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结合双树复小波的平移不变性、多分辨率性和剪切波变换的灵活可选的多方向性,提出一种新的图像表达方法——复Shearlet变换。针对合成孔径雷达(Synthetic Aperture Radar,SAR)图像的相干噪声特点,建立了复Shearlet系数域的高斯混合模型(Gaussian Mixture Model,GSM),在此基础上应用贝叶斯最小二乘法进行系数估计,最后进行复Shearlet反变换得到去噪以后的SAR图像。仿真结果和分析表明:本文提出的算法相比其他变换域去噪算法,不仅去噪后的图像的峰值信噪比(Peak Signal to Noise Ratio,PSNR)有所提高,而且去噪后的图像更平滑,且与Shearlet域高斯混合模型相比,本文算法速度快了两倍多。
Combining with the translatory invariance, multi-resolution and shear-wave transforms of the double tree complex wavelet, we propose a new image representation method called complex Shearlet transform. Aiming at the characteristics of coherent noise of synthetic aperture radar (SAR) image, a Gaussian Mixture Model (GSM) with complex Shearlet coefficients is established. Based on this, a Bayesian least square method is used to estimate the coefficients. Finally, the complex Shearlet inverse transform to get the SAR image after denoising. The simulation results and analysis show that compared with other transform domain denoising algorithms, the proposed algorithm not only improves the PSNR of the de-noised image, but also improves the de-noised image Smooth, and compared with the Shearlet-Gaussian mixture model, the proposed algorithm is more than twice as fast.