Recursive biorthogonal interpolating wavelets and signal-adapted interpolating filter banks

In this paper, by combining the ideas of the recursive wavelets with second-generation wavelets, a family of recursive biorthogonal interpolating wavelets (RBIWs) is developed. RBIW’s have simple shape parameter vectors on each level, which allows a multichannel decomposition algorithm and provides a flexible structure for designing signal-adapted interpolating filter banks. In the single-level case, an efficient approach to design an optimum two-channel biorthogonal interpolating filter bank is proposed, which maximizes the coding gain under the traditional quantization noise assumption. Furthermore, in the multilevel case, using level-wise optimization of the shape parameter vectors, signal-adapted tree-structured recursive biorthogonal interpolating filter banks (RBIFBs) are designed, which are efficient in computation and can remarkedly improve coding gain. Finally, numerical results demonstrate the effectiveness of the proposed methods.