Fourier magnitude is very small and, therefore, the
absorbance is sensitive to small changes even in low-
humidity conditions. In Fig. 11, the multiscale re-
storation obtains similar results for the DNB sample.
The restored Fourier spectrum is very close to that of
the reference signal measured in a low-humidity con-
dition. The reference spectrum of a DNB sample goes
as low as the noise level in the 1–1:8 THz range, as
shown in Fig. 11(a). Therefo re, the absorbance, which
is the ratio of spectral magnitudes of the restored and
the reference signals, becomes very sensitive in this
frequency range. Even though the restored spectral
magnitude is very close to the reference spectrum,
nonstationary absorbance peaks are observed in this
range. We could observe a similar pattern for a DNT
sample in the 2:5–3 THz range.
In order to compare different THz signal restora-
tion methods using a metric that shows relative im-
provement (RI), the ratio of the mean-square errors
of the restored signal and the refere nce signal is used
in Table 1:
ðtÞ denotes the error between restored signal
xðtÞ and the reference signal rðtÞ, ε
ðtÞ¼xðtÞ − rðtÞ,
ðtÞ denotes the error between degraded signal
uðtÞ and the reference signal rðtÞ, ε
ðtÞ¼uðtÞ − rðtÞ.
Table 1 summarizes RI of various restoration
schemes for the two chemical samples, Wiener filter
only, ANN only, a combination of Wiener and ANN
filters, and the multiscale restoration. For both che-
micals, a combined Wiener and ANN filter shows
some improvement over single-restoration-filte r
cases (Wiener only and ANN only). The multiscale
Wiener and ANN restoration technique shows the
biggest improvement of all combinations in THz
signal restoration. The wavelet-based multiscale
restoration method represents a THz signal with ap-
proximation and detail components that reveal low-
and high-frequency characteristics of the signal.
Wavelet transforms have a pyramidal tree structure,
allowing successive decomposition of the lowest sub-
band at each level, which means finer resolutions
toward the lower frequency bands. In level-2 decom-
position, the approximation component contains a
low-frequency trend of a THz signal under 2:5 THz.
The detail component (D
) contains higher-frequency
signal details for the range of approximately 1.3 to
3 THz, as shown in Fig. 5. A combined restoration
filter designed for each individual component
reduces the degradation effect separately.
Although THz radiation has demonstrated potential
in detecting chemical substances from a distance, the
sensing range is significantly limited due to strong
attenuation by humid atmosphere. THz beams are
absorbed by water molecules in the air when they
propagate through the atmosphere. Therefore, it is
difficult to obtain high signal-to-noise ratio with
the power and efficiency of most currently available
THz radiation sources and detectors. Material-
specific THz signatures can be easily obscured by
strong attenuation and spurious peaks in the absorp-
tion spectrum. This paper addresses a THz signal
restoration technique to remove atmospheric degra-
dation of a THz signal measured in the open air. THz
signal restoration from atmospheric attenuation is
important to increase the sensing range of THz sig-
nals in humid environments. The proposed ap-
proach is based on multiscale signal decomposition
with combined signal restoration filters, a Wiener
deconvolution filter and an ANN, for each signal com-
ponent. A THz signal is decomposed into approxima-
tion and detail components using the DWT. A set of
Wiener deconvolution filter and an ANN restore each
signal component from the fluctuations and the noise
that cause strong absorption bands in the spectrum.
A restored THz signal is obtained by the inverse
DWT of the filtered signal components. Experimen-
tal results with two chemical substances demonstra-
te that the multiscale signal restoration technique is
effective in removing atmospheric degradation when
compared to individual approaches.
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934 APPLIED OPTICS / Vol. 49, No. 5 / 10 February 2010