圆对称轮廓波变换的构造

Construction of the Circular Symmetric Contourlet Transform

提出了具有类似于视皮层变换频带划分的圆对称轮廓波变换.在该变换中,圆对称滤波器组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.文中利用遗传算法设计满足重构要求的圆对称滤波器组,应用伯恩斯坦多项式设计的映射函数将9/7双正交滤波器组映射为扇形滤波器组.利用自适应阈值法对Lena图像去噪的实验结果表明,两种圆对称轮廓波变换(CSCT1和CSCT2)的去噪性能与轮廓波变换相比有显著提高.

The contourlet transform is a novel multiscale geometric analysis method. It can represent geometric features such as edges and texture more effectively than wavelet transform. In this paper, the circular symmetric contourlet transform （CSCT） which has similar frequency partition with cortex transform is proposed. In the CSCT, the circular symmetric filter banks decomposes image into multi-resolution detail subbands and one low-frequency subband, and the detail subbands are decomposed into directional subbands by directional filter bank. The circular symmetric filter bank satisfying reconstruction conditions is designed by genetic algorithm. The 9/7 biorthogonal filter bank is mapped to fan filter bank by the mapping function which derived from the Bernstein polynomial. Denoising experiments for Lena image using adaptive thresholding show that the denoising performance of the CSCT1 and CSCT2 outperform the contourlet transform significantly.