state, a dominant TF com-

ponent, following a specific instantaneous frequency

law, does not exist, as shown in the example Fig. 2b.

Our previous investigation of the newborn EEG

seizure state using TF analysis methods showed that

the TF patterns of newborn EEG seizures can be

generally characterized by piecewise linear frequency

modulated (LFM) components with slowly varying

amplitudes [6–9]. The analysis also showed that the

newborn EEG seizure is quite often multicomponent.

Both these characteristics can be seen in the example

TF representations, Fig. 2c and d, of two newborn

EEG seizure epochs.

The piecewise LFM components characterizing

newborn EEG seizure suggests that the design of a

decomposition dictionary, coherent with newborn

EEG seizure structures, is feasible. A more detailed

analysis of the TF structures of EEG seizures [27],

from a significantly larger database than the one used

in [6–9], allowed for the specific characterization of

the newborn EEG TF structures. It was found in [27]

that the LFM components of the seizures had a

starting frequency of nb 2 [0.425,6.875] Hz and LFM

slopes of ns 2 [–0.06,0.06] Hz/s. It was concluded from

these observations that a TF dictionary coherent with

the newborn EEG seizure state must include LFM

atoms covering the observed ranges for nb and ns. It

was also decided that only LFM atoms would be in-

cluded in the dictionary and not piecewise LFM

atoms, as this would cause a combinatorial explosion

in the number of atoms in the dictionary, resulting in

unrealistic processing times.

1 2 3 4 5 6

2

4

6

8

10

12

14

Frequency (Hz)

Tim

e (s

econ

ds)

Fs=20Hz N=300Time-res=5

Background, burst-suppression pattern

1 2 3 4 5 6

2

4

6

8

10

12

14

Frequency (Hz)

Tim

e (s

econ

ds)


Background lacking specific pattern

1 2 3 4 5 6

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

econ

ds)


Seizure exhibiting piecewise LFM, multicomponent

1 2 3 4 5 6

2

4

6

8

10

12

14

Frequency (Hz)

Tim

e (s

econ

ds)


Seizure exhibiting quasi-constant, multicomponent

(a) (b)

(c) (d)

Fig. 2 Time–frequencyrepresentations of newbornelectroencephalogram (EEG)using modified B distributionwith b = 0.02. This figureshows two backgroundpatterns (a, b) and two seizurepatterns (c, d)


123

The set of LFM atoms to be included in the pro-

posed dictionary are of the form

/LFMi ðnÞ ¼ A cos

2pðnib þ

nis

2 nÞnFs

þ h

!;

n ¼ 0; 1; . . . ;N � 1 ð11Þ

where Fs is the sampling frequency, h 2 [0,2p) is the

starting phase and A is a scalar value chosen such that

||uiLFM||2 = 1. For the analysis of newborn EEG, a

sampling frequency of Fs = 20 Hz was chosen as

approximately 95% of the newborn EEG power is

found in frequencies less than 8 Hz [28].

Since the described set of LFM atoms do not, in

general, form a complete dictionary, we construct an

overcomplete coherent dictionary by combining the set

of LFM atoms with an overcomplete Gabor dictionary

[24, 25]. This dictionary is used for the RSC analysis of

real and synthetic newborn EEG data.

2.2.4 Illustration of coherent newborn EEG dictionary

To illustrate the efficiency of the proposed dictionary

in representing the newborn seizure state, a MP

decomposition of a 12.8 s newborn EEG seizure was

performed. By choosing a short enough epoch

length, the piecewise LFM structures of newborn

EEG seizure can easily be approximated by LFM

structures.

The TF representation of the newborn EEG sei-

zure epoch, shown in Fig. 3a, can be characterized by

two LFM components. The atom chosen by MP from

the proposed coherent dictionary in the first iteration

is shown in Fig. 3b. It can be seen that the atom

chosen clearly resembles the dominant LFM com-

ponent in the newborn EEG seizure epoch. The

residual after the first MP iteration is shown in

Fig. 3c. It should be noted that the TF representation

in Fig. 3c has been rescaled to clearly show how the

remaining signal energy is distributed in the TF do-

main. This explains why the second LFM component

appears to have larger amplitude in Fig. 3c than it

did originally in Fig. 3a. The TF representation of

the atom chosen in the second MP iteration is shown

in Fig. 3d. This atom closely resembles the second

LFM component in the EEG seizure epoch. The

residual after two iterations, shown in Fig. 3e, illus-

trates that no clearly recognizable TF patterns re-

main in the residual.

-250-50150Time signal



26

x 107

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Seizure epoch

-0.100.1Time signal

-0.100.1Time signal

525

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Atom 1214

x 106

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Residual: R1

520

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Atom 2

28

x 106

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)Residual: R2

(a) (b) (c)

(e)(d)

Fig. 3 The matching pursuit (MP) decomposition of a seizureepoch using the proposed TF dictionary. The first two atomsselected by the MP algorithm, (b) and (d), clearly capture the

main characteristic of the EEG seizure epoch, as can be judgedby looking at the time–frequency distribution of the originalsignal (a) and that of the second residual (e)


123

3 Newborn EEG data

3.1 Synthetic newborn EEG data

In [27], a method for simulating newborn EEG back-

ground and newborn EEG seizure was presented.2 For

the initial investigation of the RSC measure applied to

newborn EEG, we created a number of realistic syn-

thetic newborn EEG signals using the simulation

methods of [27]. The synthetic newborn EEG signals

are composed of four time periods; namely, preictal,

seizure onset, seizure and postictal. The preictal and

postictal periods were created using the newborn EEG

background model described in [27], each lasting 60 s.

The seizure period was created using the seizure model

of [27] and lasted for 50 s. The seizure onset period was

constructed using a combination of synthetic back-

ground and seizure signals. The seizure onset period

was synthesized with a gradual increase in signal to

background ratio (SBR), given by

SBR ¼ 20 logjjsszjj2jjsbkjj2

� �dB ð12Þ

where ssz is the seizure signal and sbk is the background

signal. The seizure onset was synthesized to start 24 s

before the full-fledged seizure. The SBR was changed

every 4 s with the following successive values

[-2.5,0,2.5,4,5,6] dB. Fifty synthetic newborn EEG sig-

nals of this form were created for the synthetic RSC

analysis in Sect. 4.1.

3.2 Real newborn EEG data

The EEG from six neonates exhibiting EEG seizure

periods, as marked by a pediatric neurologist from the

Royal Children’s Hospital, Brisbane, Australia, were

analyzed using the RSC measure. The EEG data was

recorded at the Royal Brisbane and Women’s Hospi-

tal, using the MEDELEC Profile System. The raw

EEG was bandpass filtered with cutoff frequencies at

0.5 and 70 Hz, and was sampled at 256 Hz. For the

RSC analysis, the EEG data were digitally bandpassed

filtered with cutoff frequencies at 0.5 and 10 Hz, before

being downsampled to 20 Hz.

4 Application of RSC to newborn EEG

4.1 RSC analysis of synthetic newborn EEG

Synthetic newborn EEG signals were used in the initial

investigation for two main reasons. Using a mathe-

matical model, we can generate a signal that captures

the main characteristics of the newborn EEG without

the added complexity introduced by artefacts. Also,

synthetic signals allow us to specify the exact time

locations of the transitions between the two EEG

states; a matter which is subjective and reviewer-

dependent for the case of real newborn EEG [33].

These two characteristics of the synthetic signals allow

us to assess the strengths and the weaknesses of the

new complexity measure before being applied to real

newborn EEG.

The RSC was implemented using a sliding, rectan-

gular window, of length N = 256 samples. The overlap

between successive windows was set at 60 samples (i.e.,

3 s). The stopping criterion for the MP decomposition

was chosen to be gD � 13 dB:

An example of a synthetic signal, along with its

RSC, are illustrated in Fig. 4a and b. The four events,

namely preictal, seizure onset, seizure and postictal are

marked in Fig. 4a. It can be seen that the RSC is quite

high during the preictal state. As the EEG progresses

through the seizure onset section, the RSC measure

decreases. This RSC is at its lowest and is relatively

stable in the seizure period before a sharp increase at

the beginning of the postictal period. This general

trend of the RSC was observed for all 50 synthetic

newborn EEG signals.

0 20 40 60 80 100 120 140 160 1800

10

20

30

40

50

RS

C

Relative Structural Complexity

0 20 40 60 80 100 120 140 160 180

−50

0

50

Time (sec)

Am

plitu

de (

µV)

Synthetic EEG

PreIctal Onset Seizure PostIctal

(a)

(b)

Fig. 4 a The RSC measure corresponding to the (b) syntheticnewborn EEG signal

2 The MATLAB code used to create the synthetic newborn EEGbackground and EEG seizure used in this paper is based on themodels described in [27]. The code is freely available from http://www.som.uq.edu/research/sprcg.


123

Table 1 shows the mean and standard deviation

(std) for the RSC in the preictal, onset, seizure and

postictal periods for all 50 synthetic signals. It can be

seen from Table 1 that the general trend is for signifi-

cantly lower RSC during the seizure period than either

of the nonseizure periods (i.e., preictal and postictal),

with the onset period producing an intermediary value

illustrating the transition between preictal (back-

ground) and seizure states.

4.2 RSC analysis of real newborn EEG

As in the case of the synthetic newborn EEG, the RSC

was implemented using a sliding, rectangular window,

of length N = 256 samples and a window shift of 60

samples. The MP stopping criterion was set at

gD � 13 dB:

Figure 5 shows a real newborn EEG signal, along

with its respective RSC. The time periods for the

preictal, onset, seizure and postictal are indicated in

both Fig. 5a and b. It can be seen in Fig. 5a that the

RSC in the preictal state begins with high values and

then starts to decline during the seizure onset period.

The RSC drops significantly as the newborn EEG

evolves into a fully developed electrographic seizure

event. As this seizure event wanes, the RSC gradually

increases until the seizure event vanishes and the EEG

enters into the postictal state. Similarly, an increase in

nonlinear-based complexity towards the end of a sei-

zure event was previously observed in [2] for the case

of adult EEG. The example in Fig. 5 is typical of what

was observed in the analysis of the six newborn EEG

recordings.

The TF representations, using the modified B dis-

tribution, of epochs from the preictal, seizure and po-

stictal states are shown in Fig. 6a–c respectively. It can

be seen in the preictal and postictal epochs, Fig. 6a and

c, that there are no clearly recognizable continuous TF

patterns. However, the TF representation of the sei-

zure epoch, Fig. 6b, shows three piecewise LFM com-

ponents.

The example in Fig. 5 exhibits similar results to the

synthetic EEG data analyzed in Sect. 4.1. However, in

Fig. 5a, it can be seen that there is a significant and

unexpected drop in the RSC for the period between 70

and 85 s (preictal state). This sharp and unexpected

drop is caused by short-time and high-amplitude arte-

facts [12, 29], as marked in Fig. 5b. This type of tran-

sient artefact often represents a large percentage of

epoch energy. These signal structures also correlate

highly with some small-scaled Gabor atoms causing

low RSC measures for the epochs in which they are

contained.

Table 2 shows the variation in RSC between non-

seizure and seizure periods of selected epochs from six

newborn EEG recordings. Although the RSC differs

between patients, the general trend is a decline in RSC

as the signal progresses towards the seizure state.

5 Discussion

When a system undergoes an internal change in its

state, (e.g., brain seizing, power-line affected by dis-

turbances, knock in internal combustion engine, etc.),

the signals emanating from it, as measured by external

sensors, usually reflect this change through a change in

their structure. This enables non-invasive methods for

detecting this change in state of the system.

In this paper, we presented a new method for

analyzing changes in signal structure using a relative

measure of signal complexity based on the MP-

decomposition technique. This new measure is strongly

dependent on the nature of the decomposition TF

dictionary and the desired level of accuracy in the

signal approximation. This new signal complexity

measure can also be taken as a measure of the coher-

ency between the signal structure and the decomposi-

tion dictionary.

Table 1 Mean and standard deviation of relative structuralcomplexity measures for the preitcal, seizure and postictal peri-ods

Preitcal Onset Seizure Postictal

Mean 32.4 26.5 11 31.8Standard deviation 5.35 5.58 3.52 5.85

0 50 100 150 200 250 3000

20

40

60

RS

C

Relative Structural Complexity

0 50 100 150 200 250 300−50

0

50

Time (sec)

Am

plitu

de (

µV)

Real EEGPreictal Onset Seizure Postictal

Preictal Onset Seizure Postictal

Artefact

Artefact

(b)

(a)

Fig. 5 a The relative structural complexity measure correspond-ing to the (b) real newborn EEG signal


123

Compact signal approximations using MP decom-

position can be achieved by choosing a decomposition

dictionary that is highly coherent with the signal under

analysis. This prompted the development of a newborn

EEG specific TF dictionary that was used to analyze

newborn EEG.

To build a TF dictionary that is coherent with

newborn EEG seizures, it was shown that the specific

TF patterns in newborn EEG seizure could be trans-

lated into a set of TF atoms. This set of atoms, which

was a set of LFM atoms, was combined with an over-

complete Gabor dictionary to form the new overcom-

plete TF dictionary. Using this dictionary, the RSC

measure was applied to synthetic and real newborn

EEG. The analysis indicated a significant fall in the

RSC, as the newborn EEG transitioned between

background and seizure periods.

Due to clear differences in RSC observed between

seizure and nonseizure newborn EEG, the next logical

step would be to incorporate the RSC measure into an

online automatic newborn EEG seizure detection

algorithm. However, there are a few limitations that

need to be overcome before such an automatic detec-

tion algorithm becomes practical.

The major limitation in using the RSC as a stand-

alone feature for automatic newborn EEG seizure

detection is the difficulty in determining a threshold

level to distinguish seizure from nonseizure. In our

analysis of real newborn EEG, it was observed that

the level of RSC for nonseizure and seizure varied

significantly between patients. This result suggests that

a patient-specific method of threshold determination,

possibly through neural network training, would be

required. Artefacts, particularly short-time and high-

amplitude artefacts, severely limit the application of

RSC. It was shown in Fig. 5 that a large amplitude

artefact caused a significant and undesirable drop in

the RSC. Therefore, artefacts may introduce numerous

false detections. The drop in RSC for this type of

artefact is due to the high coherency between artefact

structures and some small-scaled Gabor atoms. The

use of an appropriate artefact removal technique may

alleviate the effects of artefacts. Another possibility

worth investigating is the development of a new TF

dictionary, which does not include atoms that are

coherent with any artefacts or background structures,

while still coherent with the newborn EEG seizure

state.

6 Conclusion

Relative structural complexity, introduced in this pa-

per, is a new MP-based measure of signal complexity,

where the relativity is associated with the chosen

decomposition dictionary. Development of a new TF

dictionary, which is highly coherent with newborn

EEG seizure structures has provided us with a method

for analyzing the changes in newborn EEG signal

structures as it evolves from the background state to

the seizure state. The proposed methodology for ana-

lyzing changes in signal structure using the RSC mea-

sure is generic and may be used in many other signal

detection problems. This method, however, is limited

by the necessary a priori information for suitable dic-

tionary selection and/or design. This limitation can be

overcome via in-depth analysis of the embedded

structures of the signals under analysis, as was dem-

onstrated for the case of newborn EEG.

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Preictal

Time signal

PS

D

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Seizure

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

Frequency (Hz)

Tim

e (s

)

Postictal

(a) (c)(b)

Fig. 6 Time–frequency representations of real newborn EEG: a preictal, b seizure and c postictal periods

Table 2 Relative structuralcomplexity for selectednonseizure and seizureperiods in the newbornelectroencephalogram

Patientnumber

Nonseizure Seizure

1 54 112 51 113 46 134 52 225 51 176 47 27


123

Acknowledgments The authors gratefully acknowledge Prof.Paul Colditz for organizing the acquisition of the real newbornEEG data and Dr. Chris Burke and Jane Richmond for theirexpertise in newborn EEG reading.

References

1. Aminoff M (1992) Electroecephalograhy: general principlesand clinical applications. In: Aminoff M (ed) Electrodiag-nosis in clinical neurology, 3rd edn. Churchill Livingstone,New York, pp 41–91

2. Bergey G, Franaszczuk P (2001) Epileptic seizures arecharacterised by changing signal complexity. Clin Neuro-physiol 112(2):241–249

3. Boashash B (2003) Heuristic formulation of TFDs. In:Boashash B (ed) Time–frequency signal analysis and pro-cessing: a comprehensive reference, Chap 2. Elsevier, Lon-don, pp 29–57

4. Boashash B (2003) Theory of quadratic TFDs. In: Boashash B(ed) Time–frequency signal analysis and processing: a com-prehensive reference, Chap 3. Elsevier, London, pp 59–81

5. Boashash B (2003) Time–frequency concepts. In: BoashashB (ed) Time–frequency signal analysis and processing: acomprehensive reference, Chap 1. Elsevier, London, pp 4–27

6. Boashash B, Mesbah M (2001) A time–frequency approachfor newborn seizure detection. IEEE Eng Med Biol Mag20(5):54–64

7. Boashash B, Mesbah M (2003) Time–frequency methodol-ogy for newborn electroencephalographic seizure detection.In: Papandreou-Suppappola A (ed) Applications in time–frequency signal processing. CRC Press, Boca Raton

8. Boashash B, Mesbah M, Colditz P (2001) Newborn EEGseizure pattern characterisation using time–frequency anal-ysis. In: Proceedings of IEEE international conference onacoustics, speech and signal processing, Salt Lake City, USA,pp 1041–1044

9. Boashash B, Mesbah M, Colditz P (2003) Time–frequencydetection of EEG abnormalities. In: Boashash B (ed) Time–frequency signal analysis and processing: a comprehensivereference, Chap 15.5. Elsevier, London, pp 663–670

10. Boashash B, Putland G (2003) Discrete time–frequencydistributions. In: Boashash B (ed) Time–frequency signalanalysis and processing: a comprehensive reference, Chap6.1. Elsevier, London, pp 232–241

11. Boashash B, Sucic V (2003) Resolution measure criteria forthe objective assessment of the performance of quadratictime–frequency distributions. IEEE Trans Signal Process51(5):1253–1263

12. Celka P, Boashash B, Colditz P (2001) Preprocessing andtime–frequency analysis of newborn EEG seizures. IEEEEng Med Biol 20(5):30–39

13. Chen S, Donoho D, Saunders M (2001) Atomic decompo-sition by basis pursuit. Soc Ind Appl Math Rev 43(1):129–159

14. Donoho D, Elad M, Temlyakov V (2006) Stable recovery ofsparse overcomplete representations in the presence ofnoise. IEEE Trans Inf Theory 52(1):6–18

15. Donoho D, Huo X (2001) Uncertainty principles and idealatomic decomposition. IEEE Trans Inf Theory 46(7):2845–2862

16. Durka P (2004) Adaptive parameterization of epilepticspikes. Phys Rev E 69:051914

17. Elad M, Bruckstein A (2002) A generalized uncertaintyprinciple and sparse representation in pairs of bases. IEEETrans Inf Theory 48(9):2558–2567

18. Gotman J, Flanagan D, Zhang J, Rosenblatt B (1997)Automatic seizure detection in the newborn: methods andinitial evaluation. Electroencephalogr Clin Neurophysiol103(3):356–362

19. Kantz H, Shreiber T (1997) Nonlinear time series analysis.Cambridge University Press, Cambridge

20. Lombroso C (1993) Neonatal EEG polygraphy in normaland abnormal newborns. In: Niedermeyer E, Silva FLD (eds)Electroencephalography: basic principles, clinical applica-tions and related fields, 3rd edn. Williams and Wilkins,Baltimore, pp 803–875

21. Mallat S, Zhang Z (1993) Matching pursuits with time–fre-quency dictionaries. IEEE Trans Signal Process 41(12):3397–3415

22. Mizrahi E, Kellaway P (1998) Diagnosis and management ofneonatal seizure. Lippincott–Raven, Philadelphia

23. Rangayyan RM, Krishnan S (2001) Feature identification inthe time–frequency plane by using the Hough–Radontransform. Pattern Recognit 34(6):1147–1158

24. Rankine L (2006) Newborn EEG seizure detection usingadaptive time–frequency signal processing. Ph.D. thesis,Queensland University of Technology, Brisbane

25. Rankine L, Mesbah M, Boashash B (2004) A novel algo-rithm for newborn EEG seizure detection using matchingpursuits with a coherent time–frequency dictionary. In:Proceedings of international conference on scientific andengineering computation, Singapore, pp CD-ROM

26. Rankine L, Mesbah M, Boashash B (2006) IF estimation formulticomponent signals using image processing techniques inthe time–frequency domain. Signal Process (accepted)

27. Rankine L, Stevenson N, Mesbah M, Boashash B (2007) Anonstationary model of newborn EEG. IEEE Trans BiomedEng 54(1):19–28

28. Scher M, Sun M, Steppe D, Guthrie R, Sclabassi R (1994)Comparison of EEG spectral and correlation measures be-tween healthy term and preterm infants. Pediatr Neurol10(2):104–108

29. Teixeira A, Tome A, Lang E, Gruber P, da Silva AM (2006)Automatic removal of high-amplitude artefacts from single-channel electroencephalograms. Compu Methods ProgramsBiomed 83(2):125–138

30. Tropp J (2004) Greed is good: algorithmic results for sparseapproximation. IEEE Trans Inf Theory 50(10):2231–2242

31. Tropp J, Gilbert A, Strauss M (2006) Algorithms for simu-lataneous sparse approximation. Part I: greedy pursuit. Sig-nal Process 86(3):572–588

32. Umapathy K, Krishnan S, Parsa V, Jamieson D (2005) Dis-crimination of pathological voices using a time–frequencyapproach. IEEE Trans Biomed Eng 52(3):421–430

33. Wilson S, Scheuer M, Plummer C, Young B, Pacia S (2003)Seizure detection: correlation of human experts. Clin Neu-rophysiol 114:2156–2164


123

A matching pursuit-based signal complexity measure for the analysis of newborn EEG

Documents