中文摘要：

针对Shearlet收缩去噪引入的Gibbs伪影和＂裂痕＂现象,提出一种结合非局部自相似的Shearlet自适应收缩图像去噪方法。首先,对噪声图像进行多方向多尺度的Shearlet分解;然后,基于高斯比例混合（GSM）模型的Shearlet系数分布建模,利用贝叶斯最小二乘估计对Shearlet系数进行自适应收缩去噪,重构得到初始去噪图像;最后,利用非局域自相似模型对初始去噪图像进行滤波处理,得到最终的去噪图像。实验结果表明,所提方法在更好地保留边缘特征的同时,有效地去除噪声和收缩去噪引入的Gibbs伪影,该方法获得的峰值信噪比（PSNR）和结构自相似指标（SSIM）比基于非抽样剪切波变换（NSST）的硬阈值去噪方法提高1.41 d B和0.08;比非抽样Shearlet域GSM模型去噪方法提高1.04 d B和0.045;比基于三变量模型的剪切波去噪方法提高0.64 d B和0.025。

英文摘要：

For the Gibbs artifact and ＂ cracks＂ phenomenon which introduced by the Shearlet shrinkage denoising, a Shearlet adaptive shrinkage and nonlocal self-similarity model-based method for image denoising was proposed in this paper.First, the noisy image was firstly decomposed with multi-scale and multi-orientation by Shearlet transform. Second, based on the modeling of Shearlet coefficients by using Gaussian Scale Mixture（ GSM） model, the image noises were reduced by adaptively approaching Shearlet coefficients with Bayesian least squares estimator, and then, the preliminary denoised image was reconstructed by inverse Shearlet transform. Finally, the preliminary denoised image was further filtered by nonlocal selfsimilarity model, and the final denoised image was produced. The experimental results show that the proposed method can better preserve the edge information. Meanwhile, it can effectively reduce the image noise and Gibbs-like artifacts produced by shrinkage. Compared with Non-Subsampled Shearlet Transform（ NSST）-based image denoising with hard-thresholding, the proposed method improves the Peak-Signal to-Noise-Ratio（ PSNR） and Structural Similarity（ SSIM） by 1. 41 d B and 0. 08respectively; compared with GSM model-based image denoising in the Shearlet domain, the proposed method improves the PSNR and SSIM by 1. 04 d B and 0. 045 respectively; compared with shearlet-based image denoising using trivariate prior model, the proposed method improves the PSNR and SSIM by 0. 64 d B and 0. 025 respectively.