New image transforms using hybrid wavelets and directional filter banks: analysis and design

We propose a new family of perfect reconstruction, non-redundant, and multiresolution geometrical image transforms using the wavelet transform in conjunction with modified versions of directional filter banks (DFB). In the proposed versions of DFB, we use either horizontal or vertical directional decomposition. Taking advantage of the wavelet transform that has efficient nonlinear approximation property, we add the important feature of directionality by applying the modified and regular DFB to the subbands of a few finest wavelet levels. This way we can eliminate a major portion of the artifacts usually introduced when DFB are used. The proposed hybrid wavelets and DFB (HWD) transform family provides visual and PSNR improvements over the wavelet and contourlet transforms.