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Abstract- Medical images are affected by the mixed noise, which is the combination of speckle and Gaussian noise. This paper proposes an efficient algorithm for reducing the mixed noise in ultrasound images. The proposed method reduces the noise and also preserves edges effectively and hence the quality of the image is enhanced. Based on wavelet thresholding, ST-PCNN and Bayesian maximum a posteriori (MAP) are fused together to denoise the ultrasound images. Experimental results show a significant improvement in removing the mixed noise from the ultrasound images and this method outperforms the other methods in the calculation of PSNR and MSE.
Keywords- ST-PCNN, Bayesian Map estimator, PSNR, MSE, MAE, Spatially adaptive thresholding, soft-thresholding
Medical ultrasonography uses high frequency broadband sound waves in the megahertz range that are reflected by tissue to varying degrees to produce (up to 3D) images. It has several advantages which make it ideal in numerous situations, in particular it studies the function of moving structures in real-time, emits no ionizing radiation. The main advantage of ultrasonography is noninvasive imaging since it uses mechanical waves. The noise considered in this paper, is the mixed noise, which is the combination of speckle noise and Gaussian noise. The ultrasound images are badly degraded by the speckle noise, which is formally known as multiplicative noise. Due to the speckle noise, the detailed information in the ultrasound image is not easily identified. So the detail of the image should be preserved by removing the speckle noise. Thus the reduction of multiplicative noise becomes an important aspect in the application of the medical images. White Gaussian noise, which is also known as the atmospheric noise, comes from many natural sources, such as the thermal vibrations of atoms in conductors, shot noise, black body radiation from the earth and other warm objects, and from celestial sources such as the Sun.
The proposed method, the combined Bayesian MAP estimator and ST-PCNN method, attains better results, to reduce the mixed noise efficiently.
Yongqiu Tu1 & Shaofa Li1 Minqin Wang  proposed "Modified PCNN Model and Its Application to Mixed-noise Removal". In this method, ,a new approach named, L&A PCNN method is introduced to remove the mixed noise, in which this model has linear attenuated threshold and weighted-averaging-firing-pixel-intensity outputs. Initialize the parameters to determine the result matrix Y, then inverse the result of Y to smooth the small Gaussian noise, and again inverse the result to smooth the noisy pixel. Median filter is used to recover the original pixel values. The main drawback of this method is, since the parameters are set by using the heuristic method, this model is not good in adaptivity. So this method is restricted to the real-time applications.
Zhao Chunhong, et.al.  proposed "A new speckle reduction method of medical ultrasonic image". A robust method for de-noising the speckled image by wavelet transformation. The logarithmic transformation is applied to the noisy image and wavelet transformation is applied to reduce the speckle noise. The adaptive thresholding is used to identify the noisy co-efficients from the wavelet co-efficient and set the co-efficients to zero and remaining co-efficients are processed. Take inverse wavelet transformation to the output and apply the exponential transformation to retrieve the original image. The main disadvantage of this method is edges are not preserved effectively and the noise is not much reduced.
M. I. H. Bhuiyan, et.al  proposed "New Spatially Adaptive Wavelet-based Method for the de-speckling of Medical Ultrasound Images" In this approach, log transformation is applied to the noisy image. Then the Discrete continuous wavelet transformation is applied to the log transformed co-efficients. Model the wavelet co-efficient, using the Gaussian distribution and the maxwell's distribution is used to model the log transformed speckle co-efficients. Spatially adaptive thresholding method is used for Denoising. Then the inverse discrete continuous wavelet transformation is taken and exponential transformation is applied to retrieve back the original image. The major drawback of this approach is the complexity, as two prior models are used. Discrete continuous wavelet transformation causes the blurring and ringing noise.
Alin Achim  has proposed a "Novel Bayesian Multi-scale Method for Speckle Reduction" the logarithmic transform of the original image is analyzed into the multi-scale wavelet domain. Bayes MMAE estimator or Bayes MAP estimator and then inverse DWT is applied and then mean for the log-transformed image is taken in which Cauchy and Gaussian distribution is used to model the speckle noise. The main disadvantage of this method is, time taken for execution is large.
Petruq Bdulescu & Radu Zaciu  proposed "Removal Of Mixed-Noise Using Order Statistic Filter And Wavelet Domain Wiener Filter"In this paper, two methods are evaluated. First method is, using of order statistic prefilter and empirical weiner filtering, which is used to reduce the Gaussian noise. The disadvantage of this method is, time consumption is high. Second method is,order statistic filter for each decomposition level,where decomposition is carried out by the wavelet thresholding. The drawback of this method is, improvement is less than the first method (about 1dB) in removing the mixed noise.
Zong X, et.al  proposed "Speckle reduction through multi-scale nonlinear processing" which presents an algorithm for speckle reduction. This speckle reduction method based on, soft-thresholding the wavelet coefficients of the logarithmically transformed medical ultrasound image. Shrinkage of wavelet coefficients through soft-thresholding in 1 and 2 scales, within finer levels of scale is carried out on coefficients of logarithmically transformed medical image. Then hard-thresholding of wavelet coefficients is applied within selected (mid-range) spatial-frequency levels of analysis is done in 3 and 4 scale to preserve the features to eliminate the noise. Then inverse discrete wavelet transformation is performed to reconstruct the de-noised image. And then exponential transformation is applied.
The main disadvantage of this method is that the parameters that are used for Wavelet shrinkage for de-noising were adjusted by the trial and error method. The computational time is high.
II .PROPOSED ALGORITHM
In order to increase the PSNR and MSE values, and to make the image noise-free and to preserve the edges, the following algorithm is used. Fig 1.explains the proposed method. The noise used is the mixed noise, which is the combination of speckle noise and Gaussian noise. The Log transformation is applied to the noisy image and the wavelet transformation is applied over the log transformed image. The combined Bayesian MAP estimator and ST-PCNN method is used to de-noise the image. The inverse wavelet transformation is applied and the exponential transformation is used to recover the original image.
Fig 1. Overview of the proposed method (Combined Bayesian MAP Estimator and ST-PCNN)
The noisy ultrasound image is given as ,
H(k, l ) =i(k, l )*J(k, l ) +£(k, l )
Where, i is the noise free original image, J is the speckle noise and £ is the additive Gaussian noise, (k,l) are the variables of spatial location (K represents the row and l represent the column).
1 .LOGRATHMIC TRANSFORMATION
The dynamic range of an image can be compressed by replacing each pixel value with its logarithm. This has the effect that low intensity pixel values are enhanced. Applying a pixel logarithm operator to an image can be useful in applications where the dynamic range may too large to be displayed on a screen. Logarithmic transformation can be expressed as,
Hl (k, l) = il(k, l) +Jl(k, l )
Since the speckle noise is formally known as multiplicative noise, J is multiplied with the input image, i. It can be converted into additive noise by applying the logarithmic transformation to the noisy ultrasound images.
2. WAVELET TRANSFORMATION
Wavelet transformation is used for the reduction of mixed noise, because of its high energy concentration. After applying the Discrete wavelet transformation, the image is decomposed into four sub bands (LL, HL, LH and HH). Where HL, LH, HH sub bands contain the detail components and LL sub band contain the low frequency components. Again the sub band LL is divided into four smaller sub bands for further filtration.
3. BAYESIAN MAP ESTIMATOR
Bayesian MAP estimator, which is developed by Symmetric Normal Inverse Gaussian Probability density function (SNIG PDF) , is used to de-noise the ultrasound images. There are two types of thresholding.
1. Hard thresholding
2. Soft thresholding
Hard thresholding deletes all its coefficients that are smaller than the threshold, and retains the other co-efficients unchanged. On the other hand soft thresholding also deletes its coefficients under the threshold, but scales the ones that are left. Hard thresholding creates discontinuities in the reconstructed signal, while soft does not. In this method, adaptive thresholding is used, where different thresholds are used for different regions in the image. This may also be known as local or dynamic thresholding.
The Bayesian MAP estimator is obtained from the equation below:
Where, L is the SNIG PDF, which is given as,
is used for thresholding function which is spatially adaptive.
C is the tuning factor, which is used to control the smoothing effect.
The cumulant of the SNIG PDF can be obtained as
Using (1), the ¬rst four cumulant are obtained as
Using (2), expressions for the parameters are obtained as
In order to make the Bayesian MAP estimator spatially adaptive, the cumulants are estimated from the local neighbors. For the (k, l)-th coefficient, the second and fourth-order signal moments are denoted, respectively,
The values of and are obtained using DxD square window as,
Where M = Q -1. Next, the corresponding second and fourth-order cumulants are obtained as
The value of is obtained using the coefficients in the lowest subbands with diagonal orientation as,
where D1=MAD (h(k,l))/0.6745), h(k,l) â‚¬ HH1, and D2= MAD(h(k,l))/0.6745), h(k,l) â‚¬ HH2, and MAD denotes the median absolute.
4. ST-PCNN METHOD:
In this method, Denoising is done by soft-thresholding the wavelet co-efficient. PCNN is used to determine the heavy tailed co-efficient in the wavelet domain. The neural model  ,for the PCNN is shown below.
Fig. 2 PCNN Neural model
- the input signal given to the PCNN model.
- the feedback input.
the linking input.
- the weight matrix.
- the pulse input.
- the internal activity.
Î² - the linking constant.
Î± - the thresholding constant.
V is the amplitude constant of
n -number of iterations
Initialize E,G, Î²=0.1, V=* 1.3499
Assign =[0.5 1 0.5; 1 0 1; 0.5 1 0.5]
Using the above equations, determine the result value for E and G.
Based on the condition in equation (3), E can be found.
Inverse discrete wavelet transformation is applied to the output of the ST-PCNN. Exponential transformation is applied to output of IDWT to retrieve back the original image.
III. RESULTS AND DISCUSSION:
The evaluation of parameters are calculated namely PSNR and MSE,
PSNR=max size /mean (mean(original image-enhanced image),
MSE=original image - corrupted image.
In this section, Mean, Median filters are compared with the wavelet filter, to determine which filter performs better over the speckle noise effectively. Experimental results are compared by means of PSNR, MSE
By comparing the experimental results, we gain the following conclusions: Mean Filter can reduce the Gaussian noise effectively. Whereas, median filter reduces the salt & pepper noise. By using wavelet filter, a considerable amount of speckle noise is removed, than the mean and median filter. The standard comprising method, combined ST-PCNN and Bayesian MAP estimator is superior to ST-PCNN and Bayesian MAP estimator. The performance of the proposed method is compared with the existing methods, which include ST-PCNN and Bayesian MAP estimator. From the tables, it can be observed that the proposed method outperforms the other methods in terms of PSNR, MSE, and MAE. From table 1 and 2, it is inferred that, as the speckle noise density is higher than the Gaussian noise density, the proposed method removes the speckle noise in a considerable amount than the gaussian noise from the ultrasound images.In this case, the PSNR value is higher than when the speckle noise density is lower than the gaussian noise density.From the tables, we conclude that, the proposed method works well for higher speckle noise densitythan the higher gaussian noise density.
(b) (c) (d) (e)
Fig. 3 Face Ultrasound Image a) Original image b) Noisy image c) Results of Mean Filter d) Results of Median Filter e) Results of Wavelet Filter.
(b) (c) (d) (e)
Fig. 4 Face Ultrasound Image a) Original image b) Noisy image c) Results of Lograthmic transformation d) Results of Inverse Discrete Wavelet transformation e) Results of Exponential transformation.
(b) (c) (d) (e)
Fig. 5 Pelvic Ultrasound image a) Original image b) Noisy image c) Results of Lograthmic transformation d) Results of Inverse Discrete Wavelet transformation e) Results of Exponential transformation.
(b) (c) (d) (e)
Fig. 6 Baby Ultrasound image a) Original image b) Noisy image c) Results of Lograthmic transformation d) Results of Inverse Discrete Wavelet transformation e) Results of Exponential transformation.
Table 1: Comparative results between proposed method and ST-PCNN and Bayesian MAP Estimator
MIXED NOISE DENSITY(Variance)
ESTIMATOR AND ST-PCNN
Table 2: Comparative results between proposed method and ST-PCNN and Bayesian MAP Estimator
MIXED NOISE DENSITY
ESTIMATOR AND ST-PCNN
In this paper an efficient technique for de-noising the medical ultrasound images has been proposed. Combined Bayesian MAP estimator and ST-PCNN method has been proposed for mixed noise reduction. This method is experimented on the test images like Lena, SAR and ultrasound images, where these images are corrupted by mixed noise at different densities. Experimental results show that the combined Bayesian MAP estimator and ST-PCNN method is more efficient in removing mixed noise and preserving edges than other de-noising techniques.
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