中文摘要：

针对Contourlet变换基图像不具备局部频率特性的缺点,分析了在频域楔形支撑区域外部出现潜在混叠的原因,并结合易操纵金字塔结构的优良特性,提出一种改进结构的Contourlet变换.该变换采用易操纵金字塔替换了原变换的拉普拉斯金字塔,保证了其平移不变性.非线性逼近实验和基图像分析的结果表明,该变换能够稀疏表示图像,避免了频域出现混叠.去噪实验结果表明,改进结构的Contourlet变换可以有效地提高去噪图像的峰值信噪比和去噪图像质量.

英文摘要：

A major drawback of the Contourlet transform is that its basis images are not localized in the frequency domain. After analyzing the cause of frequency domain aliasing and many fine properties of the steerable pyramid, an improved Contourlet transform is proposed to overcome this problem. The proposed transform employs the steerable pyramid instead of the Laplacian pyramid to complete multiscale decomposition, which makes the transform shift invariant. By doing nonlinear approximation experiment and an analysis of the basis images, it is concluded that this transform can sparsely express images and avoid frequency domain aliasing. Our image denoising experimental results show that the proposed transform outperforms the original Contourlet transform in terms of both the peak signal noise rate （PSNR） and the visual quality.