عنوان مقاله [English]
The presence of speckle as multiplicative noise in ultrasound and radar images defects the image perception. Therefore, it is necessary to reduce the speckle before processing like segmentation, edge detecting, and target navigation. In general, denoising is performed either in spatial or transform domain where in this paper, we focused on transform domain as well. Bayesian method and BiShrink approach which is the two-variable Bayesian, are addressed in the domains of separable, stationary, and Dual-tree wavelets for speckle noise reduction by thresholding. Based on simulation results, the Dual-tree wavelet is appropriate because of being separate the real and imaginary parts. In addition, the BiShrink method is more efficient than the Bayesian. To compare the performance of different methods, the standard Lena and Barabra test images and a real SAR image are used, MSE, PSNR, SSIM, ENL, and NV are computed as quantitative criteria. Also, in order to evaluate the coefficients sparsity, the histograms are shown and the average standarad devition values for all subbands are obtained.
 B. Hou, X. Zhang, X. Bu, H. Feng, “SAR image despeckling based on nonsubsampled shearlet transform”, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, Vol. 5, No. 3, pp. 809-823, June 2012.
 N. Kingsbury, “The dual-tree complex wavelet transform: a new efficient tool for image restoration and enhancement”, Proceeding of the IEEE/ EUSIPCO, pp. 1-4, Rhodes, Greece, Sep. 1998.
 M.C. Motwani, M.C. Gadiya, R.C. Motwani, F.C. Harris, "Survey of image denoising techniques", Proceedings of GSPX, pp. 27-30, Sept. 2004.
 Z. Vahabi, F. Almasgang, "Denoising in wavelet packet domain via approximation coefficients", Journal of Intelligent Procedures in Electrical Technology, Vol. 2, No. 8, pp. 31-38, Winter 2012.
 H.A. Chipman, E.D. Kolaczyk, R.E. McCulloch, "Adaptive bayesian wavelet shrinkage", Journal of the American Statistical Association, Vol. 92, No. 44, pp. 1413-1421, Dec. 1997.
 S. Jafari, S. Ghofrani, M. Sheikhan, “Comparing undecimated wavelet, nonsubsampled contourlet and shearlet for sar images despeckling”, Majlesi Journal of Electrical Engineering, Vol. 9, No. 3, Sept. 2015.
 N. Farhangi, S. Ghofrani, “Using bayesshrink, Bishrink, Weighted bayesshrink, and weighted bishrink in NSST and SWT for despeckling SAR images”, EURASIP Journal on Image and Video Processing, DOI 10.1186/s13640-018-0244-3, pp. 1- 18, Dec. 2018.
 Z. De-xiang, W. Xiao-pei, G. Qing-wei, G. Xiao-jing, "SAR image despeckling via bivariate shrinkage based on contourlet transform", IEEE International Symposium on Computational Intelligence and Design, vol. 2, pp. 12-15, China, Oct. 2008.
 Q. Guo, S. Yu, X. Chen, C. Liu, W. Wei, "Shearlet-based image denoising using bivariate shrinkage with intra-band and opposite orientation dependencies", IEEE International Joint Conference on Computational Sciences and Optimization, Vol. 1, pp. 863-866, China, April 2009.
 I.W. Selesnick, “Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency”, IEEE Trans. on Signal Processing, Vol. 50, No. 11, pp. 2744-2756, Nov. 2002.
 D.-X. Zhang, Q.-W. Gao, X.-P. Wu, “Bayesian based speckle suppression for SAR image using contourlet transform”, Journal of Electronic Science and Technology of China, Vol. 6, No. 1, pp. 79-82, Jan. 2008.
 F. Lenzen, “Statistical regularization and denoising”, Chapter 1, 2006.
 A. Hyvärinen, “Sparse code shrinkage: Denoising of nongaussian data by maximum likelihood estimation”, Neural Computation, Vol. 11, No. 7, pp. 1739-1768, Oct. 1999.
 S. Xing, Q. Xu, D. Ma, “Speckle denoising based on bivariate shrinkage functions and dual-tree complex wavelet transform”, Int. Arch. Photogrammetry Remote Sens. Spatial Inform. Sci, Vol. 38, pp. 1-57, 2008.
 H. Cao, W. Tian, C. Deng, "Shearlet-based image denoising using bivariate model", IEEE International Conference on Progress in Informatics and Computing, Vol. 2, pp. 819-821, China, Dec. 2010.
 D. Min, Z. Jiuwen, M. Yide, “Image denoising via bivariate shrinkage function based on a new structure of dual contourlet transform”, Signal Processing, Vol. 109, pp. 25-37, April 2015.
 M. Alioghli Fazel, S. Homayouni, V. Akbari, M. Mahdian Pari, "Speckle reduction of SAR images using curvelet and wavelet transforms based on spatial features characteristics", Proceeding of the IEEE/IGARSS, pp. 2148-2151, Germany, July 2012.
 S. Yin, L. Cao, Y. Ling, G. Jin, “Image denoising with anisotropic bivariate shrinkage”, Signal Processing, Vol. 91, No. 8, pp. 2078-2090, Aug. 2011.
 Z. Wang, A.C. Bovik, H.R. Sheikh, E.P. Simoncelli, “Image quality assessment: from error visibility to structural similarity”, IEEE Trans. on Image Processing, Vol. 13, No. 4, pp. 600-612, April 2004.
 S. Jafari, S. Ghofrani, "Using two coefficients modeling of nonsubsampled shearlet transform for despeckling", Journal of Applied Remote Sensing, Vol. 10, No. 1, pp. 18-32, Jan. 2016.
 J. Zhang, T.M. Le, S. Ong, T.Q. Nguyen, “No-reference image quality assessment using structural activity”, Signal Processing, Vol. 91, No. 11, pp. 2575-2588, Nov. 2011.