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An algorithm combining threshold method and modulus
maxima method was chosen in the de-nosing process. Through
the theory of tracking maximum modulus in the scales, modulus
maxima method can search the characteristic points of the
signals in the lower scale on the basic of the maximum modulus
chosen in the highest scale (MALLAT S, 1992). However, a lot
of noise is contained in the detail information of the first scale.
Thus, noise cannot be completely reduced because the reserved
modulus maximum points often contain part of noise. To solve
the problem, threshold method was applied to combine with the
modulus maxima method. In detail, principle of wavelet entropy
was introduced in the first scale to obtain the adaptive threshold
value (Zhengyou He, et al, 2004).
4. EXPERIMENT AND EVALUATION
4.1 Experiment
The de-nosing method based on the combination of threshold
method and modulus maxima method was proposed and
experiment should be carried out to testify the ability of
reducing signal noise. In the two-wavelength lidar system, there
are two backscatter signals respectively in red channel and near
infrared channel. In order to better display the ability of de-
nosing, the worse signal which is in red channel was chosen.
According to the proposed method based on wavelet transform,
the de-noising process was made according to the flow shown in
the Figure 3.
| Noisy signal |
Wavelet
Decompasition
Removal ofthe singular
value based on 30 rule
Threshold quantification with threshold
method and modulus maxima method
Signal
Reconstruction
De-noising
signal
Figure. 3 Flow of de-noising process
*db3" was chosen to be the basis function of wavelet transform,
and the noisy signal was decomposed to 4 layers. Firstly, the
mean square value of the high-frequency coefficients was
calculated to remove the singular values, and all the wavelet
transform coefficients greater than 3o were set to zero while the
others remain unchanged. Then further improvement on the
signal is made based on the combination of modulus maxima
method and threshold method. Finally the decomposition
coefficients were reconstructed by remodelling function, and the
result of the reconstruction was de-noising signal.
4.) De-noising effect evaluation
In order to testify the ability of the method, an evaluation of the
noise reduction should be given. As a result, some other
classical algorithms were applied in the experiment to make
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
comparison with the combination method of modulus maxima
method and threshold method. Direct average method, forced
de-noising method and FFT method were chosen, and the result
of de-noising is shown in the Figure 4.
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c. Forced de-noising method d. FFT method
Figure 4. Comparison of different de-noising algorithms
As the Figure 4 shows, the backscatter signal becomes smooth
after de-noising of all the algorithms. However, the effects of
different algorithms are obviously different. The noisy signal
reduced by combination method has most smooth waveform
and has best effeteness. On the contrary, direct average method
makes the signal lose some useful component, while there were
still peaks exist in the edge of the signal by forced de-noising
method. For the FFT method, noise cannot be correctly reduced
from the signal because of the lack of local analysis.
Besides, measurement criteria were also defined to further
evaluate the effects of signal noise reduced. In detail, signal-to-
noise ratio (SNR) and mean-square deviation (RMSE) are
expressed as the measurement criteria in the following
calculation formulas.
SNR =10xlog,,(S/N) (1)
Where S= power of raw signal
N= power of noise
RMSE = XL f) Q)
Where f(n)* de-noising signal
f(n)* raw signal
The effects of de-noising will be better when SNR are higher
and RMSE are smaller. SNR and RMSE of different algorithms
were calculated and the results were shown in the Table 1.
