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.
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: Section 2 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 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 and scaling function . 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 and scaling functions for one-dimensional case can be defined as
| (1) |
| (2) |
| (3) |
| (4) |
| (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., trees a, b, c, and d) for analysis and also for synthesis (see Figure 1).
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) |
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) |
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)
| (9) |
| (10) |
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.
In our experiment, six scene images as shown in Figure 3, 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.
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) |
| (12) |
| (13) |
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. Table 1 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.
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.
Table 2 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.
The value in the parenthesis is the PSNR measure.
For visual evaluation Figures 5, 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.
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 level σ = 40 as shown in Table 3.
|
Table 3 MSE and PSNR (dB) results of proposed method at five-levels of decomposition and noise level σ =40.
Through Table 3, 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 with σ = 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).
Figure 12 The denoising results of Image 5 from test sample. (a) Noisy image with σ = 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).
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 levels σ = 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.
From Figures 13–18 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 Table 4.
|
Table 4 Average processing time in seconds of three de-noising methods on our test samples.
From Table 4, 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.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgment
This project was funded by the National Plan for Science, Technology and Innovation (MAARIFAH), King Abdulaziz City for Science and Technology, Kingdom of Saudi Arabia, Award no. INF2696-02-12.
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