# An Efficient Image Denoising Method for Wireless Multimedia Sensor Networks Based on DT-CWT

Authors: Rachid Sammouda; Abdul Malik S. Al-Salman; Abdu Gumaei; Nejmeddine Tagoug
Journal: International Journal of Distributed Sensor Networks
 (2015)

---

## Abstract

Wireless multimedia sensor network (WMSN) is a developed technology of wireless sensor networks and includes a set of nodes equipped with cameras and other sensors to detect ambient environment and produce multimedia data content. In this context, many types of noises occur due to sensors problems, change of illumination, fog, rain, and other weather conditions. These noises usually degrade the digital images acquired by camera sensors. Image denoising in spatial domain is more difficult and time-consuming for real-time processing of WMSNs applications. In this study, an efficient method based on Dual-Tree Complex Wavelet Transform (DT-CWT) is developed to enhance the image denosing in WMSNs. This method is designed to reduce the image noises by selecting an optimal threshold value estimated from the approximation of wavelet coefficients. In our experiment, the proposed method was tested and compared with standard Discrete Wavelet Transform (DWT) and Stationary Wavelet Transform (SWT) on a set of natural scene images. Better results were achieved by using the DT-CWT in terms of image quality metrics and processing time.


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## Body

## 1. Introduction

WMSN is a developed technology of wireless sensor networks which contains a set of nodes connected with camera sensors to acquire and transfer images and videos through sensor networks [1–3]. However, digital images and videos generated by camera sensors can be affected by noise during capturing, transmitting, and retrieving processes. As a result, many dots can be spotted in an image under low lighting conditions, change of illumination, fog, rain, and other weather problems. In general, the noisy images impose excessive limitations on the performance of image processing techniques such as detection and segmentation which need a clean image to work effectively [4–7]. Thus, image denoising methods are mainly used to remove these noises from captured images without affecting the images information as much as possible.The literature showed that there are many different methods of image denoising. These methods can be divided into two groups based on the image representation domain used: spatial domain-based and frequency domain-based. In fact, applying one of these techniques depends on the domain of image processing applications and the statistical property of image noises. In spatial domain, every pixel of the original image can be processed independently based on some relations with its neighbors and correspondence values of their filter matrix. Median filter [8], neighborhood average method [9], and weighted median filter and the center-weight median filter [8, 10] are some common methods that have been applied for image denoising in spatial domain. However, these methods had some limitations such as a high computation load. Furthermore, recent methods [11–17] tried to combine the median filter with the impulse detection to reduce median filters limitations. However, the performance of these methods is totally depending on the impulse detector performance. In addition, mean-based filters [18–20] can be used as an alternative solution in reducing the high load computation. Recently, some methods [21–24] have been proposed for image noise reduction by using some fuzzy logic approaches. Unfortunately, most existing methods are still suffering from the high load computations which delay the processing time of images and the response of WMSNs applications as a real-time application. In frequency domain, images are transformed into another domain to perform some operations on image coefficients [25, 26]. Then, the inverse of the transformation is calculated and returned back into image domain. Discrete Fourier Transform (DFT) is the most popular transformation that is widely used for signal and image processing applications with satisfactory accuracy [27, 28]. However, DFT filter method loses the correct localization in both time and frequency domains. Thus, it is not suitable to be used for nonstationary signals like images. The other common transformation method is Discrete Cosine Transform (DCT). DCT is a simple and effective tool for denoising [28]. Nevertheless, some drawbacks of DCT such as high loss of information and low resolution make it unsuitable for real-time processing of critical applications. Over the past decade, Discrete Wavelet Transform (DWT) was widely used as a more accurate tool than DFT and DCT because of its excellent localization property. DWT was considered an essential signal and image processing tool for many applications such as compression and denoising [26, 29–33]. It provides applications with a suitable basis for separating the noise signal from the image signal by using the appropriate threshold value without affecting information of the original image. Several researches were conducted to find the appropriate selection for the wavelet threshold that can be used for signal and image denoising [29, 32–35]. In most of them, DWT was commonly used, but it has three major problems. These problems are lack of shift invariant, poor directionality, and lack of phase information. The problem of shift-variant can be reduced by applying the Stationary Wavelet Transform (SWT) as introduced in 1996 as an improvement of standard DWT [36]. Although SWT improves the power of wavelet in image denoising considerably, it suffers from the cost of very high redundancy which makes it computationally expensive [37]. Recently, many mathematical algorithms have been proposed to solve the DWT problems by using different forms of Complex Wavelet Transforms (CWT) [38–43]. Dual-Tree Complex Wavelet Transform (DT-CWT) is considered as one of the most efficient forms of CWT as reported in [44, 45]. It gives texture information oriented in six different directions with limited redundancy. Consequently, in this study, we proposed an efficient image denoising method by using the DT-CWT for real-time image processing of WMSNs applications.The rest of the paper is organized as follows: Section2 introduces the mathematical basics of DT-CWT. Section 3 presents the proposed 2D DT-CWT-based method for image denoising. Section 4 explains the research experiment that used to verify the reliability of the proposed method. Finally, a brief conclusion about this work is drawn in Section 5.


## 2. Dual Tree-Complex Wavelet Transform (DT-CWT)

Dual Tree-Complex Wavelet Transform (DT-CWT) is an enhancement extension of DWT with important properties of wavelet. It uses analytic filter to perform the wavelet analysis instead of real-valued filter coefficients; therefore it solves problems of DWT at the cost of limited redundancy. Kingsbury proposed the DT-CWT technique to achieve an accurate reconstruction while providing the other advantages of complex wavelets [44]. It is closely shift invariant and directionally selective in two and higher dimensions. This can be achieved with redundancy factor of only 2
d for d-dimensional signals, which is significantly lower than the Stationary Wavelet Transform (SWT) [45]. In fact, DT-CWT gives more information about the detail of an image by producing six directional subbands per level for each pixel oriented at angles ±15°, ±45°, and ±75° with 4 : 1 redundancy [38]. While DWT produces three directional subbands per level for each pixel conveying image features oriented at angles 90°, ±45°, and 0°, it decomposes a signal into real (r) and imaginary (i) parts in terms of mother wavelet ψ
(
x
) and scaling function φ
(
x
). The coefficients of real and imaginary parts can be used to compute amplitude and phase information. The real (r) and imaginary (i) parts of the wavelet ψ
(
x
) and scaling φ
(
x
) functions for one-dimensional case can be defined as(1)
ψ
r
t
=
2
∑
i
=
0
n
H
a
n
φ
r
2
t
-
n
,
(2)
ψ
i
t
=
2
∑
i
=
0
n
H
b
n
φ
i
2
t
-
n
,
(3)
φ
r
t
=
2
∑
i
=
0
n
L
a
n
ψ
r
2
t
-
n
,
(4)
φ
i
t
=
2
∑
i
=
0
n
L
b
n
ψ
i
2
t
-
n
,
(5)
ψ
c
t
=
ψ
r
t
+
j
ψ
i
t
,where ψ
r and ψ
i represent the wavelet functions, L represents the low-pass filters, and H represents the high-pass filters. The wavelet functions ψ
r and ψ
i yield the complex wavelet function ψ
c, which is given by (5).To compute DT-CWT of an image, it can be extended to two-dimensional case by applying its filter bank in all dimensions separately. 2D structure of DT-CWT needs four trees (e.g., treesa, b, c
, and d) for analysis and also for synthesis (see Figure 1).Figure 1
Filter bank structure for 2D DT-CWT.The signal of the input image is decomposed up to a desired level by two separable 2D DWT branches, (a) and (b) in parallel to the same data. Each filtering process is followed by a downsampling by two and the pairs of DT-CWT trees are applied to rows (x) and then to columns (y) of the image, which can be represented as(6)
h
x
+
j
g
x
h
y
+
j
g
y
=
h
x
h
y
+
g
x
g
y
+
j
h
x
g
y
+
g
x
h
y
.


## 3. Proposed Method

The proposed denoising method assumes that the signal of image is corrupted by different types of noise. However, the power of these types of noise is still much lower than the power of the original image signal. In this work, we focus on a zero mean additive white Gaussian noise (AWGN) which is generally more difficult to remove. Based on this assumption, the problem of image denoising can be mathematically expressed as follows:(7)
Y
=
X
+
σ
N
,where Y is the observed noisy image, X is the original image, and σ
N is the AWGN noise with standard deviation σ and zero mean. Both Y and X are of the same sizes. The block diagram that is shown in Figure 2 represents the main steps of the proposed method. The method starts with converting the input color image to a gray scale image, where 2D DT-CWT is applied to decompose image into four levels; then filter bank is applied for each level of image rows and columns. A hard threshold function with optimal threshold value is used for each subband coefficient, except the lowest subband. Therefore, all high frequency subband coefficients which are less than the optimal threshold are set to zeros. Finally, coefficients yielded from previous step are used as an inverse of 2D DT-CWT to reconstruct the original image after reducing image noises.Figure 2
Flow chart of 2D DT-CWT-based method for image denoising.In general, there are mainly two methods: soft threshold function and hard threshold function; the hard threshold function has been adopted and defined by the following:Hard threshold:(8)
ω
i
,
j
Z
=
ω
i
,
j
Y
if
ω
i
,
j
Y
>
T
0
if
ω
i
,
j
Y
≤
T
,where ω
i
,
j
Y is the signal wavelet coefficients of input image before threshold, ω
i
,
j
Z is the generic wavelet coefficients after threshold, and T is the threshold value. Our method adjusts the coefficients of 2D DT-CWT by optimal or near-optimal universal threshold values. They are computed based on the Median Absolute Deviation (MAD) and the length of wavelet coefficients at each decomposition level as follows:(9)
T
j
=
M
A
D
j
∗
2
∗
log
⁡
N
j
,where N
j is the length of detail coefficients at jth decomposition level and M
A
D
j is the median absolute deviation of empirical wavelet coefficients which can be given as follows [25]: (10)
M
A
D
j
=
m
e
d
i
a
n
ω
L
-
1
,
j
0.6745
,
j
=
0,1
,
…
,
2
L
-
1
-
1
,where L is the number of decomposition levels of analyzed image signal which depends on the application. Here, it is enough to consider the number of decomposition levels as four levels, where an energy criterion can help to remove the noise. The reason behind selecting the median absolute deviation of detail coefficients as noise estimator because of it is a robust noise estimator, and much less sensitive than the usual standard deviation and mean to extreme values [25]. The denoised image (output image) can be obtained by performing the inverse of 2D DT-CWT after modifying the wavelet coefficients according to some thresholds or rules. The 2D DT-CWT gives the 2D images a four-time redundancy (expensive) and this redundancy allows both shift invariance and good directional sensitivity.


## 4. Experiment

This section shows the results of applying our image denoising based on 2D DT-CWT to a set of natural indoor-outdoor scene images. Moreover, we make a comparison between the results of proposed method with the results of applying 2D DWT and 2D SWT for the same set of images. The proposed method is developed with MATLAB R2012a programming environment. Coefficients in the wavelet domain have been modified by hard threshold function before image reconstruction. The hardware configuration is composed of Intel Core 2 Duo T6500 2.10 GHz processor with 2 GB of RAM and 320 GB Hard Disk. The operating system is Microsoft Windows 7 Professional. Under these configurations, the test samples, the performance metrics, and the experimental results will be given in the following subsections.


### 4.1. Test Samples of Indoor-Outdoor Scene Images

In our experiment, six scene images as shown in Figure3, of dimensions 640 × 480 pixels, are used as test samples. Four of which (Image 1 to Image 4) are selected from KAIST scene images database English subset taken by Sony Cyber-Shot DSC-T70 camera [46]. They are captured in both outdoors and indoors environments under different lighting conditions. The two remaining images (Image 5 and Image 6) are outdoor images, taken by Kodak EasyShare C613 ZOOM camera from two places (preparatory year and SAMBA bank) at King Saud University.Figure 3
Test samples of indoor-outdoor scene images numbered from left to right row by row from 1 to 6.


### 4.2. Performance Metrics

Performance of the proposed image denoising approach is quantitatively evaluated by using three image quality metrics: Normalized Absolute Error (NAE), Peak Signal to Noise Ratio (PSNR), and Mean Square Error (MSE), as well as the processing time of the proposed method. The image quality metrics are computed based on the original and the denoised scene images. NAE is a criterion to evaluate the ability of preserving the information of the original image where the large value of NAE means that denoised image is poor quality [47]. It is defined as follows:(11)
N
A
E
=
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
-
D
m
,
n
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
,where O is the original image and D is the denoised image and, also, m and n are the number of pixels in row and column directions, respectively. On the other hand, the PSNR is a typical metric used to measure the ability of noise reduction performance, where the small value of PSNR means that denoised image is of poor quality [47]. PSNR is defined as follows:(12)
P
S
N
R
=
10
log
10
⁡
M
a
x
2
M
S
E
,where M
a
x is the maximum gray scale of pixels, for example, 255 for 8 bits, and M
S
E is the mean square error between the original image (O) and denoised image (D) which is defined as [47](13)
M
S
E
=
1
M
N
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
-
D
m
,
n
2
,where m and n represent the number of pixels in row and column directions, respectively. The last performance metrics is the processing time of method which can be calculated by running the codes of method in MATLAB R2012a on the same hardware configuration mentioned above. Processing time is an important measure for image denoising methods in real-time image processing applications. Here, it can be calculated by running the codes of different image denoising methods in MATLAB R2012a on the same hardware configuration mentioned above.


### 4.3. Results and Discussion

In order to verify the reliability of our proposed approach, all test samples were degraded artificially with Gaussian white noise of different levels 10%, 20%, 30%, and 40%, respectively. The experimental results of different denoising methods are assessed and computed using NAE, as well as processing time. Table1 exhibits the experiment results of NAE at different noise levels for the denoised images of three methods. Graphical representation of NAE results versus noise standard deviation (σ) for Image 1 and Image 6 can be seen clearly in Figure 4. It proves that the proposed method results in less NAE compared with the other methods for all tested images.Table 1
NAE results of de-nosing methods at different noise levels and four-levels of decomposition.
Image # with Noise Level
Image De-noising Methods
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Image 1
σ
=
10
0.0329
0.0284
0.0236
σ
=
20
0.0409
0.0353
0.0313
σ
=
30
0.0464
0.0410
0.0364
σ
=
40
0.0516
0.0473
0.0423
Image 2
σ
=
10
0.0247
0.0220
0.0175
σ
=
20
0.0329
0.0290
0.0256
σ
=
30
0.0408
0.0363
0.0334
σ
=
40
0.0479
0.0434
0.0405
Image 3
σ
=
10
0.0236
0.0212
0.0152
σ
=
20
0.0317
0.0307
0.0238
σ
=
30
0.0376
0.0369
0.0313
σ
=
40
0.0427
0.0423
0.0369
Image 4
σ
=
10
0.0326
0.0274
0.0205
σ
=
20
0.0471
0.0416
0.0339
σ
=
30
0.0590
0.0516
0.0448
σ
=
40
0.0701
0.0616
0.0573
Image 5
σ
=
10
0.0308
0.0193
0.0190
σ
=
20
0.0459
0.0365
0.0348
σ
=
30
0.0588
0.0495
0.0480
σ
=
40
0.0705
0.0605
0.0606
Image 6
σ
=
10
0.0229
0.0181
0.0158
σ
=
20
0.0336
0.0296
0.0254
σ
=
30
0.0418
0.0378
0.0345
σ
=
40
0.0496
0.0450
0.0437Figure 4
NAE versus noise standard deviation,σ at four levels of decomposition by different denoising methods for (a) Image 1 and (b) Image 6.
(a)
(b)In addition, the value of NAE is decreased with low noise conditions and is increased with high noise conditions. However, the proposed 2D DT-CWT-based method of image denoising gives better quantitative results than 2D DWT and 2D SWT-based methods of image denoising for all comparison parameters.Table2 shows the results of MSE and PSNR at different noise levels for the denoised images of three methods, where the values in the parenthesis are the PSNR measure. Large values of MSE mean that images are of poor quality and the large values of PSNR mean that images are of high quality. Here we can see that the results of 2D SWT-based method are better than 2D DWT-based method in terms of MSE and PSNR, but the results of proposed 2D DT-CWT-based method are the best for all comparisons. It is worth mentioning that whenever the value of noise level increases the value of MSE also increases and the value of PSNR decreases in all of the three methods.Table 2
MSE and PSNR (dB) results of De-nosing methods at different noise levels and four-levels of decomposition.
Image # with Noise Level
Image De-noising Methods
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Image 1
σ
=
10
55.53   (30.69)
36.64   (32.49)
23.92 (34.34)
σ
=
20
94.06   (28.40)
80.02   (29.10)
46.42 (31.46)
σ
=
30
127.02 (27.09)
110.61 (27.70)
64.09 (30.06)
σ
=
40
156.00 (26.20)
146.88 (26.46)
85.57 (28.81)
Image 2
σ
=
10
23.10   (34.50)
17.85   (35.62)
10.14   (38.07)
σ
=
20
46.71   (31.44)
39.30   (32.19)
24.87   (34.18)
σ
=
30
72.41   (29.53)
59.83   (30.36)
43.83   (31.71)
σ
=
40
97.44   (28.24)
80.85   (29.05)
61.56   (30.24)
Image 3
σ
=
10
28.66   (33.56)
89.39   (28.61)
10.25   (38.05)
σ
=
20
53.39   (30.86)
50.85   (31.07)
26.32   (33.93)
σ
=
30
74.59   (29.40)
70.31   (29.66)
44.01   (31.70)
σ
=
40
94.82   (28.36)
90.25   (28.58)
58.74   (30.44)
Image 4
σ
=
10
36.02   (32.57)
22.90   (34.53)
12.17   (37.28)
σ
=
20
75.88   (29.33)
60.98   (30.28)
36.77   (32.48)
σ
=
30
110.77 (27.69)
86.36   (28.77)
59.69   (30.37)
σ
=
40
146.19 (26.48)
113.94 (27.56)
90.02   (28.59)
Image 5
σ
=
10
53.83   (30.82)
17.18   (35.78)
15.17   (36.32)
σ
=
20
103.10 (28.00)
65.06   (30.00)
46.06   (31.50)
σ
=
30
153.26 (26.28)
117.74 (27.42)
88.70   (28.65)
σ
=
40
207.63 (24.96)
166.10 (25.93)
142.97 (26.58)
Image 6
σ
=
10
26.23   (33.94)
11.02   (37.71)
8.70     (38.74)
σ
=
20
63.21   (30.12)
46.53   (31.45)
26.29   (33.93)
σ
=
30
95.01   (28.35)
80.54   (29.07)
50.10   (31.13)
σ
=
40
124.97 (27.16)
110.68 (27.69)
70.84   (29.63)
The value in the parenthesis is the PSNR measure.For visual evaluation Figures5, 6, 7, 8, 9, and 10 show the result of three denoising methods on all images in the test sample. They contain the noisy image with noise level (σ = 40) and the denoised image of the proposed method and the other two methods.Figure 5
The denoising results of Image 1 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 6
The denoising results of Image 2 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 7
The denoising results of Image 3 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 8
The denoising results of Image 4 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 9
The denoising results of Image 5 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 10
The denoising results of Image 6 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)The visual evaluation emphasizes that the proposed 2D DT-CWT-based method gives best results of patterns and edges on denoised images with no degradation or artifacts because it deals with the edges on the images in six directions. Also, we can see that the DWT-based method does not achieve good results of patterns on denoised images in all cases because of its lack of directionality and shift invariant.Results of NAE and visual evaluation show that the denoised images by 2D SWT-based method are better than 2D DWT-based method because it is shift invariant, but they are not better than the denoised images of the proposed 2D DT-CWT-based method since it does not consider the six directions of edges information of decomposed images.Although the results of all used images in our experiment show that the decomposition process until four levels is practically good to remove Gaussian noise from images acquired by WMSNs devices, however, more real demonstrations with deeper analysis are investigated to show how the accuracy of the proposed method can be affected by varying the number of decomposition levels. Accordingly, we tested our proposed method by applying several values of decomposition level (1–5) on all the test images at noise levelσ = 40 as shown in Table 3.Table 3
MSE and PSNR (dB) results of proposed method at five-levels of decomposition and noise levelσ =40.
Image #:level of noise
Number of decomposition level
MSE
PSNR
Image 1:
σ = 40
1
308.089
23.244
2
115.1715
27.5174
3
85.9083
28.7905
4
85.5702
28.8076
5
85.5702
28.8076
Image 2:
σ = 40
1
298.8552
23.3762
2
99.408
28.1566
3
63.8291
30.0806
4
61.5572
30.238
5
66.874
29.8782
Image 3:
σ = 40
1
303.6185
23.3075
2
97.354
28.2473
3
60.672
30.3009
4
58.7403
30.4414
5
63.8291
30.0806
Image 4:
σ = 40
1
299.9368
23.3605
2
113.4212
27.5839
3
84.4663
28.864
4
90.0184
28.5875
5
96.5508
28.2832
Image 5:
σ = 40
1
241.2989
24.3053
2
160.5966
26.0734
3
140.6729
26.6487
4
142.9727
26.5783
5
147.8107
26.4337
Image 6:
σ = 40
1
208.3282
24.9433
2
106.6155
27.8526
3
75.2598
29.3652
4
70.8417
29.6279
5
72.0599
29.5539Through Table3, we note that most restored images have high PSNR and low MSE values (bold black values) at four levels of decomposition, except two cases (Image 4 and Image 5). These two cases have high PSNR and low MSE values (bold black values) at three levels of decomposition. Therefore, the limitation of the proposed method is how to determine the optimum value of decomposition level. However, the obtained results of the proposed method compared to other methods confirm that the four levels of decomposition are good enough to remove Gaussian noise from images of WMSNs applications. Figures 11 and 12 show the denoised images obtained by the proposed method at four and three levels of decomposition, respectively, at noise level σ = 40. From Figures 11 and 12, we can see that the denoised images in three levels of decomposition have a better quality than those denoised images in four levels of decomposition.Figure 11
The denoising results of Image 4 from test sample. (a) Noisy image withσ = 40; (b) denoised scene image using the proposed 2D DT-CWT at four levels of decomposition; (c) denoised scene image using the proposed 2D DT-CWT at three levels of decomposition which is better quality than denoised image in (b).
(a)
(b)
(c)Figure 12
The denoising results of Image 5 from test sample. (a) Noisy image withσ = 40; (b) denoised scene image using the proposed 2D DT-CWT at four levels of decomposition; (c) denoised scene image using the proposed 2D DT-CWT at three levels of decomposition which is better quality than denoised image in (b).
(a)
(b)
(c)Sensitivity analysis for different threshold values versus PSNR metric is employed here to validate the ideal value of MAD threshold. We applied different threshold values ranked from 0 to 100, incremented by 5 on all tested images at noise levelsσ = 20 and σ = 40. Then, for each threshold value used to denoise the noisy image, the PSNR metric is computed as shown in Figures 13–18. This step is employed technically to search for the optimal threshold point which yields the maximum PSNR value. Eventually, we compared the obtained maximum PSNR values with the PSNR values produced by the MAD technique as illustrated in Table 2.Figure 13
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 1.Figure 14
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 2.Figure 15
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 3.Figure 16
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 4.Figure 17
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 5.Figure 18
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 6.From Figures13–18 and Table 2, we can notice that the maximum PSNR values obtained by applying different thresholds are approximately the same as the PSNR values calculated by MAD-based threshold. For example, Figure 13 for denoised image (Image 1) showed that the maximum PSNR values are 31.46 and 28.81 with noise variances σ = 20 and σ = 40, respectively. These values are roughly equal to the PSNR values calculated by MAD-based threshold in Table 2. Added to that, Figures 13–18 illustrated the effects of the threshold parameter for determining the amount of useful signals and smoothness. Thus, the selected threshold values based on the MAD are almost optimal which consequently showed the effectiveness of using MAD strategy in the proposed method.Finally, a comparison of the average processing time of the 2D DWT- and 2D SWT-based methods and the proposed method for our test samples is presented in Table4.Table 4
Average processing time in seconds of three de-noising methods on our test samples.
De-noising Method
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Avg. Processing Time (s)
0.4837
1.3354
0.8138From Table4, it is clear to show that the average processing time of 2D SWT-based method is higher than that of the proposed 2D DT-CWT- and 2D DWT-based methods. Even though the proposed method consumes more processing time than the 2D DWT-based method, the above qualitative and quantitative results of image quality metrics support the efficiency of the proposed 2D DT-CWT-based method for image denoising. Experimental results prove that the proposed method is efficient and appropriate for image denoising. Thus, this method can be embedded as preprocessing stage to improve the efficiency of current WMSNs applications.


## 4.1. Test Samples of Indoor-Outdoor Scene Images

In our experiment, six scene images as shown in Figure3, of dimensions 640 × 480 pixels, are used as test samples. Four of which (Image 1 to Image 4) are selected from KAIST scene images database English subset taken by Sony Cyber-Shot DSC-T70 camera [46]. They are captured in both outdoors and indoors environments under different lighting conditions. The two remaining images (Image 5 and Image 6) are outdoor images, taken by Kodak EasyShare C613 ZOOM camera from two places (preparatory year and SAMBA bank) at King Saud University.Figure 3
Test samples of indoor-outdoor scene images numbered from left to right row by row from 1 to 6.


## 4.2. Performance Metrics

Performance of the proposed image denoising approach is quantitatively evaluated by using three image quality metrics: Normalized Absolute Error (NAE), Peak Signal to Noise Ratio (PSNR), and Mean Square Error (MSE), as well as the processing time of the proposed method. The image quality metrics are computed based on the original and the denoised scene images. NAE is a criterion to evaluate the ability of preserving the information of the original image where the large value of NAE means that denoised image is poor quality [47]. It is defined as follows:(11)
N
A
E
=
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
-
D
m
,
n
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
,where O is the original image and D is the denoised image and, also, m and n are the number of pixels in row and column directions, respectively. On the other hand, the PSNR is a typical metric used to measure the ability of noise reduction performance, where the small value of PSNR means that denoised image is of poor quality [47]. PSNR is defined as follows:(12)
P
S
N
R
=
10
log
10
⁡
M
a
x
2
M
S
E
,where M
a
x is the maximum gray scale of pixels, for example, 255 for 8 bits, and M
S
E is the mean square error between the original image (O) and denoised image (D) which is defined as [47](13)
M
S
E
=
1
M
N
∑
m
=
1
M
∑
n
=
1
N
O
m
,
n
-
D
m
,
n
2
,where m and n represent the number of pixels in row and column directions, respectively. The last performance metrics is the processing time of method which can be calculated by running the codes of method in MATLAB R2012a on the same hardware configuration mentioned above. Processing time is an important measure for image denoising methods in real-time image processing applications. Here, it can be calculated by running the codes of different image denoising methods in MATLAB R2012a on the same hardware configuration mentioned above.


## 4.3. Results and Discussion

In order to verify the reliability of our proposed approach, all test samples were degraded artificially with Gaussian white noise of different levels 10%, 20%, 30%, and 40%, respectively. The experimental results of different denoising methods are assessed and computed using NAE, as well as processing time. Table1 exhibits the experiment results of NAE at different noise levels for the denoised images of three methods. Graphical representation of NAE results versus noise standard deviation (σ) for Image 1 and Image 6 can be seen clearly in Figure 4. It proves that the proposed method results in less NAE compared with the other methods for all tested images.Table 1
NAE results of de-nosing methods at different noise levels and four-levels of decomposition.
Image # with Noise Level
Image De-noising Methods
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Image 1
σ
=
10
0.0329
0.0284
0.0236
σ
=
20
0.0409
0.0353
0.0313
σ
=
30
0.0464
0.0410
0.0364
σ
=
40
0.0516
0.0473
0.0423
Image 2
σ
=
10
0.0247
0.0220
0.0175
σ
=
20
0.0329
0.0290
0.0256
σ
=
30
0.0408
0.0363
0.0334
σ
=
40
0.0479
0.0434
0.0405
Image 3
σ
=
10
0.0236
0.0212
0.0152
σ
=
20
0.0317
0.0307
0.0238
σ
=
30
0.0376
0.0369
0.0313
σ
=
40
0.0427
0.0423
0.0369
Image 4
σ
=
10
0.0326
0.0274
0.0205
σ
=
20
0.0471
0.0416
0.0339
σ
=
30
0.0590
0.0516
0.0448
σ
=
40
0.0701
0.0616
0.0573
Image 5
σ
=
10
0.0308
0.0193
0.0190
σ
=
20
0.0459
0.0365
0.0348
σ
=
30
0.0588
0.0495
0.0480
σ
=
40
0.0705
0.0605
0.0606
Image 6
σ
=
10
0.0229
0.0181
0.0158
σ
=
20
0.0336
0.0296
0.0254
σ
=
30
0.0418
0.0378
0.0345
σ
=
40
0.0496
0.0450
0.0437Figure 4
NAE versus noise standard deviation,σ at four levels of decomposition by different denoising methods for (a) Image 1 and (b) Image 6.
(a)
(b)In addition, the value of NAE is decreased with low noise conditions and is increased with high noise conditions. However, the proposed 2D DT-CWT-based method of image denoising gives better quantitative results than 2D DWT and 2D SWT-based methods of image denoising for all comparison parameters.Table2 shows the results of MSE and PSNR at different noise levels for the denoised images of three methods, where the values in the parenthesis are the PSNR measure. Large values of MSE mean that images are of poor quality and the large values of PSNR mean that images are of high quality. Here we can see that the results of 2D SWT-based method are better than 2D DWT-based method in terms of MSE and PSNR, but the results of proposed 2D DT-CWT-based method are the best for all comparisons. It is worth mentioning that whenever the value of noise level increases the value of MSE also increases and the value of PSNR decreases in all of the three methods.Table 2
MSE and PSNR (dB) results of De-nosing methods at different noise levels and four-levels of decomposition.
Image # with Noise Level
Image De-noising Methods
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Image 1
σ
=
10
55.53   (30.69)
36.64   (32.49)
23.92 (34.34)
σ
=
20
94.06   (28.40)
80.02   (29.10)
46.42 (31.46)
σ
=
30
127.02 (27.09)
110.61 (27.70)
64.09 (30.06)
σ
=
40
156.00 (26.20)
146.88 (26.46)
85.57 (28.81)
Image 2
σ
=
10
23.10   (34.50)
17.85   (35.62)
10.14   (38.07)
σ
=
20
46.71   (31.44)
39.30   (32.19)
24.87   (34.18)
σ
=
30
72.41   (29.53)
59.83   (30.36)
43.83   (31.71)
σ
=
40
97.44   (28.24)
80.85   (29.05)
61.56   (30.24)
Image 3
σ
=
10
28.66   (33.56)
89.39   (28.61)
10.25   (38.05)
σ
=
20
53.39   (30.86)
50.85   (31.07)
26.32   (33.93)
σ
=
30
74.59   (29.40)
70.31   (29.66)
44.01   (31.70)
σ
=
40
94.82   (28.36)
90.25   (28.58)
58.74   (30.44)
Image 4
σ
=
10
36.02   (32.57)
22.90   (34.53)
12.17   (37.28)
σ
=
20
75.88   (29.33)
60.98   (30.28)
36.77   (32.48)
σ
=
30
110.77 (27.69)
86.36   (28.77)
59.69   (30.37)
σ
=
40
146.19 (26.48)
113.94 (27.56)
90.02   (28.59)
Image 5
σ
=
10
53.83   (30.82)
17.18   (35.78)
15.17   (36.32)
σ
=
20
103.10 (28.00)
65.06   (30.00)
46.06   (31.50)
σ
=
30
153.26 (26.28)
117.74 (27.42)
88.70   (28.65)
σ
=
40
207.63 (24.96)
166.10 (25.93)
142.97 (26.58)
Image 6
σ
=
10
26.23   (33.94)
11.02   (37.71)
8.70     (38.74)
σ
=
20
63.21   (30.12)
46.53   (31.45)
26.29   (33.93)
σ
=
30
95.01   (28.35)
80.54   (29.07)
50.10   (31.13)
σ
=
40
124.97 (27.16)
110.68 (27.69)
70.84   (29.63)
The value in the parenthesis is the PSNR measure.For visual evaluation Figures5, 6, 7, 8, 9, and 10 show the result of three denoising methods on all images in the test sample. They contain the noisy image with noise level (σ = 40) and the denoised image of the proposed method and the other two methods.Figure 5
The denoising results of Image 1 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 6
The denoising results of Image 2 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 7
The denoising results of Image 3 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 8
The denoising results of Image 4 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 9
The denoising results of Image 5 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)Figure 10
The denoising results of Image 6 from test sample at four levels of decomposition by different methods. (a) Noisy image withσ = 40; (b) denoised scene image using 2D DWT; (c) denoised scene image using 2D SWT; (d) denoised scene image using the proposed 2D DT-CWT.
(a)
(b)
(c)
(d)The visual evaluation emphasizes that the proposed 2D DT-CWT-based method gives best results of patterns and edges on denoised images with no degradation or artifacts because it deals with the edges on the images in six directions. Also, we can see that the DWT-based method does not achieve good results of patterns on denoised images in all cases because of its lack of directionality and shift invariant.Results of NAE and visual evaluation show that the denoised images by 2D SWT-based method are better than 2D DWT-based method because it is shift invariant, but they are not better than the denoised images of the proposed 2D DT-CWT-based method since it does not consider the six directions of edges information of decomposed images.Although the results of all used images in our experiment show that the decomposition process until four levels is practically good to remove Gaussian noise from images acquired by WMSNs devices, however, more real demonstrations with deeper analysis are investigated to show how the accuracy of the proposed method can be affected by varying the number of decomposition levels. Accordingly, we tested our proposed method by applying several values of decomposition level (1–5) on all the test images at noise levelσ = 40 as shown in Table 3.Table 3
MSE and PSNR (dB) results of proposed method at five-levels of decomposition and noise levelσ =40.
Image #:level of noise
Number of decomposition level
MSE
PSNR
Image 1:
σ = 40
1
308.089
23.244
2
115.1715
27.5174
3
85.9083
28.7905
4
85.5702
28.8076
5
85.5702
28.8076
Image 2:
σ = 40
1
298.8552
23.3762
2
99.408
28.1566
3
63.8291
30.0806
4
61.5572
30.238
5
66.874
29.8782
Image 3:
σ = 40
1
303.6185
23.3075
2
97.354
28.2473
3
60.672
30.3009
4
58.7403
30.4414
5
63.8291
30.0806
Image 4:
σ = 40
1
299.9368
23.3605
2
113.4212
27.5839
3
84.4663
28.864
4
90.0184
28.5875
5
96.5508
28.2832
Image 5:
σ = 40
1
241.2989
24.3053
2
160.5966
26.0734
3
140.6729
26.6487
4
142.9727
26.5783
5
147.8107
26.4337
Image 6:
σ = 40
1
208.3282
24.9433
2
106.6155
27.8526
3
75.2598
29.3652
4
70.8417
29.6279
5
72.0599
29.5539Through Table3, we note that most restored images have high PSNR and low MSE values (bold black values) at four levels of decomposition, except two cases (Image 4 and Image 5). These two cases have high PSNR and low MSE values (bold black values) at three levels of decomposition. Therefore, the limitation of the proposed method is how to determine the optimum value of decomposition level. However, the obtained results of the proposed method compared to other methods confirm that the four levels of decomposition are good enough to remove Gaussian noise from images of WMSNs applications. Figures 11 and 12 show the denoised images obtained by the proposed method at four and three levels of decomposition, respectively, at noise level σ = 40. From Figures 11 and 12, we can see that the denoised images in three levels of decomposition have a better quality than those denoised images in four levels of decomposition.Figure 11
The denoising results of Image 4 from test sample. (a) Noisy image withσ = 40; (b) denoised scene image using the proposed 2D DT-CWT at four levels of decomposition; (c) denoised scene image using the proposed 2D DT-CWT at three levels of decomposition which is better quality than denoised image in (b).
(a)
(b)
(c)Figure 12
The denoising results of Image 5 from test sample. (a) Noisy image withσ = 40; (b) denoised scene image using the proposed 2D DT-CWT at four levels of decomposition; (c) denoised scene image using the proposed 2D DT-CWT at three levels of decomposition which is better quality than denoised image in (b).
(a)
(b)
(c)Sensitivity analysis for different threshold values versus PSNR metric is employed here to validate the ideal value of MAD threshold. We applied different threshold values ranked from 0 to 100, incremented by 5 on all tested images at noise levelsσ = 20 and σ = 40. Then, for each threshold value used to denoise the noisy image, the PSNR metric is computed as shown in Figures 13–18. This step is employed technically to search for the optimal threshold point which yields the maximum PSNR value. Eventually, we compared the obtained maximum PSNR values with the PSNR values produced by the MAD technique as illustrated in Table 2.Figure 13
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 1.Figure 14
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 2.Figure 15
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 3.Figure 16
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 4.Figure 17
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 5.Figure 18
PSNR values versus threshold values with noise variancesσ = 20 and σ = 40 for Image 6.From Figures13–18 and Table 2, we can notice that the maximum PSNR values obtained by applying different thresholds are approximately the same as the PSNR values calculated by MAD-based threshold. For example, Figure 13 for denoised image (Image 1) showed that the maximum PSNR values are 31.46 and 28.81 with noise variances σ = 20 and σ = 40, respectively. These values are roughly equal to the PSNR values calculated by MAD-based threshold in Table 2. Added to that, Figures 13–18 illustrated the effects of the threshold parameter for determining the amount of useful signals and smoothness. Thus, the selected threshold values based on the MAD are almost optimal which consequently showed the effectiveness of using MAD strategy in the proposed method.Finally, a comparison of the average processing time of the 2D DWT- and 2D SWT-based methods and the proposed method for our test samples is presented in Table4.Table 4
Average processing time in seconds of three de-noising methods on our test samples.
De-noising Method
2D DWT-based Method
2D SWT-based Method
Proposed 2D DT-CWT-based Method
Avg. Processing Time (s)
0.4837
1.3354
0.8138From Table4, it is clear to show that the average processing time of 2D SWT-based method is higher than that of the proposed 2D DT-CWT- and 2D DWT-based methods. Even though the proposed method consumes more processing time than the 2D DWT-based method, the above qualitative and quantitative results of image quality metrics support the efficiency of the proposed 2D DT-CWT-based method for image denoising. Experimental results prove that the proposed method is efficient and appropriate for image denoising. Thus, this method can be embedded as preprocessing stage to improve the efficiency of current WMSNs applications.


## 5. Conclusions and Future Work

In this work, we have studied the mathematical model of DT-CWT for multilevel reconstruction of signals. Based on the properties of DC-CWT for signal image decomposition, an efficient 2D DT-CWT-based image denoising method is proposed for real-time applications of WMSNs. The excellent features of the DT-CWT such as multidirectionality and shift-invariance make it more suitable for image denoising of real-time applications. The proposed 2D DT-CWT-based method reduced the noise of images by applying an optimal threshold value of hard threshold function using MAD strategy. This threshold not only forms the near-optimal wavelet coefficients, but also makes it a more stable magnitude for patterns on the images. It was developed in the MATLAB R2012a and tested over test samples of indoor-outdoor scene images taken by Sony Cyber-Shot and Kodak EasyShare cameras. The taken images were captured in real environments which are similar to images captured by wireless sensor devices. Processing time and image quality metrics have been calculated and compared for estimating the efficiency of the 2D DT-CWT filtering method. The results obtained from this study prove the performance and efficiency of the 2D DT-CWT filtering method at four levels of decomposition. It has achieved excellent denoising characteristics in preserving the edges of texture patterns compared to the 2D DWT and 2D SWT with limited redundancy and moderate processing time for image processing-based WMSNs applications. Results showed that applying the 2D DT-CWT method to enhance WMSNs images improved its efficiency in reducing the noise of images acquired by WMSNs devices. Thus, it can be embedded as preprocessing stage to improve the efficiency of current WMSNs applications. Even though the proposed method was conducted on real sensing images, in the future works, we will test our method on images taken by camera sensors connected to wireless multimedia sensor networks.



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*Source: 632568-2015-11-10.xml*