Shearlet是一种新型的多尺度几何分析工具，通过对基本函数缩放、剪切和平移等仿射变换生成具有不同特征的Shearlet函数，能够对图像进行稀疏表示且产生最优逼近。首先提出了一种Shearlet变换的数字实现方法，然后提出了一种结合Shearlet变换和变分法的图像去噪方法。该方法采用Shearlet变换域约束条件的全变差正则化模型，可以去除简单阈值处理后产生的伪吉布斯效应。实验结果表明，该方法在抑噪和保持边缘的同时，取得了好的视觉效果和更高的PSNR值。

Shearlet is a new-style multi-scale geometry analysis tool. It creates Shearlet functions which have different characteristics through zooming, shearing, translating and other affine transforming methods, and enables its capable of optimally sparse representation. Firstly, a digital Shearlet transform implementation method is proposed in this paper. And then, a new de-noising method that combines Shearlet transform and variation is presented, which mainly been established using a total variation regularization model to constraint condition on Shearlet transform domain. The proposed model aims at reducing Pseudo-Gibbs artifacts after simple threshold methods. Numerical examples demonstrate that the method can remove noises and keep edges effectively, leading to improved visual effect and PSNR.