A New Construction Method for the Dual Tree Complex Wavelet Based on Direction Sensitivity

The conception of 'main direction' of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis (MRA) of L2(R2). Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods are given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.

The conception of ＂main direction＂ of multi-dimensional wavelet is established in this paper, and the capabilities of several classical complex wavelets for representing directional singularities are investigated based on their main directions. It is proved to be impossible to represent directional singularities optimally by a multi-resolution analysis （MRA） of L^2（R^2）. Based on the above results, a new algorithm to construct Q-shift dual tree complex wavelet is proposed. By optimizing the main direction of parameterized wavelet filters, the difficulty in choosing stop-band frequency is overcome and the performances of the designed wavelet are improved too. Furthermore, results of image enhancement by various multi-scale methods arc given, which show that the new designed Q-shift complex wavelet do offer significant improvement over the conventionally used wavelets. Direction sensitivity is an important index to the performance of 2D wavelets.