A Hybrid Technique for De-Noising Multi-Modality Medical Images by Employing Cuckoo’s Search with Curvelet Transform

De-noising of the medical images is very difficult task. To improve the overall visual representation we need to apply a contrast enhancement techniques, this representation provide the physicians and clinicians a good and recovered diagnosis results. Various de-noising and contrast enhancements methods are develops. However, some of the methods are not good in providing the better results with accuracy and efficiency. In our paper we de-noise and enhance the medical images without any loss of information. We uses the curvelet transform in combination with ridglet transform along with CS (Cuckoo Search) algorithm. The curvlet transform adapt and represents the sparse pixel informations with all edges. The edges play very important role in understanding of the images. Curvlet transform computes the edges very efficiently where the wavelets are failed. We used the CS to optimize the de-noising coefficients without loss of structural and morphological information. Our designed method would be accurate and efficient in de-noising the medical images. Our method attempts to remove the multiplicative and additive noises. Our proposed method is proved to be an efficient and reliable in removing all kind of noises from the medical images. Result indicates that our proposed approach is better than other approaches in removing impulse, Gaussian, and speckle noises.


RELATED WORK
MRI, ultrasound, and CT images are useful to diagnose diseases in the medical field. High-quality images present good diagnosis results. Therefore, making such type of noise-free images is important. In this study, we only focus on CT and MIRs. These types of images are suffering from impulse, speckle, Rician, and Gaussian noises [6].
Pizurica [7] suggested a method for de-noising magnetic resonance and ultrasound images. They exploited wavelets to remove speckle and Rician noises. Probability density function and empirically approximating probabilities are the basics for this method. The suggested method is not complex and is useful for unidentified types of noises.
Another useful method was suggested in [8]; the concept of dyadic wavelets was utilized, with soft thresholding of expansion coefficient thresholding for 3D (Three Dimensional) X-Ray images. A method for de-noising MRI with white Gaussian noise was mentioned in [9]. Bilateral filter was then used to approximate coefficients by denoising and preserving edges. The de-noised coefficient was used for the formation of reconstructed images. A technique for preserving edges of magnetic resonance images while removing noises was highlighted in [10].
Images related to tumor of breast cancer were de-noised by thresholding NNs in [11]. Qing-Hang [25] also discussed a filtering method based oncombinations of anisotropic diffusion filters and linear minimum mean square error filters. Techniques proposed in [9,26] were based on the merger of contrast enhancement and de-noising methods.
Alternately, the probability distribution function of wavelet coefficients that gives useful information was determined by unknown noise types in [27], and the Canny edge detector [25] was used after thresholding to enhance edges. The wavelet coefficients, which are helpful in Rician and speckle noise reduction from medical images, were approximated using bilateral filter [26,28]. Hence, the result satisfaction was based on these techniques.Wavelets [29] and simple curvelet [30] are not reliant on noise type.
They are applied to remove all types of noises, but their performance is not much satisfactory in terms of accuracy, morphological and structural information, and computational complexity. The quality of images can be improved further by developing more efficient techniques than NNs and wavelets.

PROPOSED METHODOLOGY
In the given section, we explain the curvelet transform by using ridgelet transforms with CS for medical image denoising. Fig. 1 shows the block diagrams of the proposed method, which consist of some essential stages.

Curvelet Transform
The frequency and time analysis decomposes a signal into the numerouso rthogonals bases. The signals are quantizes into the summations of the different coefficient basis, i.e. f=Σk ak bk whre ak is the coefficients, and bk is the basis, frame. Although wavelet can efficiently handle point discontinuity [31,32], but curvelet consider numerous coefficients for edges, as shown in Fig. 2. Fig.   2(a) shows that the wavelet approach requires many wavelet coefficients to interpret edges, singularities along lines, or curves. Fig. 2 Fig. 3.
The overview of curvelet transform is given in Fig. 3. The ridgelet transforms is then used to every blocks.We describe the bank of sub-band filter P 0 ,(Δ s , s > 0). The entities f is filters into the sub-band. This stage divided the images into several resolutions layer. Each layer includes detail of diverse frequency, as explained in the following Equation (1): Where P 0 and Δ 1 . Δ 2 ,…. are the high and low frequencies filters. Therefore, the input images can be restructured from the sub-bands through Equation (2).
A convolution operator is applied for sub-band decomposition, as explained in Equation (3).
Some connections exist among curvelets and wavelets transform. The sub-band decomposition can be estimated by using the familiar wavelet transforms. The wavelet transforms are decomposed into different decomposition levels, such as S 0 , D 1 , D 2 , D 3 . P 0 f is moderately developed from S 0 to D 1 and may comprise D 2 and D 3 . Δ s f is assembled from D 2s to D 2s+1 . P 0 f is low pass and can be capably represented using wavelet base [33]. However, the discontinuity curve affects the high-pass layers Δs f. A compilation of smooth window WQ(x 1 ,x 2 ) localize about dyadic image squares is defined.
The next step is to smooth the partitioning of the image defined as a compilation of the smooth windows, and the ridglet analysis and ridglet transform, The used of the approach in association with the ridgelet transform has been deliberated in [33][34][35].

De-Noising Coefficients
After decomposing the images into sub-bands and applying the ridglet and RT, we employing our technique to de-noise the medical image. The proposed methodology is ordinary and is outlined mostly for selfcontentedness and clearness.
Noisy data are given in the form of the following Equation (4): where f is source input image to be de-noised and enhanced, and z is the noise, i.e. z i,j~i N(0,1) added to the image and σ is used to summation the total noise in the image.

Cuckoo Search
In the given section we introduces CS algorithm to  (5) [36]. In Equation (5) μ indicate the Levy distribution and λ indicate the random walk length. The Levy flight essentially provide random steps length is drawn from the levy distribution.
Levy ~ m=t -l , (1 <l< 3) CS employs breedings and the flyings behaviors of the cuckoo. The basic CS behavior are given below [36].
• Population contains nests with eggs. •

Eggs represented problems and solution. The
Cuckoo egg is considered as the new solution.
• If the cuckooegg match to the eggs of the hosts, then the finding probability is limited. The solutions ofthefitness function is ondifferent invariance of the solution.
The CS algorithm has its roots in three rules given below [36].
• Every cuckoo can lay dump randomly one egg at the time in the selected nest.
• Next generations will inherit the best solution. Eggs represent a solution. Only the most excellent solutions are conceded to subsequent generation to attain the goal rapidly. Solution is evaluated by fitness function [37].
According to [36], several advantages of CS algorithm are presented below: • CS ensures that the local optimum problem is not occurring because most of the solutions are generated by randomization, with locations beyond the best solutions.
• CS randomization is more efficient than PSO and GA • CS is more general than GA and PSO because it needs a minimal number of parameters given that CS is adopted in optimization problems.
• CS algorithm is used to determine the sequence

Inverse Curvelet Transform
After the de-noising through the curvelet coefficients, we apply inverse curvelet transform to reconstruct image.
Inversing the procedure of curvelet transforms with some mathematic revising ridgelet synthesis means that each image square is restructured from the orthonormal ridgelet classification. All ridgelet coefficients are summed with basis, as described in Equation (6), where g is the ridglet coefficients,α and ρare the length and density of the coefficients.
( ) Renormalization means that each image square resulting in preceding stages is renormalized to its own appropriate image squares, as described in Equation (7), Where Q is the smooth combination, h indicates the stages of the images.
h Q = T Q g Q Where Q∈Q Smooth combinations means that we inverse the windows analysis to all the windows restructurings in the precedings stage of image, w indicates the sub bands window, as described in Equation (8).
In sub-bands re-compositions, we reverse bank of subband filter using the replicate Equation (9) to sum all the sub-bands, where P 0 are the sub band filters.

EXPERIMENTAL SETUP
In this his section we elaborates and discuss the experimental procedure for image de-noising using To check the performance of the proposed approach, some standard CT and MRI scan images are selected for testing.
We select a dataset of 100 images with different resolutions to evaluate the proposed technique.

Objective Evaluation
To evaluates the performance of a variety of a methods, quality assessments methods, such as PSNR, CNR, UIQI, SSIM, and distance SSIM (DSSIM), are applied on images, and the parameters included in this research are shown in Table 1.

PSNR
The PSNR is defined as follows in Equation (10) When medical images are acquired by any means, it refers to the unnecessary turbulence that induces into the image.

SSIM and DSSIM
SSIM method is used to measure similarity between two images. This method can be considered as a quality measure for one of the images being compared by fulfilling the condition that the second image has a perfect quality [39].
The SSIM metric is calculated as follows in Equation (11):

CNR
CNR is described in Equation (13).  The evaluation formula [40] is described as follows in Equation (14):

RESULTS AND ANALYSIS
In this section, images are demonstrated to confirms the achievement of the proposed technique. We apply our proposed method on some degraded images and the results is presented in Fig.6. The left column in Fig. 6 is the degraded images and on the right column is the

Single-Bleeding Pattern CT Image
Single-bleeding pattern CT and magnetic resonance images are used to analysis the behaviors of the proposed algorithm on multiplicative and additive noise models.  0.5 variance with high-resolution images. Tables 8-9 present the behavior of the proposed approach for Gaussian and speckle noises at different noise intensities, respectively.

Multi-Bleeding Patterns
We illustrates the performances of the proposed technique on an MRI images and compare it to the traditional wavelets and some other methods. In Figs. 11-12(a) is the reference image effected with noise. In Figs. 11-12(a)  Original magnetic resonance image, Fig. 12(b) image denoised with DTCWPT, Fig. 12(c) image de-noised with Visu shrink, Fig. 12(d) image de-noised with Bayes shrink, Fig. 12(e) image de-noised with Sure shrink Fig. 12(f) image de-noised with BMWT, Fig. 12(g) image de-noised with AMC-SSDA Fig. 12(h) e  p  y  T  e  g  a  m  I  d  r  a  d  n  a  t  S  n  o  i  t  a  i  v  e  D   t  n  e  m  s  s  e  s  s  A  s  r  e  t  e  m  a  r  a  P   s  d  o  h  t  e  M  g  n  i  s  i  o  N  -e  D   T  P  W  C  T  D  u  s  i  V  k  n  i  r  h  S   s  e  y  a  B  k  n  i  r  h  S   e  r  u  S  k  n  i  r  h  S  T  W  M  B  A  D  S  S  -C  M  A  d  e  s  o  p  o  r  P  e  c  n  e  u  q