05 IEEE European Modelling Symposium Performance Comparison of Discrete Orthonormal S-Transform for the Reconstruction of Medical Images Yuslinda Wati Mohamad Yusof Azilah Saparon Nor Aini Abdul Jalil Faculty of Electrical Engineering Universiti Tenologi MARA Selangor Malaysia yuslinda@salam.uitm.edu.my azilah574@salam.uitm.edu.my norain65@salam.uitm.edu.my Abstract This paper investigates the performance of the Discrete Orthonormal S-Transform (DOST) technique for the reconstruction of medical images. This technique is compared with the q-recursive ernie Moment (q-rm) and Discrete Wavelet Transform (DWT) based on the performance measurement namely Mean Square Error (MSE) and Pea Signal to Noise Ratio (PSNR) on medical images. The ultimate goal is to find the best technique that can extract the important feature of the medical image. Computer Tomography (CT) and Magnetic Resonance (MR) images are used to test the viability of the techniques to be used for image compression. The experiment is done using MATLAB tool. From the results the DOST technique has high PSNR value and outperforms q- recursive ernie Moments and Discrete Wavelet Transform Techniques. Keywords- comparative; zernie moment; s-transform; medical; image; I. INTRODUCTION Quality of the image reconstruction is important in medical image analysis. This image quality can be measured by Pea Signal-to-Noise Ratio. Various method to reconstruct image is applied including Discrete Cosine Transform Wavelet based method Principal Component Analysis and ernie Moment. The DOST is fairly young compared to other transform. owever it has been demonstrated to be useful in some fields. The DOST has been successfully applied in signal analysis to channel instantaneous frequency analysis. It has also been recently applied to image processing in image compression [][][][4] image texture analysis[5] and image restoration[6]. Research wor as in [4] introduced the DOST for image compression. Medical and normal images are used in the investigation. The PSNR comparison of DOST between Fourier Transform (FT) and Wavelet Transform (WT) shows that DOST outperforms these two methods. DOST is also used in image texture analysis as described in [5]. Normal images such as straw wood sand and grass are used in the analysis. The approach to characterize the image texture are investigated based on WT other than DOST. The experiments prove that DOST accurately recover the original image. The ability of rotation-invariant also being tested between DOST and DWT. The invariant property of DOST gives higher classification accuracy on texture image compared to DWT technique. In [6] DOST is used for image restoration whereby Lena image is used in the experiment. Again DOST outperforms DWT in term of high PSNR value. The DOST is closely related to wavelet transform. owever it has the additional benefits of maintaining the phase properties of the ST and FT retaining the ability to collapse exactly bac to the Fourier domain. In this paper the performance of the DOST is investigated and compared to the existing reconstruction techniques such as DWT and q-rm in order to find the best techniques that provide the highest quality image. The reason to investigate DOST for the reconstruction of medical images is because DOST technique is not commonly applied in medical image compression especially on D medical images. Eventhough in the investigation the images used are D but the results obtained should be sufficient to conclude on the performance of this transformation technique. II. MAPPING TECNIQUES There are several techniques used to map the medical image. Basically the process to map image is illustrated Figure.. The image is mapped to the appropriate technique and the image is converted from one domain to another. To get the reconstructed image the inverse mapping is applied. In this session DOST DWT and q-rm are discussed. Original Image Reconstructed Image Map Inverse map Figure. Basic Mapping. 978--5090-006-/5 $.00 05 IEEE DOI 0.09/EMS.05.8 8
A. Discrete orthonormal S-Transform (DOST) Discrete Orthonormal S-Transform is an orthonormal version of stocwell transform[7][4]. It has an orthonormal basis multiple scales and an absolutely referenced phase[]. Forward DOST can be implemented as explained below[7]; i. Applying an N-point DFT to calculate the Fourier spectrum of the signal [m] ii. Multiple [m + n] with the rectangular window function W [m] where W [m]= [-//(-) (m) () iii. Applying an -point inverse DFT to W[m][m + n] in order to calculate the DST coefficients s[n] where = 0 L/ L/ (-)L/ for each central frequency n = 0 / The Inverse DOST can be applied as follows; i. Applying an -point DFT to s[n] with respect to time index to obtain the windowed Fourier W[m][m+n] for each central frequency n=0./ β β Note that W[m]= for m... that returns [n] n=+ - Fourier coefficients of the signal. ii. Applying an N-point inverse DFT to [n] to recover the original signal h[ ]. B. Q-Recursive zernie Moment (q-rm) ernie Moments has widely used in image reconstruction. The investigation of the technique can be viewed in[8][9] [0]. There are several method can be used to implement M and one of them is q-recursive. The q- recursive method is proposed by C.W.Chong []. The method utilizes ernie radial polynomial of fixed order p with higher index q to derive the polynomial of the lower index q without computing the polynomial coefficients and the power series of the radius. The recurrence relation and its coefficient are defined as [] ( p+ ) V ) = () ( r f( r θ rdrdθ where V (r is ernie polynomials of order p and repetition q and is defined as imθ V ( r = R( r) e () while denotes complex conjugate. R r) = R + + R ( ( ) (4) p q r p ( q 4) ( ) r with the coefficients of and as q ( q ) ( p + q + )( p q ) = q + (5) 8 ( p + q )( p q + ) = + ( q ) (6) 4 ( q ) 4 ( q )( q ) = (7) ( p + q )( p q + 4 ) Chong also proposed two relations when p=q and p- q= by using the following equations p R = r for p q (8) pp = R p ( p ) = pr pp ( p ) R ( p )( p ) (9) for p q = To reconstruct the image the inverse ernie moments is written as n f ( r θ ) = V ( r θ ) (0) p= 0 q where the ernie moment and the ernie polynomials V (r are complex-valued while the image intensity function f(r is real-valued. The real valued polynomials R is given by f ( r θ ) = ( c ) p 0 R p 0 ( r θ ) + ( s ) + sin qθ ) R n q > 0 p = 0 ( ( r θ ) ( c ) cos q θ () (c) (s) where and are the real-valued ernie moment components define as ( c) ( p + ) = R forq 0 ( s) ( p + ) = R for q > 0 ( r f ( r cosqθrdrdθ ( r θ ) f ( r θ )sin qθrdrdθ () () 9
C. Discrete Wavelet Transform (DWT) DWT is a technique to improve the quality of images and it is the technique adopted in JPEG000 algorithm. In line with the emerging technology wavelet has been improved to overcome the disadvantages of the technique such as the computational and memory complexity. The forward equation for DWT is described as[]; ψ b j j ψ = ( j t ) () t () = f t j ψ j (4) IV. RESULT A. CT Image The original image of the anle is shown in Figure. with pixel size of 5 x 5. In this study three methods are applied which are DOST DWT and q-rm. Figure. to Figure. 5 illustrates the image reconstruction after conducting these three methods. From the figures through visual inspection the quality of the images is about similar between the DOS DWT and q-rm techniques. The inverse DWT is given by the following equation: f () t b j () t = j ψ j (5) where the f (t) is the signal ψ j is the mother wavelet and scaled by power of and b j is wavelet coefficients. In this paper the DWT utilized aar method. This method has been compared with other transformation methods as described in [4]. In [4] the transformation used was DWT (aar) DWT(Bior) DWT(Symlet) DWT(Coiflet) IWT DCT and PCA. The best result in [4] then is compared again with DOST and q-rm and reported in this paper. Figure. Original anle image. III. METODOLOGY In this research two medical image are selected as test data. This include the CT image with a size of 5 x5 pixels with 8bpp. Meanwhile the MRI image has a size of 56 x 56 pixels with 8bpp. The simulation is done using MATLAB tool. The performance is evaluated using MSE and PSR [5]. The MSE is evaluated as m n i= 0 j= 0 [ ( ) ( )] I i j K i j MSE = mn (6) While the expression for PSNR is MAX i PSNR = 0 log 0 MSE (7) Figure. DOST. Figure 4. DWT. where m and n are the size of the image and I and K are then the original and processed image respectively. Figure 5. q-rm. 0
Table I tabulates the PSNR (db) and the MSE values of the reconstructed images. In all cases the DOST has the highest PSNR value which is 68.875 db followed by DWT and q-rm is the lowest. TABLE I. COMPARISON OF PSNR AND MSE FOR CT Transformation Performance Measurement PSNR(dB) MSE DOST 68.875 9.500e-0 DWT 89.5.74e-4 Figure 9. q-rm. q-rm.747 0.006695 B. MRI Image Figure. 6 depicts the original image of the brain with a pixel size of 56 x 56. The reconstructed images of the techniques used are shown in Figure. 7 to Figure. 9. As can be seen in the figures below again the DOST and DWT techniques yielded better quality images than q-rm. Both DOST and DWT remains sharper and eeps more detail information of the images than q-rm. ` The PSNR (db) and the MSE values of these different reconstruction techniques are tabulated in Table II. From the table the DOST yields the highest PSNR and q-rm has the lowest PSNR. TABLE II. Transformation COMPARISON OF PSNR AND MSE FOR MRI Performance Measurement PSNR(dB) MSE DOST 67.9768.044e-0 DWT 96.8.5789e-5 q-rm 4.96 0.0008 Figure 6. Original MRI image. For both image the DWT method used is aar at five levels of decomposition. In q-rm the order used is 00 for MRI and 500 for CT image. The reconstruction error of q-rm is reduced with the increment of moment order. owever longer time is needed to complete the cycle. In DOST higher coefficient is used to produce better quality image. Figure 7. DOST. Figure 8. DWT. V. CONCLUSION From the experiments conducted the PSNR value of DOST technique is high and produced better quality images compared to DWT and q-rm techniques. The experiments have proven that DOST is the best transformation technique and in fact the investigation conducted in [4] also agrees that DOST outperforms other transformation techniques. Since medical image compression requires lossless information of the reconstructed image DOST should be considered for further investigation of the compression processes. The effect of encoding and decoding are the crucial processes of image compression before the image is finally reconstructed. Due to this considering DOST as the choice of transformation technique would possibly wor on D medical images for compression.
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