A Construction Method of Interpolatory Wavelet Based on Scaling Function

In classical wavelet sampling theory, interpolatory wavelets are constructed by using orthogonal wavelets. Since the analytic expressions of orthogonal wavelets are usually complex or unavailable, interpolatory wavelet construction has become an important topic in signal processing and harmonic analysis. In this paper, a new method is proposed to construct interpolating wavelets from scaling functions. Since this method has avoided using orthogonal wavelets in construction of interpolation wavelets, it can greatly improve efficiency of interpolating wavelet construction. Taking Daubechies and Coiflets MRAs as examples, our method is verified to be effective for interpolatory wavelet construction.