针对 Contourlet变换中存在的频谱混叠现象, 采用了基于抗混叠轮廓波变换的算法进行图像超分辨率重建。该算法首先用抗混叠塔式滤波器组替换掉 Contourlet变换中的拉普拉斯塔式变换, 对图像进行尺度变换; 然后, 根据尺度变换后不同尺度的高频子带之间的相似性, 对相关高频分量用双三次插值做高频外推相似变换, 再通过方向滤波器组以及最后的反变换得到比原始图像分辨率更高的插值图像。实验结果表明, 与运用普通 Contourlet变换的算法相比, 该算法避免了由于频谱混叠而带来的图像细节部分的扭曲和模糊, 具有更高的信噪比, 图像重建效果更好。

A major drawback of the Contourlet transform is frequency aliasing, which makes the basis images not localized in its frequency domain. A new algorithm is designed based on non-aliasing Contourlet after we analyze the cause of frequency aliasing. It is used to reconstruct a super-resolution image. First, an anti-aliasing pyramid is used by the new algorithm instead of the Laplacian pyramid. Then, the bi-cubic interpolation is used to do similar transformation in the high frequency domains, according to the similarity among the high frequency domains with different scales and different directions. At last, a higher-resolution image is obtained by inverse transform. Experimental results show the algorithm can get higher PSNR and better image reconstruction effect. It also avoids the distortion and blur caused by frequency aliasing compared with the algorithm based on the traditional Contourlet.