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. The RBIWs 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 the coding gain. Finally, numerical results demonstrate the effectiveness of the proposed methods.
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