Abstract: Curvelets can better represent anisotropy for objects with discontinuities along edges, but the curvelet 99 transform involves a complicated index structure which makes the mathematical and quantitative analysis especially delicate, and it uses overlapping windows increasing the redundancy. This paper applies Fast Discrete Curvelet Transform which has the optimal sparse representation. By utilizing Curvelet de-noising algorithm based on translation invariance, better MSE compared with traditional methods can be obtained. Experimental results demonstrate ，compared with MultiVisu，MultiBayes，Wavelet-domain Hidden Markov, this method (CS-FDCT) not only yields de-noised image with highest Peak Signal-to-Noise Ratio values (PSNR=30.8528 with noise variance =25), but also achieves best visual quality.

摘要： 曲波（Curvelet）可以很好的表示含曲线奇异的函数的异向性，但传统的曲波99变换采用复杂的参数结构和重叠的窗口，既不利于数学定量分析，也增加数字实现的冗余。而本文采用快速曲波变换，对物体边缘信息具有最优稀疏表示。通过平移不变的曲波萎缩算法，可获得比传统去噪方法更好的均方误差（MSE）。实验结果表明，与传统的MultiVisu，MultiBayes，WHMT去噪算法比较，本文算法CS-FDCT去噪效果最佳，在噪声方差 =25时，使用该方法的峰值信噪比（PSNR）可高达30.8528，并且去噪后的图像具有最好的视觉效果。