استفاده از تخمين‌زننده كمينه‌كننده ميانگين مربعات خطا جهت بهبود كيفيت تصاوير مقطع نگاري رايانه‌اي از شكم بر اساس مدل مخلوط لاپلاس دومتغيره در حوزه تبديل ويولت مختلط چندبعدي
محورهای موضوعی : مهندسی برق و کامپیوترحسين رباني 1 , منصور وفادوست 2
1 - دانشگاه علوم پزشكي اصفهان
2 - دانشگاه صنعتي اميركبير
کلید واژه: تبديل ويولت مختلطتخمين‌زننده كمينه‌كننده ميانگين مربعات خطامدل مخلوطمدل توأم,
چکیده مقاله :
يكي از مسايل تعيين‌كننده در زمينه حذف نويز در حوزه ويولت بر اساس تئوري بيز، استفاده از تابع چگال احتمال مناسب براي مدل‌كردن ضرايب ويولت مي‌باشد. از جمله خصوصيات ضرايب ويولت، وابستگي مابين مقياسي آنها مي‌باشد. در واقع مابين ضرايب ويولت و والد آنها در مقياس مجاور همبستگي بالايي وجود دارد. بر همين اساس در چند سال اخير به‌جاي استفاده از توزيع‌هاي تك‌متغيره در هر زيرباند ويولت از توزيع‌هاي دومتغيره استفاده شده است. در اين مقاله از مخلوط دو توزيع دومتغيره لاپلاسي براي مدل‌كردن ضرايب ويولت استفاده شده است. استفاده از اين مدل، هم خصوصيات نوك‌تيزبودن در مبدأ و دُم‌داربودن توزيع ضرايب ويولت و هم خصوصيت وابستگي مابين مقياسي آنها را به‌طور توأم به‌همراه خواهد داشت. بر اساس اين مدل توزيع احتمال و با استفاده از تخمين‌زننده كمينه‌كننده ميانگين مربعات خطا (MMSE)، الگوريتم تطبيقي جديدي براي كاهش نويز حاصل مي‌گردد. از اين الگوريتم براي كاهش نويز تصاوير مقطع نگاري رايانه‌اي (CT) از شكم در حوزه تبديل ويولت مختلط استفاده مي‌گردد. نتايج شبيه‌سازي‌هاي صورت‌گرفته با اين الگوريتم بيانگر بهبود عمليات كاهش نويز به‌طور كمي و كيفي در مقايسه با ديگر روش‌هاي مطرح‌شده در مقالات مي‌باشد.
One of the important subjects in the wavelet-based image denoising based on the Bayes theorem is choosing the appropriate density function for modeling the wavelet coefficients. The interscale dependency between parent and child coefficients is one of the statistical properties of wavelets. So, in the recent years instead of univariate distribution, bivariate density functions have been suggested by the researchers and in this paper we use a mixture of bivariate Laplacian densities for this reason. Using this distribution we are able to model both heavy-tailed property and interscale dependency of wavelets. Using the mentioned density function for a minimum mean squared error estimator, we obtain a new shrinkage function for denoising. Applying this function to each subband of discrete complex wavelet transform of abdominal computerized tomography images, we will be able to improve the quality of these images better than some reported methods.
[1] J. Starck, F. Murtagh, and A. Bijaoui, Image Processing and Data Analysis: the Multiscale Approach, Cambridge University Press, Cambridge, 1998.
[2] D. L. Donoho, "Denoising by soft-thresholding," IEEE Trans. Inform. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
[3] D. L. Donoho and I. M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, Sep. 1994.
[4] D. L. Donoho and I. M. Johnstone, "Adapting to unknown smoothness via wavelet shrinkage," J. Amer. Statist. Assoc., vol. 90, no. 432, pp. 1200-1224, Dec. 1995.
[5] S. Chang, B. Yu, and M. Vetterli, "Adaptive wavelet thresholding for image denoising and compression," IEEE Trans. Image Processing, vol. 9, no. 9, pp. 1532-1546, Sep. 2000.
[6] F. Luisier, T. Blu, and M. Unser, "A new SURE approach to image denoising: interscale orthonormal wavelet thresholding," IEEE Trans. on Image Processing, vol. 16, no. 3, pp. 593-606, Mar. 2007.
[7] A. Pizurica and W. Philips, "Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising," IEEE Trans. on Image Processing, vol. 15, no. 3, pp. 654-665, Mar. 2006.
[8] M. J. Fadili and L. Boubchir, "Analytical form for a Bayesian wavelet estimator of images using the Bessel K form densities," IEEE Trans. on Image Proc., vol. 14, no. 2, pp. 231-240, Feb. 2005.
[9] M. S. Crouse, R. D. Nowak, and R. G. Baraniuk, "Wavelet - based statistical signal processing using hidden Markov models," IEEE Trans. Signal Processing, vol. 46, no. 4, pp. 886-902, Apr. 1998.
[10] H. Rabbani and M. Vafadoost, "Wavelet based image denoising based on a mixture of Laplace distributions," Iranian J. of Science & Technology, Trans. B., Engineering, vol. 30, no. B6, pp. 711-733, 2006.
[11] E. Simoncelli, "Modeling the joint statistics of images in the wavelet domain," in Proc. of the SPIE 44th Annual Meeting, 3813, pp. 188-195, Jul. 1999.
[12] A. Srivastava, A. B. Lee, E. P. Simoncelli, and S - C. Zhu, " On advances in statistical modeling of natural images," J. Math. Imaging and Vision, vol. 18, no. 1, pp. 17-33, Jan. 2003.
[13] E. Simoncelli, Modeling the Joint Statistics of Images in the Wavelet Domain, Handbook of Image and Video Processing, pp. 431-441, Academic Press, May 2005.
[14] L. Sendur and I. W. Selesnick, "Bivariate shrinkage functions for wavelet - based denoising exploiting interscale dependency," IEEE. Tran. Signal Processing, vol. 50, no. 11, pp. 2744-2756, Nov. 2002.
[15] A. Achim, P. Tsakalides, and A. Bezerianos, "SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling," IEEE Trans. Geosci. Remote Sensing, vol. 41, no. 8, pp. 1773-1784, Aug. 2003.
[16] J. K. Romberg, C. Hyeokho, and R. G. Baraniuk, "Bayesian tree - structured image modeling using wavelet - domain hidden Markov models," IEEE Trans. Signal Processing, vol. 10, no. 7, pp. 1056-1068, Jul. 2001.
[17] I. W. Selesnick, R. G. Baraniuk, and N. Kingsbury, "The dual-tree complex wavelet transform - a coherent framework for multiscale signal and image processing," IEEE Signal Processing Magazine, vol. 22, no. 6, pp.123-151, Nov. 2005.
[18] S. Gazor and W. Zhang, "Speech enhancement employing Laplacian- Gaussian mixture," IEEE Trans. on Speech and Audio Processing, vol. 13, no. 5, pp. 896-904, Sep. 2005.
[19] N. G. Kingsbury, "A dual - tree complex wavelet transform with improved orthogonality and symmetry properties," in Proc. Int. Conf. Image Processing, vol. 2, pp. 375-378, Sep. 2000.
[20] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: from error visibility to structural similarity," IEEE Trans. Image Processing, vol. 13, no. 4, pp. 600-612, Apr. 2004.
