Quantitative Sleep Monitoring - Quantitative EEG Analysis Methods and Clinical Applications - page 282

Akin and Akgul attempt to detect sleep spindles by using the Daubechie mother
wavelet to create the family of functions for the basis [52]. The discrete wavelet
transform would easily detect sleep spindles if the mother wavelet had the same
form as a sleep spindle. Hence, the Daubechie wavelet was chosen to best approxi-
mate the form of a sleep spindle so that when the mother wavelet is scaled and trans-
lated, it is possible to detect sleep spindles of different sizes occurring at different
times. This technique, however, works only for sleep spindle detection. Therefore, it
can be used to identify only stage 2 of NREM sleep.

10.15.2 Matching Pursuit
Matching pursuit provides a solution to the adaptive approximation problem. It
was first suggested by Mallat and Zhang [53] as a signal processing tool. It is similar
in concept to the Fourier transform or the wavelet transform in that it represents
some signal x by using a linear summation of functions from some group of func-
tions, termed a dictionary .
The matching pursuit algorithm attempts to find a solution to the linear expan-
sion problem:

N

∑

x = a nn (10.6)

n = 1

Here, g n belongs to some family of functions known as a dictionary, D . The
matching pursuit algorithm attempts to find the g n that best approximate the origi-
nal function x . When the dictionary D is an orthonormal basis, the matching pursuit
algorithm yields the same results as the wavelet transform.
The matching pursuit algorithm has been applied to the problem of sleep stage
detection in various ways [51, 54]. In these studies, the Gabor functions were the
family of functions used as the dictionary. Gabor functions are a mixture of a sinu-
soidal and a Gaussian and have the form shown in (10.7). In addition to a tradi-
tional time-frequency analysis, matching pursuit is better equipped than wavelets to
identify transients (waveforms such as K complexes or sleep spindles) [55]. Because
there are fewer restrictions on the dictionary used in matching pursuit than there are
on an orthonormal wavelet basis, a Gabor function closely resembling these wave-
forms can easily be chosen from the dictionary.

z

⎛
⎜

tu
s

− ⎞

⎟

− π

() ()

(

( )

)

gt = K e λ cos ω tu − + φ (10.7)

λ

10.16 Statistics of Sleep State Detection Schemes

With so many sleep state detection methods available, there needs to be a way to
compare them so that the “best” method can be used. However, a challenge facing
such a metric is that sleep state detection is a multicategory classification problem,
as opposed to a binary classification problem. In sleep state detection there are five
possible classifications for a feature point that is extracted from a given epoch of the
polysomnograph (or EEG). It can be a feature from either the wake state, NREM