186
5 Optimization Algorithm and RFID System Physical Anti-Collision
wavelet inverse transformation to obtain the denoised signals. The detailed steps are
as follows:
(1) Noisy signal f (t) is decomposed by wavelet transform method. Furthermore,
we obtain the decomposition coefficients w j,k .
(2) Wavelet coefficients w j,k are processed by threshold λ. The processed wavelet
coefficients are recorded as ¯
w j,k .
(3) The wavelet coefficients w j,k are reconstructed by the wavelet inverse
transform to obtain estimation signal f (t), which is the denoised signal.
The soft threshold method is used to select the wavelet transform coefficients.
The equation is shown in (5.40).
f (x) =
sgn(x)(|x| − λ) |x| > λ
0
|x| ≤ λ
(5.40)
In Eq. (5.40), sgn(x) stands for a symbolic function which is shown in Eq. (5.41).
sgn(x) =
1 x > 0
−1 x < 0
(5.41)
In order to verify the effectiveness and superiority of the wavelet threshold
denoising algorithm, a noisy image obtained in a typical scene is selected, and
different methods are used to denoise it, respectively. Experimental results are shown
in Fig. 5.26 and Table 5.4.
The equation of SNR is shown in (5.42).
SNR = 10 lg
⎡
⎢
⎢
⎢
⎣
M
i=1
N
j=1
g(i, j)
2
M
i=1
N
j=1
[g(i, j) − f (i, j)] 2
⎤
⎥
⎥
⎥
⎦
(5.42)
In Eq. (5.42), M represents the image’s length. N represents the image’s width.
f (i, j) and g(i, j), respectively, represent the gray values of the original image and
the denoised image.
Figure 5.27 and Table 5.5 show that the denoising method based on sym4 wavelet
threshold is superior to other denoising methods, either from subjective visual effects
or from objective quality evaluation criteria. In order to further verify the validity
and practicability of this algorithm, different images of different scenes and the
same noise degree of different images are used to conduct denoising experiments.
Experimental results are shown in Fig. 5.27 and Table 5.5.
From Fig. 5.27 and Table 5.5, comparing with other methods, the sym4 wavelet
threshold denoising method performs best. By using the sym4 wavelet threshold
denoising method, the quality of the noisy images has been greatly improved not only
from the subjective visual aspect but also from the objective quality evaluation aspect.
5 Optimization Algorithm and RFID System Physical Anti-Collision
wavelet inverse transformation to obtain the denoised signals. The detailed steps are
as follows:
(1) Noisy signal f (t) is decomposed by wavelet transform method. Furthermore,
we obtain the decomposition coefficients w j,k .
(2) Wavelet coefficients w j,k are processed by threshold λ. The processed wavelet
coefficients are recorded as ¯
w j,k .
(3) The wavelet coefficients w j,k are reconstructed by the wavelet inverse
transform to obtain estimation signal f (t), which is the denoised signal.
The soft threshold method is used to select the wavelet transform coefficients.
The equation is shown in (5.40).
f (x) =
sgn(x)(|x| − λ) |x| > λ
0
|x| ≤ λ
(5.40)
In Eq. (5.40), sgn(x) stands for a symbolic function which is shown in Eq. (5.41).
sgn(x) =
1 x > 0
−1 x < 0
(5.41)
In order to verify the effectiveness and superiority of the wavelet threshold
denoising algorithm, a noisy image obtained in a typical scene is selected, and
different methods are used to denoise it, respectively. Experimental results are shown
in Fig. 5.26 and Table 5.4.
The equation of SNR is shown in (5.42).
SNR = 10 lg
⎡
⎢
⎢
⎢
⎣
M
i=1
N
j=1
g(i, j)
2
M
i=1
N
j=1
[g(i, j) − f (i, j)] 2
⎤
⎥
⎥
⎥
⎦
(5.42)
In Eq. (5.42), M represents the image’s length. N represents the image’s width.
f (i, j) and g(i, j), respectively, represent the gray values of the original image and
the denoised image.
Figure 5.27 and Table 5.5 show that the denoising method based on sym4 wavelet
threshold is superior to other denoising methods, either from subjective visual effects
or from objective quality evaluation criteria. In order to further verify the validity
and practicability of this algorithm, different images of different scenes and the
same noise degree of different images are used to conduct denoising experiments.
Experimental results are shown in Fig. 5.27 and Table 5.5.
From Fig. 5.27 and Table 5.5, comparing with other methods, the sym4 wavelet
threshold denoising method performs best. By using the sym4 wavelet threshold
denoising method, the quality of the noisy images has been greatly improved not only
from the subjective visual aspect but also from the objective quality evaluation aspect.