Construction of symmetric tight wavelet frames from quasi-interpolatory subdivision masks and their applications

Abstract

This paper presents tight wavelet frames with two compactly supported symmetric generators of more than one vanishing moments in the Unitary Extension Principle. We determine all possible free tension parameters of the quasi-interpolatory subdivision masks whose corresponding refinable functions guarantee our wavelet frame. In order to reduce shift variance of the standard discrete wavelet transform, we use the three times oversampling filter bank and eventually obtain a ternary ( low, middle, high) frequency scale. In applications to signal/ image denoising and erasure recovery, the results demonstrate reduced shift variance and better performance of our wavelet frame than the usual wavelet systems such as Daubechies wavelets.