非抽样轮廓波变换构造及其在图像去噪中的应用

提出了一种由非抽样塔式分解和非抽样方向滤波器组实现的具有平移不变性的非抽样轮廓波变换，文中利用McClellan变换设计非抽样塔式分解中的满足精确重构条件的圆对称滤波器组。非抽样轮廓波变换具有与视皮层变换相似的频带划分，符合人眼视觉特性。利用非抽样轮廓波变换系数的局部高斯模型及最大后验概率法对图像去噪，其峰值信噪比和视觉效果均有较大改善。

The Undecimated Contourlet Transform and Its Application on Image Denoising

The translation-invariant undecimated contourlet transform implemented by undecimated pyramidal decomposition and undecimated directional filter bank is proposed.The circular symmetric filter bank satisfying perfect reconstruction conditions in the undecimated pyramidal decomposition is designed by McClellan transform.The undecimated contourlet transform conforms well to the human visual system and its frequency plane partition resembles cortex transform.Experiments on image denoising using local Gaussian model and MAP estimator in the undecimated contourlet domain show that the undecimated contourlet transform outperforms the contourlet transform both in peak signal-to-noise ratio and visual quality.