A Wavelet-Based Approach for Ultrasound Image Restoration

Ultrasound's images are generally affected by speckle noise which is mainly due to the scattering phenomenon’s coherent nature. Speckle filtration is accompanied with loss of diagnostic features. In this paper a modest new trial introduced to remove speckles while keeping the fine features of the tissue under diagnosis by enhancing image’s edges; via Curvelet denoising and Wavelet based image fusion. Performance evaluation of our work is done by four quantitative measures: the peak signal to noise ratio (PSNR), the square root of the mean square of error (RMSE), a universal image quality index (Q), and the Pratt’s figure of merit (FOM) as a quantitative measure for edge preservation. Plus Canny edge map which is extracted as a qualitative measure of edge preservation. The measurements of the proposed approach assured its qualitative and quantitative success into image denoising while maintaining edges as possible. A Gray phantom is designed to test our proposed enhancement method. The phantom results assure the success and applicability of this paper approach not only to this research works but also for gray scale diagnostic scans’ images including ultrasound’s Bscans.


INTRODUCTION
Ultrasound medical imaging which has been widely accepted as an essential safe tool for biological tissue medical diagnosis, are generally affected by speckle noise due to the scattering phenomenon's coherent nature.Speckle noise is a well known phenomenon inherent most B-mode ultrasonic scans' images caused by the constructive and destructive interferences of the wavelets scattered by the tissue components as they arrive at the transducer [1], [2].Speckle degrades the resolution and contrast of ultrasound images [3].Speckle noise poses a well known problem in ultrasound imaging [4].It acts as a mask of the small differences in grey level images [5].Therefore the pre filtering process of Speckle noise cannot be avoided.It is a critical pre-processing step, providing clinicians with enhanced diagnostic ability [13].The filtration is accompanied with loss of diagnostic features.The amount of these losses differs according to the techniques reported so far.
In this paper; we introduce an approach to remove speckles while keeping the fine features of the tissue under diagnosis as possible by enhancing image's edges; via the Curvelet denoising and Wavelet based image fusion.The study was done on a normal kidney ultrasonic scan taken from a man; 27 years old, by an ultrasound console: Aloka-ProSound 3500SX, in DICOM format [49].Beside; an original Gray phantom is built to prove the success of our proposed enhancement method into better speckle reduction with edge enhancement for ultrasound scans, than the only Curvelet based denoising; qualitatively and quantitatively.A general quality optimization index S&M (S.Badawy and M. GadAllah) is newly introduced for selecting the best parameter's value for any parameter-based image fusion method being firstly introduced into image processing research.The paper is organized as follows: In Section II; we display the materials and methods had been used in our paper including our proposed approach, been applied on a human right kidney scan and the gray phantom study.The numerical and graphical results are displayed in Section III.A brief discussion of our results is represented in Section IV.Finally, we give some concluding remarks in Section V. www.ijacsa.thesai.org

A. Curvelet Based Image Denoising:
The Curvelets is to represent a curve as a superposition of functions of various lengths and widths [11].Curvelet transforms gave close and improved delineation to edges [14].Curvelet construction based on three essential ideas: firstly, Ridgelets; a method of analysis suitable for objects with discontinuities across straight lines.Secondly, Multiscale Ridgelets, a pyramid of windowed Ridgelets, renormalized and transported to a wide range of scales and locations.Thirdly, Band-pass Filtering, a method of separating an object out into a series of disjoint scales [15].We used a Matlabbased Toolbox: [33] made by Sandeep P.; for performing Image denoising in Curvelet domain using thresholding.This toolbox [33]; when computing the Curvelet of an image, it makes that as given in [12].

B. Wavelet Based Image Fusion:
The principle of image fusion using wavelets is to merge the wavelet decompositions of the two original images using fusion methods applied to approximations coefficients and details coefficients [50].There are more techniques for image fusion [41]- [44].
We used the Wavelet toolbox, built-in Matlab-R2011b to perform: wavelet based image fusion; a kind of a Multiscale-Decomposition Based Fusion.The fusion been made, was inbetween the noisy image (N) and the reconstructed (denoised) image (R) produced from the denoising process in Curvelet transform domain.The resulted fused image, we called the final processed image (FP).An illustrative block diagram of the used fusion method is shown in Fig. 1, where; N is referred to the Noisy image -input.R is referred to the Reconstructed image -input.A is referred to Approximation.D is referred to Details.FP is referred to Final Processed image -output.
We applied the User-Defined Fusion method; mentioned in [50] for merging the approximation coefficients of the two input images; A N and A R , as the following Matlab code:

-F)* A N (~D); end
The parameter F; we called the fusion ratio; for the Approximation fusion method.The value of F can be changed from 0 to 1.In our study we used different values of F. The best used value of F was 0.5; achieving a maximum image's edge preservation as well as maintaining its quality as possible.So, we recommend using a value of 0.5 for F.

C. Performance Evaluation:
1) RMSE is the square root of MSE calculated from the following equation (1):

… (1)
Where; m = number of rows in the image, n = number of columns, O is the original image pixel values matrix, R is the reconstructed image pixel values matrix, and finally (i,j) are the x, y coordinates for every pixel in each image.MSE has been the dominant quantitative performance metric in the field of signal processing for more than 50 years [45].We had programmed; equation (1) of MSE, on Matlab-R2011b and implemented it in our measurements.
2) PSNR is represented in the following equation (2): Where, MAX o is the maximum pixel value in image O [here; MAX o = 255], MSE here is the mean square error calculated from equation ( 1).We used Matlab-R2011b and [33] for calculating PSNR.PSNR and RMSE measures are used in more papers which are about sonograms' denoising [11].
3) Q is the Universal Image Quality Index, introduced in [46], it is based on three basic components measured inbetween the original image and the image which to be compared; correlation coefficient, mean luminance, and contrast [46].Its value ranges from 0 till 1, if Q = 1, it means the two images are same.We used [46] and Matlab to calculate Q in our measurements.4) FOM is the Pratt's Figure of Merit; introduced in 1978 by W. K. Pratt as a quantitative measure for edge preservation [47].FOM is defined by: Where; I N = MAX {I I, I A } and I I and I A represent the number of ideal and actual edge map points; respectively, a is a scaling constant, and D is the separation distance of an actual edge point normal to a line of ideal edge points.The rating factor is normalized so that R = 1 for a perfectly detected edge [47].We used [48] by Matlab to calculate FOM in our measurements, but in percent % values, so if FOM = 100, it means that FOM = 1 in (3).

D. The Proposed Approach
An ultrasound scan of a normal human right kidney was taken by ultrasound console: Aloka-ProSound 3500SX; [49].The interested area of the resulted image had been put on a black background with an appropriate dimensions match with Curvelet transform domain; as shown in Fig. 2.

Manipulation was done as follow:
i. Noising the image by an added noise determined by the value of the Signal to Noise Ratio (Snr).
ii. Denoising the resulted image in Curvelet transform domain, as mentioned previously in A.
iii.Applying the wavelet based fusion method been explained previously in B.; in-between the noised and the denoised image produced from i. and ii., respectively taking F = 0.95959595.
iv. Measurements:  The edge detection map of Canny had been extracted as a qualitative measure of edge preservation for each image of the three images produced from i., ii., and iii. A four quantitative performance evaluation measures PSNR, RMSE, Q, and FOM; had been calculated inbetween the original image and each one of its three derivatives produced in i., ii., and iii.
v. Repeating the previous four steps i., ii., iii., and iv.; along 20 different values for Snr.
vi.The FOM's 20 results is plotted for each image vs. the corresponding Snr, into Fig.3-A, where: the three colored lines; Blue, Green, and Red represents: in the three cases: Noisy, denoised (CVT), and the final wavelet fused image (WT), respectively.

Optimizing the Applied Fusion Method:
Our goal is to find the better performance of the applied fusion method that makes maximum edge preservation as well as maintains image's quality and PSNR as possible.For that we introduce here, a general quality optimization index be named S&M index.This index can be used in general for selecting the best parameter's value (F in our study) for any parameter-based image fusion method being firstly introduced into image processing research.S&M index is defined as follow: Where, _n: means after normalization to the nearest maximum value.This equation calculates maximum values for PSNR, FOM, Q, and minimum value for RMSE.

We applied S&M optimization for the applied fusion method as follow:
1) Taking one result from the right kidney scan's image, where Snr = 10, after step ii; i.e. after noising and denoising process, then, we made step iii for this result not only at (F) = 0.95959595, But, instead we made this step 25 times for different values of F; starting from 0.05 to 1.0.
2) Calculating the four measurements; PSNR, RMSE, Q, and FOM; for all the 25 results, and normalized all to the nearest maximum value.
3) Drawing in percentage %; the 25 final wavelet fused numerical results for PSNR, RMSE, Q, and FOM, after being approximately normalized; all vs. the fusion ratio (F); as www.ijacsa.thesai.orgshown in Fig. 3-B; where: the four colored lines; Blue, Green, Red, and Blue-Light represents: the four measurements: PSNR, RMSE, Q, and FOM; respectively.4) Finally, we applied equation ( 4), for S&M optimization index, on the 25 results from the previous step 2, producing the optimization figure; shown in Fig. 3-C; where: the y-axis; represents: S&M index value, and the x-axis; represents: F; starting from 0.05 to 1.0.

Repeating Manipulation taking F = 0.5:
From equation (4); we can deduce that the optimum performance of the proposed approach, making maximum edge preservation as well as maintaining image's quality and PSNR as possible; can be founded where S&M index has a maximum value.From Fig. 3-C; the maximum value of S&M index on the curve can be founded when F = 0.5.Taking F = 0.5 instead of the last empirical value of F (0.95959595) and repeating our proposed approach's manipulation steps on the same image shown in Fig. 2, we will obtain another 20 optimized results.The FOM's measurement values during the 20 results are plotted into Fig.3-D; where: the three colored lines; Blue, Green, and Red represents: in the three cases: Noisy, CVT, and WT; respectively.

E. Our Gray Phantom Study:
A new Gray phantom shown in Fig. 4; been introduced by S. Badawy and M. GadAllah; consists of gray scale vertical and horizontal bars used for testing strait boundaries and intensities of the gray levels.It is designed especially to test and assure the applied method for all gray scale images in radiology including Ultrasound's B-Scans.

A. Kidney scan image Results with F = 0.95959595:
After applying our proposed approach on the right kidney scan's image, where; F = 0.95959595, and along 20 different value of Snr; the result is 20 by 3 images produced 60 resulted images beside the original one.After Canny edge map had been extracted producing another 60 result edge maps for each image beside the edge map of the original one.
The results was good but after being optimized; it became better; so, we satisfied here only by displaying the final average quantitative results of the 20 different results for: PSNR, RMSE, Q, and FOM, in comparison by the same average results after being optimized by the suitable fusion ratio based on applying S&M index enhancement, see Table I.Analytically; the FOM's 20 results had been plotted vs. the corresponding Snr, as shown in Fig. 3-A.

B. Kidney scan image Results with F = 0.5:
After applying the S&M optimization on the right kidney scan's image, selecting (F) = 0. 5, and along 20 different value of Snr; the result is 20 by 3 images produced 60 resulted images beside the original one.After Canny edge map had been extracted producing another 60 result edge maps for each image beside the edge map of the original one.A sample result from the 20 results, where Snr = 10; can be seen in Fig. 5; where: The lower four images in the two figures are the canny edge map for the upper four images correspondingly.Those maps are a qualitative measure for edge preservation in each image.The numbers on images are as follow: The final average quantitative results of the 20 different results for: PSNR, RMSE, Q, and FOM, after being optimized by the suitable fusion ratio; are shown in Table I.The FOM's 20 results had been plotted vs. the corresponding Snr, as shown in Fig. 3-D.

C. Our Phantom Study Results:
Applying our enhancement approach on the gray scale phantom image, selecting (F) = 0. 5, and along 12 different value of Snr; the result is 12 by 3 images produced 36 resulted images beside the original one.After Canny edge map had been extracted producing another 36 result edge maps for each image beside the edge map of the original one.According to the tabulated results into Table II; we have up to twelve figures.A sample Result of our Gray Scale Phantom is shown in Fig. 6; Where; Snr = 25 for the noisy image.Where: The lower three images are the canny edge maps for the upper three images correspondingly.This is a qualitative measure for edge preservation in each image.The numbers on images are as follow: 1) Is stated for the Noisy-Image.
2) Is stated for the Reconstructed -Image after the denoising process in Curvelet Transform (CT) domain.3) Is stated for the Final Processed -Image after making the wavelet based image fusion in between 1 & 2.
The quantitative measurements taken from processing our Gray Phantom image had been tabulated into Table II; representing 12 Results' measurements, taking F_ratio = 0.5.Table II has

Result -No.: is the number of result
Parameter + N: N refers to Noisy and means that this parameter is calculated in-between the noisy image and the reference original one shown in Fig. 3.
Parameter + FP: FP refers to Final Processed by the applied approach, and means that this parameter is calculated in-between the Final Result wavelet-fused image and the reference original one.
The four calculated measures' 12 results; PSNR, RMSE, Q, and FOM; had been plotted for each image vs. the corresponding Snr; producing four curves shown in Fig. 7: A,  B, C, and D respectively.Where: The Blue line represents the quantity before applying the processing approach (Noisy) and the Green line represents the same quantity after image being processed (FP).

IV. DISCUSSION
Looking at Fig. 3-A & Fig. 3-D, obviously; we can see the enhancement in the edge preservation index FOM for the final fused kidney scan image, before and after applying S&Moptimization; represented by the red line.
Quantitatively, Looking at Table I, we can notice the increase in FOM after the optimization process, where the value of Q is still constant; assuring our optimized approach in preserving edges while maintaining quality as possible.
Qualitatively; comparing in between the Canny edge map for the final fused images shown in Fig. 5-3, and the denoised image using Curvelet only shown in Fig. 5-2; we can see the effect of our proposed approach in recovering image details which lost in denoising process.Comparing in between the Canny edge map for the final processed image shown in Fig. 5-3, and the noisy image shown in Fig. 5-1; we can see the enhanced denoising produced while keeping edges as possible.Looking at Fig. 7-A, Fig. 7-B, and Fig. 7-C; for PSNR, Q, and FOM, respectively; we can see analytically the resulted enhancement in the final processed gray scale image after applying our enhancement procedure; represented by the green line instead of the blue line before enhancement.Also, RMSE had been decreased throw all the curve shown in Fig. 7-D; represented by the green line instead of the blue line before.
Comparing in between the Canny edge map for the final fused phantom image shown in Fig. 6-3, and the denoised image using Curvelet only shown in Fig. 6-2; we can obviously; see the effect of our proposed approach in recovering some of image's details which lost in denoising process.
Comparing in between the Canny edge map for the final fused phantom image shown in Fig. 6-3, and the noisy image shown in Fig. 6-1; we can see qualitatively; the enhanced denoising produced by our proposed enhancement approach while keeping edges as possible preservation.
A clear improvement in the average value for FOM and Q can be shown quantitatively in Table II On the other hand the average value of RMSE had been decreased to be 6.76 instead of 37.61 before; which assures that the applied approach is effective in enhanced denoising with little values of error.
The gray phantom results displayed is a step towards generalizing our introduced enhancement method for all gray scale diagnostic scans' images including Ultrasonography.

V. CONCLUSION
Wavelet based image fusion after Curvelet denoising, successfully used to improve the removal of image's speckles (here, kidney's ultrasound scan) while enhancing its edges as possible.Moreover, a gray phantom was introduced to help in testing and assuring the ability of the proposed work as an enhancement method for gray scale diagnostic scans' images including Ultrasonography.Also; a general quality optimization index be named S&M is newly introduced for selecting the best parameter for any parameter-based image fusion method being firstly introduced into image processing research.

Fig. 1 .
Fig. 1.Illustrative Block Diagram of the Used Fusion Method

Fig. 2 .
Fig. 2. The Right Kidney Scan On A Black Background the phantom by an added noise determined by the Snr value.b.Denoising the produced image in Curvelet transform domain.c.Applying the wavelet based fusion method been explained previously in B.; in-between the noised and the denoised image produced from a. and b., respectively taking F = 0. 5. d.Measurements:  The edge detection map of Canny had been extracted as a qualitative measure of edge preservation for each image of the three images produced from a., b., and c.  A four quantitative performance evaluation measures PSNR, RMSE, Q, and FOM; had been calculated inbetween the original phantom image and each one of its three derivatives produced in a., b., and c. e. Repeating the previous four steps a., b., c., and d.; along 12 different values for Snr.

1 )
Is stated for the Noisy-Image.2) Is stated for the Reconstructed -Image after the denoising process in Curvelet transform domain.3) Is stated for the Final Processed -Image after making the wavelet based image fusion in between 1 & 2. 4) Is stated for the Original Base Image as a reference.
equal number of elements.Each row describes one complete result measurements for a specified Signal to Noise Ratio (SNR) value taken for the noised image.The last row is the mean or Avg.(Average) values of each parameter.The first-left column represent the value of SNR, the next column is the result number, the next 8 columns are the measurements values, Where;

Fig. 5 .
Fig. 5.A Sample Result for the Right Kidney Scan After Using S&M Index at Fusion Ratio, F = 0.5, Where; Snr = 10

Fig. 6 .
Fig. 6.A Sample Result of Our Gray Scale Phantom Where; Snr = 25

TABLE I .
THE RIGHT KIDNEY SCAN AVERAGE RESULTS Average Results for: Final Wavelet Fused Image 09 www.ijacsa.thesai.orgIII.RESULTS

; to be 72.05 and 0.61 instead of 60.04 and 0.31, respectively.
www.ijacsa.thesai.orgAlso, the average value of PSNR was better enhanced after applying our probosed wavelet based approach to be 35.50instead of 23.65 before.
Fig. 7. Gray Scale Phantom Image's Analytical Results Curves