Rayleighmaximumlikelihood bilateral filter for ultrasound image enhancement
 Haiyan Li†^{1},
 Jun Wu†^{1},
 Aimin Miao^{1}Email author,
 Pengfei Yu^{1},
 Jianhua Chen^{1} and
 Yufeng Zhang^{1}
DOI: 10.1186/s1293801703369
© The Author(s) 2017
Received: 17 November 2016
Accepted: 31 March 2017
Published: 17 April 2017
Abstract
Background
Ultrasound imaging plays an important role in computer diagnosis since it is noninvasive and costeffective. However, ultrasound images are inevitably contaminated by noise and speckle during acquisition. Noise and speckle directly impact the physician to interpret the images and decrease the accuracy in clinical diagnosis. Denoising method is an important component to enhance the quality of ultrasound images; however, several limitations discourage the results because current denoising methods can remove noise while ignoring the statistical characteristics of speckle and thus undermining the effectiveness of despeckling, or vice versa. In addition, most existing algorithms do not identify noise, speckle or edge before removing noise or speckle, and thus they reduce noise and speckle while blurring edge details. Therefore, it is a challenging issue for the traditional methods to effectively remove noise and speckle in ultrasound images while preserving edge details.
Methods
To overcome the abovementioned limitations, a novel method, called Rayleighmaximumlikelihood switching bilateral filter (RSBF) is proposed to enhance ultrasound images by two steps: noise, speckle and edge detection followed by filtering. Firstly, a sorted quadrant median vector scheme is utilized to calculate the reference median in a filtering window in comparison with the central pixel to classify the target pixel as noise, speckle or noisefree. Subsequently, the noise is removed by a bilateral filter and the speckle is suppressed by a Rayleighmaximumlikelihood filter while the noisefree pixels are kept unchanged. To quantitatively evaluate the performance of the proposed method, synthetic ultrasound images contaminated by speckle are simulated by using the speckle model that is subjected to Rayleigh distribution. Thereafter, the corrupted synthetic images are generated by the original image multiplied with the Rayleigh distributed speckle of various signal to noise ratio (SNR) levels and added with Gaussian distributed noise. Meanwhile clinical breast ultrasound images are used to visually evaluate the effectiveness of the method. To examine the performance, comparison tests between the proposed RSBF and six stateoftheart methods for ultrasound speckle removal are performed on simulated ultrasound images with various noise and speckle levels.
Results
The results of the proposed RSBF are satisfying since the Gaussian noise and the Rayleigh speckle are greatly suppressed. The proposed method can improve the SNRs of the enhanced images to nearly 15 and 13 dB compared with images corrupted by speckle as well as images contaminated by speckle and noise under various SNR levels, respectively. The RSBF is effective in enhancing edge while smoothing the speckle and noise in clinical ultrasound images. In the comparison experiments, the proposed method demonstrates its superiority in accuracy and robustness for denoising and edge preserving under various levels of noise and speckle in terms of visual quality as well as numeric metrics, such as peak signal to noise ratio, SNR and root mean squared error.
Conclusions
The experimental results show that the proposed method is effective for removing the speckle and the background noise in ultrasound images. The main reason is that it performs a “detect and replace” twostep mechanism. The advantages of the proposed RBSF lie in two aspects. Firstly, each central pixel is classified as noise, speckle or noisefree texture according to the absolute difference between the target pixel and the reference median. Subsequently, the Rayleighmaximumlikelihood filter and the bilateral filter are switched to eliminate speckle and noise, respectively, while the noisefree pixels are unaltered. Therefore, it is implemented with better accuracy and robustness than the traditional methods. Generally, these traits declare that the proposed RSBF would have significant clinical application.
Keywords
Ultrasound image enhancement Noise Speckle Rayleighmaximumlikelihood filter Bilateral filterBackground
Ultrasound imaging has been used as one of the most prevalent diagnostic techniques due to its advantage of being noninvasive, portable and costeffective. However, ultrasound images are affected by many types of artifacts, therefore it is hard for an observer to interpret the images and obtain quantitative information from them. Noise in ultrasound can be modeled as the combined effect of two components: one is additive, such as electronic and thermal noise, and the other is multiplicative, called “speckle”. Speckle is the result of the constructive and destructive coherent summation of ultrasound echoes when ultrasound pulses randomly interfere with objects of comparable size to the sound wavelength and then the superposition of acoustical echoes produces an intricate interference pattern [1]. Noise and speckle, considered as undesirable consequence of the image formation process in coherent imaging, directly impact the visualization of the ultrasound image by the physician, deteriorate the quality and the perceivable resolution of diagnostically important features and thus lead to inaccuracy in clinical diagnosis. Therefore, it is essential to remove noise and speckle in the ultrasound images without compromising important image details.
To alleviate the negative effects of noise and speckle, many efforts have been done to enhance ultrasound images and made the images more valuable after they had been generated and digitized. The stateoftheart denoising methods for ultrasound images include the median filter [2], adaptive filters such as the Lee filter [3], the Frost filter [4], the Kuan filter [5] as well as the nonlocal means filter and the anisotropic diffusion method [6].
The median filtering [2] and numerous improved versions [7–9] are often effective for noise reduction. The median intensity of a properly sized and shaped filtering window surrounding the central pixel is used as the output of the target pixel. It thus can eliminate impulsive artifacts whose size is less than a half of the filtering window. Since the amount of smoothing performed by the median filter is determined only by the size of the filtering window, the median filter removes some of the high frequency signal while it results in obscuring the edges. Moreover, the median filter is ineffective when the speckle size is larger than a half of the window size since the filtering scheme does not take into account the statistical characteristics of speckle. Therefore, it undermines the despeckling effectiveness.
Statistical adaptive filters replace the regions within the image whose statistical characteristics similar to those of speckles with the local mean value while keeping the regions with property least similar to speckle unaltered. Therefore they remain effective for speckle suppression. Two of these works are the filters proposed by Lee [3] and Frost [4]. They were first applied on synthetic aperture radar images and then were used on ultrasound images. Lee used the minimum mean square error (MMSE) method to design the filter for additive noise, multiplicative noise and a mixed of the two, its output was estimated by a weighted average based on the mean and the variance of the subregions. The frost filter was designed by using an exponentially damped convolution kernel adapted to image fine details and the output was calculated based on local statistics. The Kuan filter [6] is closely similar to the Lee filter but with a different weighting function. Although these filters perform well for removing speckle, they have to compromise between averaging in homogeneous regions and preserving sharp features in the original image.
Nonlocal means (NLM), a weighted Gaussian filter was proposed for denoising by making use of the high degree of redundancy in the original ultrasound image [10]. NLM performs well in Gaussian noise suppression and sharp edge reservation since it uses the region comparison instead of pixel comparison, which the pattern redundancy is not restricted to be local. However, NLmeans cannot be directly applied to ultrasound images since speckle differs from Gaussian noise significantly and is subject to Rayleigh distribution. To extend the application of the NLM method to speckle reduction, relevant NLMbased methods have been studied and proposed. Because these methods determine pixel similarity based on the noisy image patches, speckle in US images will lead to inaccurate computation of the similarity and thus lead to fine detail distortion [11–15]. Furthermore, additional time is required for computing the scale and shape parameters of the distribution of speckle [16].
The anisotropic diffusion was first proposed to reduce noise in images by smoothing in homogeneous regions without blurring the edges [17]. Thereafter, Yu and Acton [6] analyzed the statistical methods for speckle suppression and developed speckle reducing anisotropic diffusion (SRAD), a nonlinear and spacevariance filter. The SRAD approach reduced speckle by applying isotropic diffusion in homogeneous regions and enhanced edges by inhibiting diffusion across edges, which achieved a balance between despeckling and edge preservation. Flores et al. [18] extended the SRAD to a LogGabor guided anisotropic diffusion (ADLG), handling the tradeoff between smoothing level and preservation of lesion contour details. Thereafter, a lot of work has been done with anisotropic diffusion equations in such a way that the important structural information can be retained in the denoised images [19–21]. But these SRAD based methods often produce a visually disappointing outputs when they are applied to filter the primary noise contained in ultrasound images, which is subject to Gaussian distribution.
Based on the assumption of Rayleigh distribution of speckle, Aysal [22] first proposed a Rayleightrimmed filter for speckle reduction in medical images. For ensuring high efficiency of removing the primary noise and speckle in ultrasound images, two filters are applied to the original image. An alphatrimmed mean filter was used for suppressing the primary noise and the anisotropic diffusion was subsequently used to further reduce speckle. In addition, Deng et al. [23] proposed a Rayleightrimmed anisotropic diffusion filter for speckle reduction in ultrasound images. A Rayleightrimmed filter was first applied to estimate the relative standard deviations of local signals and then the anisotropic diffusion was utilized to reduce speckle. However, fine details were simultaneously removed by each filter because speckle detection was not performed before removing.
Elad proposed a new denoising method, named bilateral filter (BF) [24]. It is a nonlinear weighted Gaussian filter, taking advantage of adaptive weights based upon spatial and radiometric similarity. Compared with the abovementioned denoising methods, the BF replaced each pixel by a weighted average of the intensities in the window, which the weighting function gave high weight to those pixels near or similar to the central pixel. Hence it performed well in Gaussian noise reduction and sharp edges preservation. Lin [25] proposed a switching BF (SBF), where the BF could classify a pixel as Gaussian noise, impulse noise or noisefree one. And then the improved SBF switched between the Gaussian and impulse mode depending on the classification result to effectively remove Gaussian noise and impulse noise. However, these BF methods suffered from the drawback that they became ineffective when denoising speckle since the speckle model in ultrasonic images is subject to Rayleigh distribution.
Though these denoising and despeckling approaches operate well in some situations, they have several limitations. Firstly, some approaches do not take into account the statistical characteristics of noise or speckle, undermining the denoising effectiveness. Secondly, most algorithms, for example, the above mentioned approaches, except SBF, do not identify pixel property, such as noise, speckle or edge, before denoising, so they cannot balance effectively in enhancing edges and small structure while reducing noise and speckle, especially when the quality of the original image is poor. Finally, these methods can effectively suppress Gaussian noise or speckle but their performances are not satisfactory in the case of enhancing ultrasound images since ultrasound image is contaminated by addictive background noise and multiplicative speckle.
In order to effectively remove the primary noise and speckle contained in ultrasound images while preserving fine edges and details, a novel and robust method, named as Rayleighmaximumlikelihood switching bilateral filter (RSBF), which performs the “detect and replace” mechanism before filtering, is proposed. To detect noise, a reference median [25] in the filtering window is first calculated based on the property of the edge in an image, and then the target pixel is identified as noise, speckle or noisefree texture according to the absolute difference between the target pixel and the reference median. Subsequently, noise is removed by the bilateral filter and speckle is suppressed by the Rayleighmaximumlikelihood filter while noisefree pixels are kept unaltered. The performance and effectiveness of the proposed approach are demonstrated by experiments by using both simulated and clinical ultrasound images.
The remainder of this paper is organized as follows. "Methods" introduces the noise speckle model and the bilateral filter, followed by the detailed description of the proposed RSBF. "Experiments" gives a brief introduction to the experiment environment. "Results and discussion" presents the simulation of the ultrasound images and experiment results on synthetic ultrasound images and real clinical cases in which the proposed method is compared with six stateoftheart methods for ultrasound speckle reduction. Finally, some conclusions are drawn in "Conclusions".
Methods
In this section, the characteristics of noise and speckle is first analyzed. Based on the analysis, a sorted quadrant median vector (SQMV) scheme is performed to classify the target pixel as noise, speckle or noisefree. Thereafter, the bilateral filter is applied to remove noise based on the Gaussian distribution of noise. And the Rayleighmaximumlikelihood filter is proposed to suppress speckle based on the Rayleigh distribution of speckle. Noise free pixels are kept unchanged in order to enhance images and meanwhile preserve the edge details.
The ultrasound noise model and the bilateral filter
Thermal noise and speckle model
The bilateral filter
The Bilateral filter was proposed to remove Gaussian noise while preserving edges [24]. Each pixel is replaced by a weighted average of the intensities in the filtering window, where the pixels near or similar to the target one are assigned a high weight.
The bilateral filter performs well in suppressing Gaussian noise while keeping the edge, but it is hard to remove ultrasound speckle because speckle is a type of multiplicative noise and it follows Rayleigh distribution. In order to effectively filter noise and speckle in ultrasound image, we propose a Rayleighmaximumlikelihood bilateral filter (RSBF) with noise/speckle detection scheme, discussed in the following.
The Rayleighmaximumlikelihood switching bilateral filter(RSBF)
Noise/texture detection with the sorted quadrant median vector [25]
 1.
The Sorted Quadrant Median Vector (SQMV)
 2.
Edge/texture detection based on the \( SQMV \) clusters
 3.
Features of edge/texture
 4.
Reference median
 5.
Noise and edge/texture identification
The Rayleighmaximumlikelihood filter
The Rayleighmaximumlikelihood bilateral filter
Inspired by the “noise/speckle detection and reduction” scheme and statistics of noise and speckle, we combine the bilateral filter and Rayleighmaximumlikelihood filter together after performing noise/texture identification. Firstly, the target pixel is classified as noise, speckle or noisefree one. Subsequently, noise is removed by using the bilateral filter and speckle is suppressed by using the Rayleighmaximumlikelihood filter while the noise free pixels are kept unaltered. The detailed algorithm is described below, which can be directly implemented by MATLAB or C language.
 1.
Take the search window, size of \( (2N + 1) \times (2N + 1) \), and the corresponding subwindows size of \( (N + 1) \times (N + 1) \).
 2.
 3.
Identify edge feature according to the cluster of \( SQMV \).
 4.
 5.
Detect \( u_{i,j} \) as noise, speckle or noisefree pixel.
 6.
If \( u_{i,j} \) is classified as noise, replace the target pixel with a weighted average intensities in the window by using Eq. (5).
 7.
If \( u_{i,j} \) is detected as speckle, filter the target pixel with the Rayleighmaximumlikelihood filter in the window by using Eq. (24).
 8.
If \( u_{i,j} \) is noisefree then the original intensity is kept unaltered.
Experiments
In the experimental study, synthetic and clinical ultrasound images are used as test sources to evaluate the performance of the proposed RSBF by comparing it with those of six previously proposed filters, including the switching bilateral filter (SBF), the median filter, the SRAD, the NLmeans filter, the Lee filter and the Kuan filter.
The proposed RSBF is implemented by using Matlab 7.1 and the experiments are performed on a PC with 2.66 GHz Intel Core 2 processor. Here the parameter \( \sigma_{S} \) and \( \sigma_{R} \) of the bilateral filter are set as 35 and 40 based on the experiments, respectively. The parameter \( \sigma \) of the Rayleighmaximumlikelihood filter is set as 1. The size of the observation window is \( 5 \times 5 \).
The higher value of SNR and PSNR indicate better performance of denoising.
The less the RMSE, the better the image quality.
Results and discussion
Synthetic images with speckle
To visually evaluate the performance of the proposed method compared with other methods, seven algorithms, including the proposed method, the SBF, the Median filter, the SRAD, the NLmeans filter, the Lee filter and the Kuan filter, are applied to the simulated images. The windows size of the Median filter and the Lee filter are \( 5 \times 5 \), the iteration time of the SRAD is 300.
The SNR comparison of the synthetic images corrupted by speckle under different noise levels (dB)
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  30.5639  28.2034  25.8091  23.9633  21.6541  18.3528  16.2720 
SBF  22.3715  19.0805  16.9216  13.8543  11.9803  9.9208  8.0415 
Median  19.7635  17.1132  15.2007  12.3096  10.4227  8.1360  5.6368 
SRAD  31.5266  26.3032  19.3339  11.5845  8.1085  5.0146  2.6095 
NLmeans  19.6304  19.5233  19.3788  18.9897  18.7536  18.1153  16.0211 
Lee  20.3398  18.8931  17.5508  15.3167  14.0998  12.1313  10.306 
Kuan  24.9467  18.9903  17.7373  15.7109  14.0892  12.0872  10.3109 
The PSNR comparison of the synthetic images corrupted by speckle under different noise levels (dB)
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  40.0128  40.1669  39.9244  37.6524  35.2580  33.4122  31.1031 
SBF  31.4337  28.1467  25.9877  22.9204  21.0456  18.9869  17.0807 
Median  28.8297  26.1794  24.2668  21.3757  19.4888  17.2021  14.7029 
SRAD  40.5927  35.3693  28.4001  20.6506  17.1747  14.0807  11.6757 
NLmeans  28.6967  28.5895  28.4449  28.0558  27.8197  27.1815  25.5873 
Lee  35.0228  33.1100  31.9598  30.6620  30.0365  29.6552  29.0178 
Kuan  29.3561  28.0564  26.8034  24.7770  23.1643  21.1534  19.3770 
The RMSE comparison of the synthetic images corrupted by speckle under different noise levels
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  0.00008  0.00017  0.00013  0.00014  0.00032  0.00058  0.00074 
SBF  0.0007  0.0015  0.0023  0.0072  0.0071  0.0115  0.0182 
Median  0.0013  0.0024  0.0036  0.0072  0.0104  0.0177  0.0306 
SRAD  0.00013  0.00037  0.0014  0.0083  0.0174  0.0355  0.0624 
NLmeans  0.0018  0.0019  0.0019  0.0020  0.0021  0.0024  0.0031 
Lee  0.0014  0.0018  0.0022  0.0029  0.0041  0.0056  0.0096 
Kuan  0.0012  0.0016  0.0021  0.0033  0.0048  0.0077  0.0115 
The synthetic images corrupted by speckle and Gaussian noise
In this section, the synthetic image is generated by multiplying the original image with Rayleighdistributed speckle of various levels, and then additive Gaussian noise of zero mean with the variance of 0.002 is mixed into obtain the noisy images.
The SNR comparison of the synthetic images corrupted by speckle and Gaussian noise under different noise levels (dB)
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  27.7353  28.3570  28.3151  25.0501  21.7660  19.7310  17.5150 
SBF  21.9157  18.7967  16.6018  13.7071  11.8087  9.9209  7.8395 
Median  20.7309  17.6163  15.4225  11.3534  10.2713  8.0520  5.6002 
SRAD  25.5620  22.8780  17.9199  11.3920  7.9691  5.1211  2.5685 
NLmeans  17.8788  17.7779  17.7091  17.4288  17.1081  16.8585  15.1291 
LEE  18.5462  18.2778  16.7909  15.1985  13.4685  12.1603  10.1315 
Kuan  23.5905  21.8682  19.6651  13.0058  8.8894  5.7629  3.2307 
The PSNR comparison of the synthetic images corrupted by speckle and Gaussian noise under different noise levels (dB)
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  37.1843  37.8060  37.7641  34.3361  31.7660  29.1620  26.9639 
SBF  31.3647  28.2465  26.0508  23.1560  21.2576  19.3698  17.2884 
Median  30.1799  27.0653  24.8715  20.8024  19.7203  17.5010  15.0511 
SRAD  35.0140  32.3199  27.3698  20.8410  17.4187  14.5701  12.0175 
NLmeans  27.3287  27.2269  27.1580  26.8778  26.5577  26.3074  24.5780 
Lee  34.4946  32.7927  31.6582  30.5488  30.0358  26.7189  24.7268 
Kuan  36.1296  34.8856  33.1143  29.7408  28.5548  26.1472  24.8663 
The RMSE comparison of the synthetic images corrupted by speckle and Gaussian noise under different noise levels
Noise image  SNR = 15 dB  SNR = 12 dB  SNR = 10 dB  SNR = 7 dB  SNR = 5 dB  SNR = 3 dB  SNR = 1 dB 

Proposed  0.00019  0.00016  0.00017  0.00037  0.00076  0.0012  0.0020 
SBF  0.00073  0.0015  0.0025  0.0060  0.0075  0.0116  0.0187 
Median  0.00096  0.0020  0.0033  0.0083  0.0107  0.0178  0.0313 
SRAD  0.00032  0.00059  0.0018  0.0082  0.0181  0.0349  0.0628 
NLmeans  0.0019  0.0020  0.0021  0.0022  0.0023  0.0027  0.0035 
Lee  0.0015  0.0021  0.0027  0.0036  0.0058  0.0092  0.0121 
Kuan  0.0013  0.0016  0.0025  0.0045  0.0072  0.0103  0.0236 
Clinical imaging data
Figure 10a is the original image selected from the experimental dataset. Figure 10b–h are the results obtained by the proposed method, the SBF, the Median, the SRAD, the NLmeans, the Lee and the Kuan filters, respectively. It can be seen that the pixel intensity of the ROI processed by the proposed method is smoother than those of six other methods, which demonstrates that our method is more effective in enhancing edge while smoothing the speckle and noise in clinical ultrasound image.
Conclusions
A novel and robust method, RSBF, has been proposed to remove speckle and background noise in ultrasound images by implementing a “detect and replace” twostep mechanism. Firstly, each central pixel in the observation window is classified as noise, speckle or noisefree texture according to the absolute difference between the target pixel and the reference median, which is calculated based on the property of the edge in an image. Subsequently, a Rayleighmaximumlikelihood filter and a bilateral filter are switched to eliminate speckle, assumed to be Rayleigh distributed, and noise, subjecting to Gaussian distribution, respectively, while keeping the noisefree pixel unaltered. Experiments are performed on synthetic and clinical ultrasound images by comparing seven different despeckling methods. Visual evaluation and three numerical indices are applied to evaluate the performance of the proposed method. Results show that the proposed method performs effectively in speckle and noise suppression as well as edge preservation, and is superior to some wellaccepted stateoftheart filters in despeckling, especially when the image quality is poor.
The first conclusion is that the proposed method yields excellent noise/speckle attenuation and edge enhancement because it detects the target pixel as speckle, noise and noisefree before performing filter. Besides, our method achieves robust performance at various image quality levels, especially when the image is greatly deteriorated because the switched filters take into account the statistics of speckle and noise.
In the application of the RSBF, the parameter \( \sigma_{S} \) and \( \sigma_{R} \) of the bilateral filter and the parameter \( \sigma \) of the Rayleighmaximumlikelihood filter are set as fixed. It is not adaptive in processing the real clinical ultrasound images. Thus, how to optimize the parameters needs to be further researched.
In addition, even though the proposed method is theoretically suitable for ultrasound images of various organs, such as abdominal ultrasound images, the experiment only performs on one dataset of breast ultrasound images due to the limitation of the data. Therefore, more clinic ultrasound images of various organs should be utilized to test the performance of the proposed method in future research.
Notes
Abbreviations
 RSBF:

Rayleighmaximumlikelihood switching bilateral filter
 SQMV:

sorted quadrant median vector
 SNR:

signal to noise ratio
 PSNR:

peak signal to noise ratio
 RMSE:

root mean squared error
Declarations
Authors’ contributions
HL and JW implemented the experiments, draft and analyzed the data. AM suggested the proposed algorithm. PY, JC and YZ were responsible for theoretical guidance. All authors read and approved the final manuscript.
Acknowledgements
This work was supported by the Grant (61561050), (61462094), (61661050) from the Natural Science Foundation of China, the Grant (2015Z013) from the key project of scientific research foundation of Yunnan Provincial Department of Education.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The data supporting the conclusions of this article are included within the article. Any queries regarding these data may be directed to the corresponding author.
Ethics approval and consent to participate
The clinical image used in the research is provided by the third affiliated hospital of the Kunming medical university and are we have been informed that the patient were consent to participate in the study.
Funding
This work was supported by the Grant (61561050), (61462094), (61661050) from the Natural Science Foundation of China, the Grant (2015Z013) from the key project of scientific research foundation of Yunnan Provincial Department of Education.
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Authors’ Affiliations
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