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Abstract

The key of image denoising algorithms is to preserve the details of the original image while denoising the noise in the image. The existing algorithms use the external information to better preserve the details of the image, but the use of external information needs the support of similar images or image patches. In this paper, an edge-aware image denoising algorithm is proposed to achieve the goal of preserving the details of original image while denoising and using only the characteristics of the noisy image. In general, image denoising algorithms use the noise prior to set parameters todenoise the noisy image. In this paper, it is found that the details of original image can be better preserved by combining the prior information of noise and the image edge features to set denoising parameters. The experimental results show that the proposed edge-aware image denoising algorithm can effectively improve the performance of block-matching and 3D filtering and patch group prior-based denoising algorithms and obtain higher peak signal-to-noise ratio and structural similarity values.

Keywords

Image denoising edge-aware detail preserving denoising parameters noise level

Introduction

Image quality is easy to decrease in the process of acquisition, transmission, and storage. Random error is called image noise. It is one of the reasons that distort the images. Image noise has hindered people’s access to image information. It not only affects human visual perception, but also has a great impact on the digital image processing technology, such as image saliency detection, image segmentation, image recognition, and so on. Therefore, image denoising is an important research topic in digital image processing, and it can be used as preprocessing in other image processing algorithms. Image denoising algorithm is to separate and remove the noise from the noisy image. Its goal is to make the denoising result as close as possible to the original image. That means the image information should be preserved to the maximum extent. In order to simplify the discussion, we assume that the cleaned image is distorted by Additive White Gaussian Noise, referred as AWGN, in this paper. AWGN is a very common type of noise. The relationship between the original image and the noisy image is as follows

y = x + n

(1)where

y

is the noisy image,

x

is the original image, and

n

represents the additive noise. The denoising algorithm is trying to get a result

\hat{x}

close to

x

as much as possible from a given image

y

As an important research topic, image denoising has attracted many researchers to study and explore. Many algorithms have been proposed. One of the most widely studied categories of denoising algorithms is using the standard deviation of noise as denoising parameter.^1–6 We call the standard deviation of noise as noise level. However, the noise level of an image is unavailable in real-world situations. It is obvious that the denoising parameter setting affects the denoised result. Therefore, a variety of image noise level estimation algorithms have appeared with the progress of research on image denoising.

There is another popular category called image blind denoising.^7,8 Image blind denoising can precede noisy images without using denoising parameter. These algorithms can avoid manual setting error and reduce labor consumption. However, it shows that if denoising algorithms use denoising parameter to denoise, they are more likely to achieve better results. Later, researchers often combine the image denoising algorithm and the image noise estimation algorithm^9–11 to obtain the effect of blind denoising.

We observed that the noisy points in the image easily mix with the image information, such as the texture details, edge information, and so on. Because of this fact, the current denoising algorithms usually lose a lot of image information due to over smoothening ofthe image, especially when the noise level is high or the texture region is large. Based on this observation, in this paper, we propose an edge-aware image denoising algorithm (EAID).

In this paper, we assume that the noise level of the noisy image is known or can be obtained using the image noise estimation algorithm. However, we use different denoising parameter settings for different regions according to the edge of the image. EAID algorithm aims to remove the noise and preserve more image information.

The experimental results show that the proposed EAID algorithm can effectively improve the denoising effect of block-matching and 3D filtering (BM3D) algorithm² and patch group prior-based denoising (PGPD) algorithm.⁴ Moreover, it can achieve higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM)¹⁴ results.

The rest of the paper is organized as follows:“ Related work” section gives an overview of related works on image denoising; “The proposed algorithm” section describes the proposed EAID algorithm in detail; “Experiments and results” section reports the experimental results. There is a conclusion of our work in “Conclusion” section.

Related work

Researchers have proposed various denoising algorithms. Buades et al.¹ proposed a nonlocal mean denoising algorithm (NLM). It uses the redundant information of the image to denoise the image. It searches similar pixels for each pixel to be denoised. The final denoised result is obtained by weighted average of its similar pixels. Although NLM algorithm can get better denoised result, it also losses a lot of information of the original image. Dabov et al.² proposed a BM3D algorithm. The algorithm also takes advantage of the redundancy of images. BM3D is one of the state-of-the-art image denoising algorithms. We combine the BM3D algorithm and our edge-aware parameter setting strategy to denoise the noisy image, and so we give a brief description of BM3D algorithm in “The proposed algorithm” section.

The algorithms mentioned above use only the internal information of the original image to denoise. Different from them, some researchers found that using the external clean image or image region can better preserve the details of an image. Some researchers proposed a category of algorithms combining internal and external information. For example, the algorithm proposed by Mosseri et al.³ is based on NLM. Different from NLM, it adopts two strategies when searching for similar image blocks. One strategy is to search within the noisy image. The other strategy is to search within the external image database. Then the algorithm combines the denoising results obtained by these two search strategies to get the final denoising result. However, this external algorithm is highly costly and needs the similar images or image regions in its external database. Xu et al.⁴ used Gaussian mixture model learning algorithm to learn the nonlocal self-similarity prior knowledge from natural images. They proposed patch group-based nonlocal self-similarity prior learning for image denoising (PGPD). Yue et al.⁵ use the graph-cut-based matching in external denoising. The algorithm first searches the external database for the correlated images of the same scene with different angle of view. It uses BM3D to replace the correlated images of the external database when the map cannot be found in external database image. This algorithm depends on the external database images which may not be applicable to real-world applications.

This paper proposed a novel image denoising algorithm combined with edge information. Different from the algorithms combining the internal and external information, the final denoising result is obtained by combining two denoising results with different parameter settings. The two denoising results are obtained by denoising the noisy image using different parameter settings, one is the known noisy level and the other is the tuned noisy level. The final result is obtained by combining the two denoising results according to the edge information.

The proposed algorithm

This section consists of two subsections. The first subsection uses a specific example to study and explain the denoising effects of using different denoising parameter settings. We found that different regions prefer the denoising results obtained using different denoising parameter settings. The second subsection introduces our algorithm using BM3D algorithm as an example in detail.

Denoising parameter settings

The denoising parameter setting affects the denoising performance. At present, most of the state-of-the-art denoising algorithms are not blind denoising. They need a priori information of noise intensity to denoise images. Generally speaking, they use noise level as denoising parameter.^1–6 In view of the necessity of obtaining noise level, researchers have proposed many noise level estimation algorithms.^9–11 Chen et al.⁹ proposed a noise level estimation algorithm which first computes the eigenvalues of the covariance matrix of patches of the input image and then computes the statistical relationship between the noise variance and the eigenvalues. The experimental results show that the root mean square error of the noise level predicted by the algorithm is 0.183 in the BSD500¹² when the standard deviation of noise is 50. Its results are very close to the true noise level. So when thenoise level is unavailable, it can be estimated by Chen et al.⁹

Figure 1 shows a specific example of the denoising results of BM3D with different denoising parameter settings. Figure 1(c) and (d) shows the results when BM3D using $σ$ which is the noise level and $0.85 \times σ$ which is a tuned noise level, respectively. As shown in Figure 1, image (d) retains more details than image (c) in the regions around the eyes. This example shows that denoising with true noise level as a parameter does not guarantee the best denoising effect in all the regions in the image, especially in the textured image regions.

Figure 1.

(a) Original image; (b) noisy image; (c) denoising result 1; (d) denoising result 2.

The finding shown in Figure 1 is also validate for blind denoising algorithms. Since most current noise level estimation algorithms estimate the noise standard deviation $σ$ , it cannot guarantee that the best denoising result for each noisy image is obtained by using the estimated $σ$ as parameter settings for blind denoising.

Based on the above findings, this paper uses different parameter settings to obtain the denoising results. The final denoising result is obtained by combining the denoising results with different denoising parameter settings based on the edge information.

Edge-aware image denoising algorithm

Most denoising algorithms use the same denoising parameter to denoise the whole image. As shown in Figure 1(d), we find that the image details can be better preserved when using $0.85 \times σ$ as parameter, especially in the regions around the edges of the image.

As shown in Figure 2, the proposed algorithm is based on the existing state-of-the-art algorithms (e.g. BM3D and PGPD). We use the denoising algorithm to denoise images with $σ$ and $rate \times σ$ as parameters, respectively (Figure 2(c) and (d)).

Figure 2.

Algorithm example diagram. (a) Original image; (b) noisy image (PNSR: 14.683 dB); (c) denoising result 1 (PSNR: 26.109 dB); (d) denoising result 2 (PSNR: 26.153 dB); (e) edge detection result; (f) expanded edge image; (g) E-BM3D result (PSNR: 26.248 dB); (h) E-PGPD result (PSNR: 26.242 dB).

BM3D is currently recognized as one of the best denoising algorithms. Since we combine the BM3D algorithm and our edge-aware parameter setting strategy to denoise the noisy image, we give a brief introduction on BM3D. BM3D is both a transform domain denoising algorithm and a spatial domain denoising algorithm. BM3D has two main steps. They are briefly described below.

The first step is to get a basic estimate of the noisy image. It first finds some groups (a collection of one block and its similar blocks is called a group). Then it aggregates all the elements of a group to obtain a three-dimensional array corresponding to the group. These arrays aim to enhance sparsity. Next, BM3D uses collaborative filtering to handle the arrays with three steps: three-dimensional transformation, transform spectral shrinkage, and three-dimensional inverse transform. After these three steps, the basic estimation of each image block is obtained and returned to their original position. It is worth noting that for overlapping image blocks, BM3D takes their weighted average.

The second step is to get the final denoising result based on the first step. The difference is that a block gets two corresponding groups. The first group is obtained from the noisy blocks by using the similarity of blocks. The second one consists of blocks of basic estimation which correspond to the elements of the first group. After the two groups undergo three-dimensional transform, Wiener filtering, and inverse transform, BM3D gets the final estimation. It puts each block back to its original position to get the denoising result.

The proposed algorithm calculates the edge detection result (e) for the denoising result 1 (c) using the Canny edge detection algorithm¹³ after the noisy image was processed by BM3D. Canny edge detection computes the edge by first smoothing the image and then computing the derivative values. The brief introduction of this algorithm is introduced below. First, it uses the Gaussian filter to smooth the grayscale image. This is because some noise points can be mixed with the textures and edge information of an image, which is mentioned in “Introduction” section. Second, it calculates the gradient and direction of the image gradient.

F = \sqrt{F_{1}^{2} + F_{2}^{2}}

(2)where

F_{1}

is the horizontal gradient,

F_{2}

is the vertical gradient, and

F

is the gradient combined by horizontal and vertical gradients. We can use the following formula to find the gradient direction

θ = arc tan (\frac{F_{2}}{F_{1}})

(3)

After that, nonedge points are removed by nonmaximum suppression and threshold processing to detect the edge of the image.

After obtaining the edge detection result shown in Figure 2(e), an expanded edge result shown in Figure 2(f) is obtained by perform expansion operation using an expanded core of radius $h$ . Expansion is one of the basic operations of morphological processing, which can be defined as follows

A \oplus B = {z | {(\hat{B})}_{z} \cap A \neq Φ}

(4)where

z

is an element of an ordered pairwise set of binary integers, denoted as

Z^{2}

z = (z_{x}, z_{y})

represents the coordinate value of a pixel.

A

B

are subsets of

Z^{2}

. That is, to say, an element in

A

is the coordinate value of a pixel of an image or an image region.

B

is structural element, like convolution template. In this paper, we choose symmetrical structural elements of

h \times h (h = 1, 2)

. Moving

B

Z^{2}

, if

B

and

A

overlap at

z

, then the position satisfies the condition. The set of all the positions that satisfy the condition is the result of the expansion.

The last step of our algorithm is using the expanded edge image shown in Figure 2(f) as a weight map to calculate the final denoising result, which is calculated as follows

X = F_{a} . \times (1 - W) + F_{b} . \times W

(5)where

X

is the final denoising result.

F_{a}

and

F_{b}

are the denoising results with

σ

and

rate \times σ

as parameter settings, respectively.

W

is the expended edge image. Figure 2(c) to (f) is the intermediate result of an example using the proposed algorithm based on BM3D. Figure 2(g) and (h) is the final denoising result using our algorithm based on BM3D and PGPD, which are denoted as E-BM3D and E-PGPD, respectively.

Experiments and results

In this paper, we propose two methods, namely, E-PGPD and E-BM3D. These two methods are modified based on BM3D and PGPD. The source codes of BM3D and PGPD can be downloaded at the authors’ home pages. Twenty widely used natural images (shown in Figure 3) are taken as experimentally original images. We use a common experimental setting described in paper.⁴ Additive white Gaussian noises with zero mean and a variety of standard deviations are added to the images to test the performance of different denoising algorithms.

Figure 3.

Twenty commonly used test images.

Besides noise level $σ$ , our proposed algorithm contains another two parameters: $rate (rate = {0.8, 0.85, 0.9, 0.95})$ and $h (h = {1, 2})$ . Tables 1 and 2 show the parameter settings of E-BM3D and E-PGPD, respectively.

Table 1.

The parameter settings of E-BM3D.

E-BM3D
$σ$	$Rate$	$h$
$(0, 40)$	0.95	1
$(40, 70)$	0.85	2
$(70, 100)$	0.8	2

Table 2.

The parameter settings of E-PGPD.

E-PGPD
$σ$	$Rate$	$h$
$(0, 40)$	0.95	1
$(40, 60)$	0.9	2
$(60, 80)$	0.85	2
$(80, 100)$	0.8	2

We evaluate the competing algorithms from three aspects: PSNR, SSIM,¹⁴ and visual quality. In Table 3, we present the PSNR results of E-BM3D and BM3D algorithms on 10 noise levels σ = 10, 20,…100. The best PSNR result on each $σ$ is shown in bold and underlined. The values of “rate = 0.8” mean the results of BM3D when using $σ \times 0.8$ . The values of “rate = 0.85,” “rate = 0.9,” and “rate = 0.95” have similar meanings. Table 3 shows that when $σ > 70$ , the denoising results of BM3D when using $rate \times σ$ have higher PSNR than the results when using $σ$ . This finding validates our motivation that denoising with true noise level as a parameter does not guarantee the best denoising effect.

Table 3.

PSNR (dB) results of E-BM3D and BM3D when using different parameter settings on 20 natural images.

$σ$	BM3D	Rate = 0.8	Rate = 0.85	Rate = 0.9	Rate = 0.95	E-BM3D
10	34.312	33.710	34.036	34.234	34.314	34.312
20	30.875	30.150	30.596	30.823	30.897	30.904
30	28.903	28.153	28.638	28.866	28.931	28.937
40	27.396	26.652	27.136	27.354	27.420	27.427
50	26.084	24.801	26.157	26.206	26.165	26.217
60	25.029	24.987	25.147	25.157	25.104	25.171
70	24.062	24.139	24.214	24.189	24.130	24.207
80	23.174	23.335	23.346	23.300	23.238	23.329
90	22.354	22.557	22.527	22.473	22.410	22.509
100	21.603	21.827	21.778	21.721	21.661	21.752
AVE	26.379	26.031	26.357	26.433	26.427	26.477

The best PSNR result on each $σ$ is shown in bold and underlined.

Table 3 also shows that across all the experimented noise levels, the proposed E-BM3D achieves better results than BM3D when using $σ$ as parameter. The average PSNR is increased by 0.098 dB. Especially when $σ \geq 50$ , the average improvements are 0.133–0.155 dB. Moreover, as shown in the last row of Table 3, the proposed E-BM3D outperforms BM3D algorithm when using $σ$ and $rate \times σ$ as parameter settings. For example, when rate is 0.9 and 0.95, the average PSNR of BM3D using $rate \times σ$ is 26.433 and 26.427 dB. They are better than BM3D when using $σ$ . But the proposed E-BM3D reaches 26.477 dB which is higher than BM3D algorithm when using $rate \times σ$ .

In Table 4, we present the PSNR results of E-PGPD and PGPD algorithms on 10 noise levels $σ = 10, 20 … 100$ . Table 4 shows similar results as Table 3. On some noise levels, PGPD algorithm when using $rate \times σ$ can achieve better results than PGPD algorithm when using $σ$ . The proposed E-PGPD achieves better results than PGPD when using $σ$ as parameter on 10 noise levels. The average PSNR is increased by 0.174 dB. Especially when $σ \geq 50$ , the average improvements are 0.105–0.321 dB. Moreover, as shown in the last row of Table 4, the proposed E-PGPD outperforms PGPD algorithm using $σ$ and $rate \times σ$ as parameter settings. For example, when rate is 0.9 and 0.95, the average PSNR of PGPD using $rate \times σ$ is 26.345 and 26.375 dB. They are better than PGPD when using $σ$ . But the proposed E-PGPD reaches 26.457 dB which is higher than PGPD algorithm when using $rate \times σ$ .

Table 4.

PSNR (dB) results of E-PGPD and PGPD when using different parameter settings on 20 natural images.

$σ$	PGPD	Rate = 0.8	Rate = 0.85	Rate = 0.9	Rate = 0.95	E-PGPD
10	34.264	33.615	33.923	34.135	34.246	34.270
20	30.860	29.677	30.290	30.690	30.867	30.879
30	28.858	27.270	28.100	28.673	28.903	28.905
40	27.355	25.662	26.633	27.291	27.480	27.460
50	26.038	24.796	25.652	26.212	26.239	26.234
60	24.925	24.102	24.728	25.153	25.111	25.177
70	23.853	23.453	24.140	24.184	24.016	24.173
80	23.025	23.149	23.330	23.183	23.120	23.294
90	22.198	22.533	22.453	22.354	22.267	22.483
100	21.455	21.743	21.654	21.570	21.506	21.693
AVE	26.283	25.600	26.090	26.345	26.375	26.457

The best PSNR result on each $σ$ is shown in bold and underlined.

SSIM is another important index to evaluate an image denoising algorithm. Table 5 shows SSIM results of E-BM3D and BM3D algorithms on $σ = 10, 20 … 100$ . Table 6 shows the SSIM results of E-PGPD and PGPD algorithms on $σ = 10, 20 … 100$ . For every $σ$ , we bolded and underlined the highest SSIM results. From Tables 5 and 6, we find that E-BM3D outperforms BM3D when using $σ$ and E-PGPD outperforms PGPD when using $σ$ in terms of SSIM. On most noise levels, our proposed algorithms can achieve better results than BM3D and PGPD algorithms when using $rate \times σ$ . It proves that our proposed algorithms retain more details in the image after denoising.

Table 5.

SSIM results of E-BM3D and different denoising algorithms on 20 natural images.

$σ$	Rate = 1	Rate = 0.8	Rate = 0.85	Rate = 0.9	Rate = 0.95	E-BM3D
10	0.920	0.914	0.920	0.922	0.922	0.921
20	0.863	0.840	0.856	0.863	0.864	0.864
30	0.817	0.777	0.803	0.815	0.818	0.819
40	0.777	0.724	0.757	0.772	0.777	0.778
50	0.740	0.653	0.731	0.741	0.742	0.745
60	0.708	0.679	0.701	0.710	0.711	0.713
70	0.680	0.658	0.676	0.682	0.682	0.686
80	0.655	0.641	0.654	0.658	0.657	0.659
90	0.631	0.626	0.634	0.635	0.634	0.637
100	0.610	0.611	0.615	0.614	0.612	0.617
AVE	0.740	0.712	0.735	0.741	0.742	0.744

The best SSIM result on each $σ$ is shown in bold and underlined.

Table 6.

SSIM results of E-PGPD and different denoising algorithms on 20 natural images.

$σ$	Rate 1	Rate 0.8	Rate 0.85	Rate 0.9	Rate 0.95	E-PGPD
10	0.916	0.906	0.912	0.915	0.917	0.917
20	0.857	0.829	0.846	0.856	0.859	0.859
30	0.811	0.761	0.793	0.810	0.814	0.814
40	0.771	0.702	0.748	0.773	0.777	0.776
50	0.732	0.672	0.714	0.739	0.740	0.742
60	0.700	0.647	0.684	0.707	0.707	0.711
70	0.667	0.629	0.673	0.679	0.673	0.681
80	0.642	0.636	0.654	0.648	0.644	0.653
90	0.617	0.628	0.624	0.622	0.619	0.629
100	0.594	0.603	0.601	0.599	0.596	0.605
AVE	0.731	0.701	0.725	0.735	0.735	0.739

The best SSIM result on each $σ$ is shown in bold and underlined.

Figures 4 and 5 are two examples of E-BM3D, E-PGPD, BM3D, and PGPD algorithms. As Figure 4 shows, the results of BM3D and PGPD lost some details so the visual qualities of denoised images are low. For example, our algorithms retain the details of the numbers better than the others. And our algorithms also make the textures of the curtain more clearly as shown in Figure 5. In terms of PSNR, E-BM3D gets higher PSNR than BM3D, and E-PGPD gets higher PSNR than PGPD. In order to show the effectiveness of our method more intuitively, we show the difference between the denoising results of various methods and the original image. We first calculate the difference images and multiply the difference images using the same multiplier. Then we get difference images shown in Figures 4(g) to (i) and 5(g) to (i). As shown in these difference images, the numbers and the curtains in the results of our algorithms are both closer to the original images than those in the results of the original algorithms.

Figure 4.

Denoising results of different algorithms when $σ = 50$ . (a) Original image; (b) noisy image (PSNR: 15.106 dB); (c) BM3D result (PSNR: 27.639 dB); (d) E-BM3D result (PSNR: 27.790 dB); (e) PGPD result (PSNR: 27.519 dB); (f) E-PGPD result (PSNR: 27.865 dB); (g) difference image between the denoising result of BM3D and original image; (h) difference image between the denoising result of E-BM3D and original image; (i) difference image between the denoising result of PGPD and original image; (j) difference image between the denoising result of E-PGPD and original image.

Figure 5.

Denoising results of different algorithms when $σ = 90$ (a) original image; (b) noisy image (PSNR: 12.564 dB); (c) BM3D result (PSNR: 22.814 dB); (d) E-BM3D result (PSNR: 22.979 dB); (e) PGPD result (PSNR: 22.580 dB); (f) E-PGPD result (PSNR: 212.892 dB); (g) difference image between the denoising result of BM3D and original image; (h) difference image between the denoising result of E-BM3D and original image; (i) difference image between the denoising result of PGPD and original image; (j) difference image between the denoising result of E-PGPD and original image.

Nowadays, most images are color images. In order to further show the effectiveness of the proposed algorithm, we experiment our algorithm with color images. As shown in Figure 6, our algorithm achieves a better denoising effect. Our algorithm also gets higher PSNR results.

Figure 6.

Denoising results of different algorithms when $σ = 80$ : (a) original image; (b) BM3D result (PSNR: 21.722 dB); (c) E-BM3D result (PSNR: 21.893 dB); (d) noisy image (PSNR: 11.725 dB); (e) PGPD result (PSNR: 21.787 dB); (f) E-PGPD result (PSNR: 20.022 dB).

To summarize, we can conclude that E-BM3D and E-PGPD outperform BM3D and PGPG when using $σ$ in terms of PSNR, SSIM values, and visual quality.

Conclusion

In this paper, we found the relationship between the denoising parameter and the noise level by using different denoising parameter settings. Combining with the image edge information, this paper developed a novel image denoising algorithm. Different from internal and external algorithms, our algorithm does not require the support of external image databases. The experimental results show that the proposed algorithm can better preserve the edge information, especially for image regions with complex texture.

Footnotes

Acknowledgements

The authors would like to thank the editor and the reviewers for their insightful and constructive comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is partly supported by the National Natural Science Foundation of China under Grants No. 61672158 and No. 61300102 and the Fujian Natural Science Funds for Distinguished Young Scholar under Grant No. 2015J06014.

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