基于可控金字塔的轮廓波变换构造及其应用

针对轮廓波变换存在频谱混淆现象等缺陷,利用满足精确重构条件的可控塔式分解替代轮廓波变换中的拉普拉斯分解,提出一种由非抽样可控金字塔和方向滤波器组实现的可控金字塔轮廓波变换SPCT(Steerable Pyramid Contourlet Transform).在该变换中,可控金字塔将图像分解为多个不同分辨率的细节子带和一个低频子带,方向滤波器组再将各细节子带分解为方向子带.该变换去掉了可控金字塔的抽样环节,方向分解具有高度灵活性,因而具有平移不变性.利用可控金字塔轮廓波变换SPCT 对Lena图像进行自适应图像去噪,并与基于小波变换和轮廓波变换的去噪算法进行比较.实验结果表明,利用本文提出的算法能有效地抑制频谱混淆现象,并且更有效地保持了细节和纹理,其峰值信噪比和视觉效果均有较大改善.

Construction of Contourlet Transform Based on Steerable Pyramid and Its Application

In order to overcome the frequency spectrum aliasing limitation,the Steerable Pyramid Contourlet Transform(SPCT) is proposed based on the nonsubsampled steerable pyramid and directional filter band. The Laplacian pyramid in the contourlet transform is replaced with the steerable pyramid which satisfies perfect reconstruction conditions. The steerable pyramid decomposes an image into multi-resolution detail subbands and one low-frequency subband ,and the detail subbands are decomposed into directional subbands by the directional filter bank. The nonsubsampled steerable pyramid has no downsampling or upsampling,and hence it is shift-invariant. Denoising Lena images using adaptive thresholding show that the proposed algorithm can efficiently suppress frequency spectrum aliasing and preserve detailed information and textures of the original image. Compared with the denoising algorithm based on the wavelet transform and contourlet transform,the proposed algorithm improves both the peak signal-to-noise ratio and visual quality significantly.