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In this paper a new method of speckle reduction of SAR images in curvelet domain is proposed. In the method, curvelet transform is integrated with wavelet filtering. The new method consists of five parts: preprocessing, curvelet transform (CT), curvelet coefficients processing and two inverse transforms. In the preprocessing step, homomorphic transform is applied to convert multiplicative noise in SAR images to an additive noise which is suitable to be dealt with curvelets. After curvelet transform, curvelet coefficients are thresholded by using soft and hard thresholding functions with improved rules. In hard thresholding rule, noise variations are obtained by using noise parameter estimation. In soft thresholding rule, a classic soft thresholding function and thresholding rule used in wavelet domain is combined with curvelets. Finally, inverse CT and exponential transform are employed to reconstruct denoising image. Comparisons of speckle removing results by using different thresholding methods are also given in this paper. It can be seen that the method presented in the paper is an effective one.