Dual-tree Complex Wavelet Transform and It''s Application to Directional Filtering of Image
二元树复小波变换及其在图象方向滤波中的应用

Complex wavelets can provide both shift invariance and good directional selectivity, which are lack in the traditional wavelet transform, but can not satisfy the condition of perfect reconstruction. Dual tree complex wavelet transform (DTCWT), which employs a dual tree of wavelet filters to obtain the real and imaginary parts of complex wavelet coefficients, can solve this problem. In this paper, the principle of DTCWT is discussed, and the directional characteristics of the twelve high frequency sub bands after DTCWT are studied. Based on the good directional characteristics of DTCWT, we propose a directional filtering method for enhancement of curve like texture images. Image filtering by using this method, the information of the local main direction in each sub band of wavelet transform domain is reserved, and the noise distributed in other directions is removed. This method is proven to be not only less complex, since it avoids the frequency and statistical estimations on characteristics of both the signal and noise, but also on better directional selectivity than real wavelet transform. The experimental results on texture image enhancement demonstrate that this method is more efficient and also more suitable for complicated textures images.