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Medical image denoising by parallel non-local means
Neurocomputing ∎ (∎∎∎∎) ∎∎∎–∎∎∎
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Medical image denoising by parallel non-local means Xu Mingliang a,b, Lv Pei a,b,n, Li Mingyuan a, Fang Hao a, Zhao Hongling b, Zhou Bing a,b, Lin Yusong b, Zhou Liwei c a
School of Information Engineering, Zhengzhou University, Zhengzhou 450000, China Cooperative Innovation Center for Internet Healthcare, Zhengzhou University, Zhengzhou 450000, China c The fifth Affiliated Hospital of Zhengzhou University, Zhengzhou 450052, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 20 March 2015 Received in revised form 15 June 2015 Accepted 14 August 2015
The generation process of medical image will inevitably introduce certain noises. These noises will degrade the image quality and affect the final clinical diagnosis. Therefore, denoising plays an important role in the pre-processing of medical image before the formal diagnosis and treatment. In this paper, the classical NLM algorithm is improved to denoise medical images by involving a novel noise weighting function and parallelizing. In our experiment, plenty of medical images have been tested and experiment results show that our algorithm can achieve better results and higher efficiency compared with the original NLM method. & 2016 Elsevier B.V. All rights reserved.
Keywords: Medical image Non-local Means Denoising Parallel algorithm
1. Introduction
2. Related work
Image denoising is one of the most important operations in computer vision. It is widely used for preprocessing various images, such as common images and MRI. During the generation process, noises will inevitably be introduced into medical images, decrease the image quality and bring lots of inconveniency for the doctor's diagnosis. Therefore, the image denoising becomes an urgent problem to be sovled. As an important and basic procedure of image processing, denoising has been studied extensively and a lot of related approaches have been proposed, such as Gaussian filter, Wiener filter, wavelet [1–5]. However, most of denoising algorithms will blur the image details when they suppress image noise. NL-Means proposed by Buades [6] is one of the state-of-the-art algorithms for denoising. NL-Means algorithm takes advantage of plenty of redundant information in the images. The key issue of NL-Means algorithm is to choose the weighted kernel function. In this paper, we propose a novel medical image denoising approach which is based on traditional NL-means algorithm. Our approach combines the inherent characteristics of kernel function with the Gaussian kernel to infer a more appropriate weighted kernel function. Moreover, our approach is more suitable to be paralleled for higher efficiency.
The purpose of image denoising is to reduce the image noise. The denoising methods can be classified into spatial domain or image transform domain. The former is one kind of algorithm for local spatial domain processing. The image will be blurred after the neighborhoods are averaged. The latter is to convert the image from the spatial domain to the transform domain. And then the coefficients in the transform domain is processed. Finally, inverse transformation is applied to convert the image back to the spatial domain. There are many transform methods for converting images from space to transform such as Fourier transform, Wavelet transform, Ridgelet transform and so on. However, the current transform approaches can not satisfy the requirements of medical image denoising. During medical imaging, a variety of factors will result in degradation of image quality mainly by imaging or reconstruction process noise such as motion artifacts, physical system artifacts, noise artifacts. Traditional noise reduction methods are mostly based on a fixed designed noise model and difficult to solve the shortcomings of medical ultrasonic image fundamentally especially for black and white B-mode ultrasonography. In theory, the ultrasound image is multiplicative speckle noise, not only depends on the organizational structure of the organ imaging, but also on the mode of transmission of the acoustic signal, more in line with a hybrid noise model [7,8]. Most of noise reduction methods for MRI based on Gaussian noise model, ignore
n
Corresponding author.
http://dx.doi.org/10.1016/j.neucom.2015.08.117 0925-2312/& 2016 Elsevier B.V. All rights reserved.
Please cite this article as: X. Mingliang, et al., Medical image denoising by parallel non-local means, Neurocomputing (2016), http://dx. doi.org/10.1016/j.neucom.2015.08.117i
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its inherent Rician distribution [9]. The smoothness will weaken some important image edges and texture, leading to misdiagnosis and missed diagnosis of some diseases. In the acquisition and transmission of medical image, the image will be subject to various forms of noise interference. In recent years, a number of new filtering technology is drawing attention from scholars and applied to medical image noise [6,10,11]. A. Buades [6] proposed non-local means filter algorithm which took into account as many similarities structural information. However, it has some disadvantages, such as time-consuming and inadequate pixel searching. There are some improved NLM filtering algorithm, such as the robust and fast non-local means algorithm [12], an improved algorithm based on kernel regression [13], Based on Singular Value Decomposition and K-means clustering algorithm for adaptive improvements [14], a moment-based nonlocalmeans algorithm [15,16]. These improved algorithms have achieved good denoising effect. However, when these algorithms are applied to medical images, the result is not so good. To improve the performance of NLM denoising algorithm, this paper presents an improved algorithm based on parallel NLM medical image denoising, and the experiments demonstrate the effectiveness and feasibility of our algorithm. The rest of this paper is organized as follows. The noise distribution and estimation in medical images are depicted in Section 3.1. The improved adaption to parallel NL-Means denoising method in Section 3.2. GPU-based parallel non-local means denoising algorithm in Section 3.3. The supporting experimental results of improved NL-means algorithm compared to other denoising methods under various conditions are illustrated in Section 4. Finally, concluding remarks are given in Section 5.
3. Parallel NL-Means denoising 3.1. Distribution and estimation in medical images There are some visual noises in medical images. This degrades the image quality and also affects the image analysis, classification and recognition. Even people can not make the right judgments because of noise. Medical image noise can be considered as the image that does not reflect the characteristics of the organ or tissue pathology region texture. The following describes the mechanism and characteristics of some typical medical image noise. Ultrasound image noise: The ultrasound images (Ultrasound image) generation is based on ultrasonic pulse echo. When the ultrasonic wave propagates in the human body, at the junction of the body's tissues or at different uneven nature of the organization, it will produce reflections and refractions. So different intensity of the echo signal will be produced. These echo signals collected by the respective transducer circuit are converted into electrical signals with different intensities. Finally, the circuit converts these electrical signals to display different gray scale image signals. Magnetic resonance image noise: MRI (Magnetic Resonance Imalting) utilizes the principle of magnetic resonance. It places the body while applying a magnetic field in a certain frequency alternating radiofrequency electromagnetic waves on the human body, this will cause to be probed proton resonance and resonance signal radiated outwards. Thus for different parts of the body, the proton resonance frequency is different. The generated electromotive force, eventually after the appropriate display circuit is formed of different gray level pixels, to give Magnetic resonance images. Overall, the final magnetic resonance noise can be considered to comply with the Rayleigh distribution additive noise
[15]. Its probability density function is: x x2 pðxÞ ¼ 2 exp 2 a 2a
ð1Þ
Infrared image noise: infrared thermography is a non-contact type of non-invasive method to measure surface temperature. It uses infrared radiation imaging principle research body surface temperature. According to the body surface, different temperature distribution form the image of different gray pixel. Factors generating image noise are mainly caused by coherent infrared light effect, so analysis method is similar to the ultrasound image. X-ray computed tomography noise: X-CT (X-ray computed tomography) is based on an X-ray computer tomography imaging. X-ray scans of the human body surrounded by body parts when imaging X-ray tube enters the body of a cross-section along the lot line. In the injection process, X-rays continue to decay. These measured attenuation data on the computer uses an image reconstruction principle to give each point of the cross section of the X-ray absorption coefficient, which will eventually be converted into different gradation pixels to form the image. X-ray attenuation law can be expressed as: n ¼ n0 e ud
ð2Þ
where n and n0 is defined penetrating X-ray dose before and after water model. And u is ray attenuation coefficient, d is water die diameter. X-CT image noise mainly contain quantum noise and electronic noise. The former is mainly produced by the X-ray photons into the image intensifier inhomogeneity and physical factors with CT tube current, the tube voltage, thickness and other closely related. CT scans of different ways and reconstruction algorithms related factors also contribute to X-CT image noise from the probability distribution, so X-CT image noise can be approximated by a Gaussian distribution considered additive noise. 3.2. Adaption to parallel NL-Means denoising method 3.2.1. Non-local mean noising algorithm In an image, there will always be a lot of redundant information. A typical noise reduction idea is to use the redundant information. The classic neighborhood filtering algorithm is based on this idea. NL-Means algorithm proposed originated in the neighborhood filtering algorithm. As shown in Fig. 1, rectangular field pixel p and q1 are more similar than the pixel p and q2 of rectangular areas. In fact, the rectangular areas of the pixel p and q2 is not similar in human vision. In an image, adjacent pixels are most likely to have similar rectangular areas. But most of the pixels in the same column, for example, p will have its similar rectangular areas [17]. So in NL-Means algorithm, the value of one pixel is based on the noise reduction of the similar rectangle area. For a discrete noise images vðiÞ ¼ vðiÞ; i A I , Gray estimation N LðvÞðiÞ of pixel i is calculated by a weighted average of all pixels: X NLðvÞðiÞ ¼ wði; jÞvðjÞ ð3Þ jAI
where the weight wði; jÞ determine the similarity of the pixel i and a pixel j with valid range in [18] and sum of weight is 1. The pixels i and j with similar intensity determine similarity gray vector between vðN i Þ and v Nj , and Nn is the n-centered rectangular neighborhood. Gaussian-weighted Euclidean distance dði; jÞ is used to measure the similarity of each neighborhood between the gray value matrix and defined as: dði; jÞ ¼ ‖v N i v N j ‖22;a ð4Þ where a is greater than zero and is difference between the standard Gaussian kernel. vðN i Þ gray pixels with similar
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Euclidean distance dði; jÞ is too small, so that either single kernel will make frequent changes of signal strength. Through the exponential kernel function, Gaussian kernel function and wavelet kernel function can be combined, this paper proposes a new wavelet Gaussian kernel function, defined as: 8 π dði;jÞ > 2 < sin h1 d ði;jÞ dði; jÞ r h1 2 π dði;jÞ exp f n ðdði; jÞÞ ¼ ð10Þ h2 > : 0 else
Fig. 1. Own similar schematic diagram.
neighborhood have a larger weight average. In Fig. 1, we can get the right weight values of the pixel i and the pixel j follows: wði; jÞ ¼
1 f ðdði; jÞÞ zðiÞ n
where X zðiÞ ¼ f n ðdði; jÞÞ
3.3. GPU-based parallel non-local means denoising algorithm ð5Þ
ð6Þ
j
is normalization coefficient weights. The core issue is the nonlocal means filtering by Eq. (2) is given to determine the Eq. (5) in the kernel function f n ðdði; jÞÞ. Eq. (5) plays a vital role in the noise performance of the algorithm. NL-means algorithm uses exponential kernel function, defined as: dði; jÞ f n ðdði; jÞÞ ¼ exp 2 ð7Þ h where h is the smoothing parameter of an image. It mainly controls exponential decay rate also affects the noise reduction performance of the algorithm and the degree of filtering. h will also affect the image resolution. 3.2.2. Improved NL-Means noise reduction algorithm The key improvements of NL-Means algorithm is to choose a more suitable noise weighted kernel function for medical image and ensure high similarity areas have greater weight. Conversely, the weights of low similarity fields are even smaller. So, we hope to get such an ideal kernel: in the neighborhood of pixels output larger weighting coefficients (weights), and the output increases rapidly when the distance decreases. The selection of the matching kernel weighting plays an important role in the quality of medical image denoising. Traditional Gaussian kernel function is defined as: ! 2 d ði; jÞ f n ðdði; jÞÞ ¼ exp ð8Þ 2 h Traditional wavelet kernel function is defined as: 8 < sin πdhði;jÞ dði; jÞ r h π dði;jÞh f n ðdði; jÞÞ ¼ : 0 else
Improved wavelet Gaussian kernel function on the basis of the Gaussian kernel adds a wavelet coefficients, combines the advantages of nuclear function and Gaussian wavelet kernel function. In a small distance, larger weighting values will be output and when distance increases the weight will be reduced which can avoid under-weighted and over-weighted. Thereby our method can effectively reduce the low degree of similarity and dissimilarity neighborhood interference, and can also take advantage of the high degree of similarity neighborhood filtering noise. So the improved algorithm can reduce the noises in different levels and guarantee better performance.
This section is to describe the parallel implementation of local means denoising algorithm and this algorithm is running on on CUDA programming platform. Experimental results show that after parallelization, our improved non-local means algorithm obtains great improvement in processing speed. The basic idea of our algorithm is a programming model. In this model, the operation of each pixel in the image is placed on a execution thread. So after parallel algorithms operate on all those pixels on the entire image can be denoised parallelly at the same time. In detail, firstly, the image data is copied from the host computer memory to GPU device memory. And then single pixel processing is performed in the GPU kernel. Finally, the denoising results are sent back to the host memory. 3.3.1. Algorithm implementation steps Step 1: The image and associated parameters are copied from the computer to the host memory device GPU memory area; Step 2: Based on formula weight wði; jÞ ¼
1 ‖vi vj ‖22;a e 2 Z ðiÞ h
ð11Þ
Weights between pixels are calculated according to the following steps; Step 3: Repeating steps 2 in a window, until the weights between the pixel and the center pixel within the each window have been calculated. Step 4: Based on X NL½vðiÞ ¼ wði; jÞvðjÞ ð12Þ jAI
calculate the estimated value of gray pixels and get the denoising result. Step 5: The denoising results is copied from GPU device memory area to the host computer memory.
ð9Þ
By comparing (7), (8) and (9), we can see that when the noise intensity is weak, the Gaussian kernel function and wavelet exponential kernels are better than NL-Means. However, the weighted value of the wavelet type functions in the Euclidean distance dði; jÞ is too large, and Gaussian kernel function in the
4. Results 4.1. Experimental data In the experiment, in order to verify the effect of parallel denoising algorithms, we use both a parallel non-local means
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The software experiment platform Microsoft Visual Studio 2010 with CUDA 4.0. The hardware environment is as follows: CPU: 4 Dual-Core AMD Opteron 2.80 GHz; Memory: 32–GB; GPU: NVIDIA Quadro FX 4800 (24 streaming multiprocessors, 192 CUDA cores); Graphics Memory: 1.5 GB GDDR5.
image as shown in Table 1. Both serial and parallel denoising method are used for medical image denoising. The evaluation results of the two methods are shown in Table 1. Firstly, the evaluation results can be seen from Table 1. The PSNR value of non-local means algorithm for image processing is higher than that of the previous denoising. This shows the effectiveness of the non-local means denoising algorithm. Secondly, from the evaluation results of two algorithms, we can see the parallel non-local means denoising algorithm presented in this paper can maintain a same good performance of the serial algorithm. This also shows the effectiveness of the parallel non-local means denoising algorithm. In addition, we randomly select two images Fig. 3(a) and (b). We denoise these two images using serial and parallel algorithms respectively and compared their results. Fig. 3(a) and (b) are those results using the serial algorithm. As shown in Fig. 3, serial non-local means denoising results in Fig. 2 (left) and parallel non-local means results in the figure (right) have the same effect.
4.3. Denoising performance analysis
4.4. Acceleration performance analysis
In Fig. 2, we use four original natural images with additive Gaussian noise and add different noise standard deviation for each
In the experiment, the time of processing different sizes of images by two algorithms are compared to quantitatively analysis
denoising algorithm and non-local means denoising algorithm proposed to process 4 series medical image. Fig. 2 shows the results of the medical image denoising using our algorithm. In order to verify the performance of parallel algorithm, the time dealing with images of different sizes are compared. The result can be refered in Fig. 3 and the resolution size is 128n128, 256n256 and 384n384 respectively. In contrast experiment, this algorithm can be different sizes for image denoising processing performance reflects do quantitative analysis. In the experiment, we set the size of searching window and the similar window as 6n6. 4.2. Experimental environment
Fig. 2. Denoised medical images.
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Fig. 3. The comparison of parallel and non-parallel algorithms.
Table 1 Results of two different evaluations.
Table 2 Comparison of two kinds of algorithms of processing time.
Image Resolution size PSNR Before denoising
Serial algorithm
Parallel algorithm
34.39 28.56 31.25 25.23 31.61 27.65 31.32 27.53
37.63 34.60 34.72 31.72 37.36 35.23 36.18 33.06
37.63 34.60 34.72 31.72 37.36 35.23 36.18 33.06
Image Resolution size Noise standard deviation a
a b c d
5 10 5 10 15 25 10 15
the performance presented in this paper. The results shown in Table 2. As shown in Table 2, when the non-local means denoising algorithm in parallel is used for image denoising processing, the efficiency of the algorithm have been improved two orders of magnitude. When the amount of image data becomes large, the algorithm efficiency is improved even more due to increasing parallel granularity. From above results, it can be drawn that this paper presents a parallel non-local means denoising algorithm to enhance the performance of traditional denoising algorithm and to achieve a higher speedup of image processing to meet the real-time requirements.
5. Conclusion In this paper, some algorithms for image denoising are introduced briefly. The basic principle of non-local means denoising algorithms, computational complexity and processing steps are analysized deeply. This paper improves the weighted kernel function in NL-means algorithm to denoise the medical image, and also propose a GPU-based parallel non-local means denoising algorithm. Results show that compared with the traditional sequential algorithm, our method can have good performance on different levels of noise. In the aspect of processing speed, the algorithm have been improved two orders of magnitude.
d
128n128 128n128 256n256 256n256
5 10 5 10
Serial algo- Parallel rithm (s) algorithm (s)
Acceleration ratio
1.56 1.56 4.21 4.21
33.9 33.9 40.1 40.1
0.046 0.046 0.105 0.105
Acknowledgments This work was in part supported by the National Natural Science Foundation of China (NSFC) (Grant nos. 61202207, 61379079, 61472370 and 61502433), the China Post-doctoral Science Foundation (Grant nos. 2012M520067, 2013T60706 and 2015M582203), the National Key Technology Research and Development Program of China (Grant no. 2013BAH23F01). We also would like to thank the anonymous reviewers for their constructive comments.
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Ming-Liang Xu is an associate professor in the School of Information Engineering of Zhengzhou University, China. His research interests include computer graphics and computer vision. Xu got his Ph.D. degree in computer science and technology from the State Key Lab of CAD&CG at Zhejiang University.
Pei Lv is an assistant professor in the School of Information Engineering of Zhengzhou University, China. His research interests include character animation, crowd simulation and tracking. He received his Ph.D in 2013 from the State Key Lab of CAD&CG, Zhejiang University, China. Before that, he received his B.S. degree in computer science, from Zhengzhou University, Zhengzhou, China, in 2008.
Hao Fang received the B.S. degree in the School of Information Engineering from Zhengzhou University in 2014. He is currently a master student in the School of Information Engineering of the Zhengzhou University. His research interest is image processing.
Hongling Zhao received the M.S. degree in computer science from Zhengzhou University, China, in 2004. He is a researcher at Cooperative Innovation Center for Internet Healthcare in Zhengzhou University.His current research focuses on virtual reality and medical data processing.
Bing Zhou received the B.S. and M.S. degrees from Xi ¡̄an Jiao Tong University in 1986 and 1989, respectively, and the Ph.D. degree in Beihang University in 2003, all in computer science.He is currently a professor at the School of Information Engineering, Zhengzhou University, Henan, China. His research interests cover video processing and understanding, surveillance, computer vision, multimedia applications.
Yusong Lin received the Ph.D. degree in Telecommunication and Information System from National Digital Swithing Research Center of IEU, China, in 2005 for research on large-scale group communications. He is currently an Associate Professor at Cooperative Innovation Center for Internet Healthcare and Software Technology School, Zhengzhou University, China. His research interests include Mobile Internet, Internet Healthcare and Medical Informatics.
Liwei Zhou is a master student at Zhengzhou University. His research interests include medical imaging and clinical application.
Mingyuan Li received the B.Sc.degree from Zhengzhou University,China,in 2008. He is currently a Ph.D candidate student in School of Information Engineering at Zhengzhou University. His current research interests include 3-D print and model simulation.
Please cite this article as: X. Mingliang, et al., Medical image denoising by parallel non-local means, Neurocomputing (2016), http://dx. doi.org/10.1016/j.neucom.2015.08.117i
Contents lists available at ScienceDirect
Neurocomputing journal homepage: www.elsevier.com/locate/neucom
Medical image denoising by parallel non-local means Xu Mingliang a,b, Lv Pei a,b,n, Li Mingyuan a, Fang Hao a, Zhao Hongling b, Zhou Bing a,b, Lin Yusong b, Zhou Liwei c a
School of Information Engineering, Zhengzhou University, Zhengzhou 450000, China Cooperative Innovation Center for Internet Healthcare, Zhengzhou University, Zhengzhou 450000, China c The fifth Affiliated Hospital of Zhengzhou University, Zhengzhou 450052, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 20 March 2015 Received in revised form 15 June 2015 Accepted 14 August 2015
The generation process of medical image will inevitably introduce certain noises. These noises will degrade the image quality and affect the final clinical diagnosis. Therefore, denoising plays an important role in the pre-processing of medical image before the formal diagnosis and treatment. In this paper, the classical NLM algorithm is improved to denoise medical images by involving a novel noise weighting function and parallelizing. In our experiment, plenty of medical images have been tested and experiment results show that our algorithm can achieve better results and higher efficiency compared with the original NLM method. & 2016 Elsevier B.V. All rights reserved.
Keywords: Medical image Non-local Means Denoising Parallel algorithm
1. Introduction
2. Related work
Image denoising is one of the most important operations in computer vision. It is widely used for preprocessing various images, such as common images and MRI. During the generation process, noises will inevitably be introduced into medical images, decrease the image quality and bring lots of inconveniency for the doctor's diagnosis. Therefore, the image denoising becomes an urgent problem to be sovled. As an important and basic procedure of image processing, denoising has been studied extensively and a lot of related approaches have been proposed, such as Gaussian filter, Wiener filter, wavelet [1–5]. However, most of denoising algorithms will blur the image details when they suppress image noise. NL-Means proposed by Buades [6] is one of the state-of-the-art algorithms for denoising. NL-Means algorithm takes advantage of plenty of redundant information in the images. The key issue of NL-Means algorithm is to choose the weighted kernel function. In this paper, we propose a novel medical image denoising approach which is based on traditional NL-means algorithm. Our approach combines the inherent characteristics of kernel function with the Gaussian kernel to infer a more appropriate weighted kernel function. Moreover, our approach is more suitable to be paralleled for higher efficiency.
The purpose of image denoising is to reduce the image noise. The denoising methods can be classified into spatial domain or image transform domain. The former is one kind of algorithm for local spatial domain processing. The image will be blurred after the neighborhoods are averaged. The latter is to convert the image from the spatial domain to the transform domain. And then the coefficients in the transform domain is processed. Finally, inverse transformation is applied to convert the image back to the spatial domain. There are many transform methods for converting images from space to transform such as Fourier transform, Wavelet transform, Ridgelet transform and so on. However, the current transform approaches can not satisfy the requirements of medical image denoising. During medical imaging, a variety of factors will result in degradation of image quality mainly by imaging or reconstruction process noise such as motion artifacts, physical system artifacts, noise artifacts. Traditional noise reduction methods are mostly based on a fixed designed noise model and difficult to solve the shortcomings of medical ultrasonic image fundamentally especially for black and white B-mode ultrasonography. In theory, the ultrasound image is multiplicative speckle noise, not only depends on the organizational structure of the organ imaging, but also on the mode of transmission of the acoustic signal, more in line with a hybrid noise model [7,8]. Most of noise reduction methods for MRI based on Gaussian noise model, ignore
n
Corresponding author.
http://dx.doi.org/10.1016/j.neucom.2015.08.117 0925-2312/& 2016 Elsevier B.V. All rights reserved.
Please cite this article as: X. Mingliang, et al., Medical image denoising by parallel non-local means, Neurocomputing (2016), http://dx. doi.org/10.1016/j.neucom.2015.08.117i
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its inherent Rician distribution [9]. The smoothness will weaken some important image edges and texture, leading to misdiagnosis and missed diagnosis of some diseases. In the acquisition and transmission of medical image, the image will be subject to various forms of noise interference. In recent years, a number of new filtering technology is drawing attention from scholars and applied to medical image noise [6,10,11]. A. Buades [6] proposed non-local means filter algorithm which took into account as many similarities structural information. However, it has some disadvantages, such as time-consuming and inadequate pixel searching. There are some improved NLM filtering algorithm, such as the robust and fast non-local means algorithm [12], an improved algorithm based on kernel regression [13], Based on Singular Value Decomposition and K-means clustering algorithm for adaptive improvements [14], a moment-based nonlocalmeans algorithm [15,16]. These improved algorithms have achieved good denoising effect. However, when these algorithms are applied to medical images, the result is not so good. To improve the performance of NLM denoising algorithm, this paper presents an improved algorithm based on parallel NLM medical image denoising, and the experiments demonstrate the effectiveness and feasibility of our algorithm. The rest of this paper is organized as follows. The noise distribution and estimation in medical images are depicted in Section 3.1. The improved adaption to parallel NL-Means denoising method in Section 3.2. GPU-based parallel non-local means denoising algorithm in Section 3.3. The supporting experimental results of improved NL-means algorithm compared to other denoising methods under various conditions are illustrated in Section 4. Finally, concluding remarks are given in Section 5.
3. Parallel NL-Means denoising 3.1. Distribution and estimation in medical images There are some visual noises in medical images. This degrades the image quality and also affects the image analysis, classification and recognition. Even people can not make the right judgments because of noise. Medical image noise can be considered as the image that does not reflect the characteristics of the organ or tissue pathology region texture. The following describes the mechanism and characteristics of some typical medical image noise. Ultrasound image noise: The ultrasound images (Ultrasound image) generation is based on ultrasonic pulse echo. When the ultrasonic wave propagates in the human body, at the junction of the body's tissues or at different uneven nature of the organization, it will produce reflections and refractions. So different intensity of the echo signal will be produced. These echo signals collected by the respective transducer circuit are converted into electrical signals with different intensities. Finally, the circuit converts these electrical signals to display different gray scale image signals. Magnetic resonance image noise: MRI (Magnetic Resonance Imalting) utilizes the principle of magnetic resonance. It places the body while applying a magnetic field in a certain frequency alternating radiofrequency electromagnetic waves on the human body, this will cause to be probed proton resonance and resonance signal radiated outwards. Thus for different parts of the body, the proton resonance frequency is different. The generated electromotive force, eventually after the appropriate display circuit is formed of different gray level pixels, to give Magnetic resonance images. Overall, the final magnetic resonance noise can be considered to comply with the Rayleigh distribution additive noise
[15]. Its probability density function is: x x2 pðxÞ ¼ 2 exp 2 a 2a
ð1Þ
Infrared image noise: infrared thermography is a non-contact type of non-invasive method to measure surface temperature. It uses infrared radiation imaging principle research body surface temperature. According to the body surface, different temperature distribution form the image of different gray pixel. Factors generating image noise are mainly caused by coherent infrared light effect, so analysis method is similar to the ultrasound image. X-ray computed tomography noise: X-CT (X-ray computed tomography) is based on an X-ray computer tomography imaging. X-ray scans of the human body surrounded by body parts when imaging X-ray tube enters the body of a cross-section along the lot line. In the injection process, X-rays continue to decay. These measured attenuation data on the computer uses an image reconstruction principle to give each point of the cross section of the X-ray absorption coefficient, which will eventually be converted into different gradation pixels to form the image. X-ray attenuation law can be expressed as: n ¼ n0 e ud
ð2Þ
where n and n0 is defined penetrating X-ray dose before and after water model. And u is ray attenuation coefficient, d is water die diameter. X-CT image noise mainly contain quantum noise and electronic noise. The former is mainly produced by the X-ray photons into the image intensifier inhomogeneity and physical factors with CT tube current, the tube voltage, thickness and other closely related. CT scans of different ways and reconstruction algorithms related factors also contribute to X-CT image noise from the probability distribution, so X-CT image noise can be approximated by a Gaussian distribution considered additive noise. 3.2. Adaption to parallel NL-Means denoising method 3.2.1. Non-local mean noising algorithm In an image, there will always be a lot of redundant information. A typical noise reduction idea is to use the redundant information. The classic neighborhood filtering algorithm is based on this idea. NL-Means algorithm proposed originated in the neighborhood filtering algorithm. As shown in Fig. 1, rectangular field pixel p and q1 are more similar than the pixel p and q2 of rectangular areas. In fact, the rectangular areas of the pixel p and q2 is not similar in human vision. In an image, adjacent pixels are most likely to have similar rectangular areas. But most of the pixels in the same column, for example, p will have its similar rectangular areas [17]. So in NL-Means algorithm, the value of one pixel is based on the noise reduction of the similar rectangle area. For a discrete noise images vðiÞ ¼ vðiÞ; i A I , Gray estimation N LðvÞðiÞ of pixel i is calculated by a weighted average of all pixels: X NLðvÞðiÞ ¼ wði; jÞvðjÞ ð3Þ jAI
where the weight wði; jÞ determine the similarity of the pixel i and a pixel j with valid range in [18] and sum of weight is 1. The pixels i and j with similar intensity determine similarity gray vector between vðN i Þ and v Nj , and Nn is the n-centered rectangular neighborhood. Gaussian-weighted Euclidean distance dði; jÞ is used to measure the similarity of each neighborhood between the gray value matrix and defined as: dði; jÞ ¼ ‖v N i v N j ‖22;a ð4Þ where a is greater than zero and is difference between the standard Gaussian kernel. vðN i Þ gray pixels with similar
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Euclidean distance dði; jÞ is too small, so that either single kernel will make frequent changes of signal strength. Through the exponential kernel function, Gaussian kernel function and wavelet kernel function can be combined, this paper proposes a new wavelet Gaussian kernel function, defined as: 8 π dði;jÞ > 2 < sin h1 d ði;jÞ dði; jÞ r h1 2 π dði;jÞ exp f n ðdði; jÞÞ ¼ ð10Þ h2 > : 0 else
Fig. 1. Own similar schematic diagram.
neighborhood have a larger weight average. In Fig. 1, we can get the right weight values of the pixel i and the pixel j follows: wði; jÞ ¼
1 f ðdði; jÞÞ zðiÞ n
where X zðiÞ ¼ f n ðdði; jÞÞ
3.3. GPU-based parallel non-local means denoising algorithm ð5Þ
ð6Þ
j
is normalization coefficient weights. The core issue is the nonlocal means filtering by Eq. (2) is given to determine the Eq. (5) in the kernel function f n ðdði; jÞÞ. Eq. (5) plays a vital role in the noise performance of the algorithm. NL-means algorithm uses exponential kernel function, defined as: dði; jÞ f n ðdði; jÞÞ ¼ exp 2 ð7Þ h where h is the smoothing parameter of an image. It mainly controls exponential decay rate also affects the noise reduction performance of the algorithm and the degree of filtering. h will also affect the image resolution. 3.2.2. Improved NL-Means noise reduction algorithm The key improvements of NL-Means algorithm is to choose a more suitable noise weighted kernel function for medical image and ensure high similarity areas have greater weight. Conversely, the weights of low similarity fields are even smaller. So, we hope to get such an ideal kernel: in the neighborhood of pixels output larger weighting coefficients (weights), and the output increases rapidly when the distance decreases. The selection of the matching kernel weighting plays an important role in the quality of medical image denoising. Traditional Gaussian kernel function is defined as: ! 2 d ði; jÞ f n ðdði; jÞÞ ¼ exp ð8Þ 2 h Traditional wavelet kernel function is defined as: 8 < sin πdhði;jÞ dði; jÞ r h π dði;jÞh f n ðdði; jÞÞ ¼ : 0 else
Improved wavelet Gaussian kernel function on the basis of the Gaussian kernel adds a wavelet coefficients, combines the advantages of nuclear function and Gaussian wavelet kernel function. In a small distance, larger weighting values will be output and when distance increases the weight will be reduced which can avoid under-weighted and over-weighted. Thereby our method can effectively reduce the low degree of similarity and dissimilarity neighborhood interference, and can also take advantage of the high degree of similarity neighborhood filtering noise. So the improved algorithm can reduce the noises in different levels and guarantee better performance.
This section is to describe the parallel implementation of local means denoising algorithm and this algorithm is running on on CUDA programming platform. Experimental results show that after parallelization, our improved non-local means algorithm obtains great improvement in processing speed. The basic idea of our algorithm is a programming model. In this model, the operation of each pixel in the image is placed on a execution thread. So after parallel algorithms operate on all those pixels on the entire image can be denoised parallelly at the same time. In detail, firstly, the image data is copied from the host computer memory to GPU device memory. And then single pixel processing is performed in the GPU kernel. Finally, the denoising results are sent back to the host memory. 3.3.1. Algorithm implementation steps Step 1: The image and associated parameters are copied from the computer to the host memory device GPU memory area; Step 2: Based on formula weight wði; jÞ ¼
1 ‖vi vj ‖22;a e 2 Z ðiÞ h
ð11Þ
Weights between pixels are calculated according to the following steps; Step 3: Repeating steps 2 in a window, until the weights between the pixel and the center pixel within the each window have been calculated. Step 4: Based on X NL½vðiÞ ¼ wði; jÞvðjÞ ð12Þ jAI
calculate the estimated value of gray pixels and get the denoising result. Step 5: The denoising results is copied from GPU device memory area to the host computer memory.
ð9Þ
By comparing (7), (8) and (9), we can see that when the noise intensity is weak, the Gaussian kernel function and wavelet exponential kernels are better than NL-Means. However, the weighted value of the wavelet type functions in the Euclidean distance dði; jÞ is too large, and Gaussian kernel function in the
4. Results 4.1. Experimental data In the experiment, in order to verify the effect of parallel denoising algorithms, we use both a parallel non-local means
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The software experiment platform Microsoft Visual Studio 2010 with CUDA 4.0. The hardware environment is as follows: CPU: 4 Dual-Core AMD Opteron 2.80 GHz; Memory: 32–GB; GPU: NVIDIA Quadro FX 4800 (24 streaming multiprocessors, 192 CUDA cores); Graphics Memory: 1.5 GB GDDR5.
image as shown in Table 1. Both serial and parallel denoising method are used for medical image denoising. The evaluation results of the two methods are shown in Table 1. Firstly, the evaluation results can be seen from Table 1. The PSNR value of non-local means algorithm for image processing is higher than that of the previous denoising. This shows the effectiveness of the non-local means denoising algorithm. Secondly, from the evaluation results of two algorithms, we can see the parallel non-local means denoising algorithm presented in this paper can maintain a same good performance of the serial algorithm. This also shows the effectiveness of the parallel non-local means denoising algorithm. In addition, we randomly select two images Fig. 3(a) and (b). We denoise these two images using serial and parallel algorithms respectively and compared their results. Fig. 3(a) and (b) are those results using the serial algorithm. As shown in Fig. 3, serial non-local means denoising results in Fig. 2 (left) and parallel non-local means results in the figure (right) have the same effect.
4.3. Denoising performance analysis
4.4. Acceleration performance analysis
In Fig. 2, we use four original natural images with additive Gaussian noise and add different noise standard deviation for each
In the experiment, the time of processing different sizes of images by two algorithms are compared to quantitatively analysis
denoising algorithm and non-local means denoising algorithm proposed to process 4 series medical image. Fig. 2 shows the results of the medical image denoising using our algorithm. In order to verify the performance of parallel algorithm, the time dealing with images of different sizes are compared. The result can be refered in Fig. 3 and the resolution size is 128n128, 256n256 and 384n384 respectively. In contrast experiment, this algorithm can be different sizes for image denoising processing performance reflects do quantitative analysis. In the experiment, we set the size of searching window and the similar window as 6n6. 4.2. Experimental environment
Fig. 2. Denoised medical images.
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Fig. 3. The comparison of parallel and non-parallel algorithms.
Table 1 Results of two different evaluations.
Table 2 Comparison of two kinds of algorithms of processing time.
Image Resolution size PSNR Before denoising
Serial algorithm
Parallel algorithm
34.39 28.56 31.25 25.23 31.61 27.65 31.32 27.53
37.63 34.60 34.72 31.72 37.36 35.23 36.18 33.06
37.63 34.60 34.72 31.72 37.36 35.23 36.18 33.06
Image Resolution size Noise standard deviation a
a b c d
5 10 5 10 15 25 10 15
the performance presented in this paper. The results shown in Table 2. As shown in Table 2, when the non-local means denoising algorithm in parallel is used for image denoising processing, the efficiency of the algorithm have been improved two orders of magnitude. When the amount of image data becomes large, the algorithm efficiency is improved even more due to increasing parallel granularity. From above results, it can be drawn that this paper presents a parallel non-local means denoising algorithm to enhance the performance of traditional denoising algorithm and to achieve a higher speedup of image processing to meet the real-time requirements.
5. Conclusion In this paper, some algorithms for image denoising are introduced briefly. The basic principle of non-local means denoising algorithms, computational complexity and processing steps are analysized deeply. This paper improves the weighted kernel function in NL-means algorithm to denoise the medical image, and also propose a GPU-based parallel non-local means denoising algorithm. Results show that compared with the traditional sequential algorithm, our method can have good performance on different levels of noise. In the aspect of processing speed, the algorithm have been improved two orders of magnitude.
d
128n128 128n128 256n256 256n256
5 10 5 10
Serial algo- Parallel rithm (s) algorithm (s)
Acceleration ratio
1.56 1.56 4.21 4.21
33.9 33.9 40.1 40.1
0.046 0.046 0.105 0.105
Acknowledgments This work was in part supported by the National Natural Science Foundation of China (NSFC) (Grant nos. 61202207, 61379079, 61472370 and 61502433), the China Post-doctoral Science Foundation (Grant nos. 2012M520067, 2013T60706 and 2015M582203), the National Key Technology Research and Development Program of China (Grant no. 2013BAH23F01). We also would like to thank the anonymous reviewers for their constructive comments.
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Ming-Liang Xu is an associate professor in the School of Information Engineering of Zhengzhou University, China. His research interests include computer graphics and computer vision. Xu got his Ph.D. degree in computer science and technology from the State Key Lab of CAD&CG at Zhejiang University.
Pei Lv is an assistant professor in the School of Information Engineering of Zhengzhou University, China. His research interests include character animation, crowd simulation and tracking. He received his Ph.D in 2013 from the State Key Lab of CAD&CG, Zhejiang University, China. Before that, he received his B.S. degree in computer science, from Zhengzhou University, Zhengzhou, China, in 2008.
Hao Fang received the B.S. degree in the School of Information Engineering from Zhengzhou University in 2014. He is currently a master student in the School of Information Engineering of the Zhengzhou University. His research interest is image processing.
Hongling Zhao received the M.S. degree in computer science from Zhengzhou University, China, in 2004. He is a researcher at Cooperative Innovation Center for Internet Healthcare in Zhengzhou University.His current research focuses on virtual reality and medical data processing.
Bing Zhou received the B.S. and M.S. degrees from Xi ¡̄an Jiao Tong University in 1986 and 1989, respectively, and the Ph.D. degree in Beihang University in 2003, all in computer science.He is currently a professor at the School of Information Engineering, Zhengzhou University, Henan, China. His research interests cover video processing and understanding, surveillance, computer vision, multimedia applications.
Yusong Lin received the Ph.D. degree in Telecommunication and Information System from National Digital Swithing Research Center of IEU, China, in 2005 for research on large-scale group communications. He is currently an Associate Professor at Cooperative Innovation Center for Internet Healthcare and Software Technology School, Zhengzhou University, China. His research interests include Mobile Internet, Internet Healthcare and Medical Informatics.
Liwei Zhou is a master student at Zhengzhou University. His research interests include medical imaging and clinical application.
Mingyuan Li received the B.Sc.degree from Zhengzhou University,China,in 2008. He is currently a Ph.D candidate student in School of Information Engineering at Zhengzhou University. His current research interests include 3-D print and model simulation.
Please cite this article as: X. Mingliang, et al., Medical image denoising by parallel non-local means, Neurocomputing (2016), http://dx. doi.org/10.1016/j.neucom.2015.08.117i