New results of phase shifting in the wavelet space

This paper investigates the relationship between even-phase coefficients and odd-phase coefficients in a two-channel perfect reconstruction filter bank. We demonstrate that they are linked to each other by a unique phase-shifting matrix. In the case of multilevel wavelet decomposition, we present an efficient recursive solution to directly perform phase shifting in the wavelet space. Our proposed solution can also be easily generalized into the case of two-dimensional wavelet transform. Direct phase-shifting methods in the wavelet space have potential applications in wavelet-based image/video coding and compressed domain processing.