Comments on "Phase-Shifting for Nonseparable
Haar Wavelets, Yiannis Andreopoulos · 2009
In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D nonsepa- rable Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can be per- formed using previously-proposed phase-shifting approaches that utilize the overcomplete DWT (ODWT), if the given image translation is mapped to the phase component and in-band position within the ODWT. Index Terms—Image translation, overcomplete discrete wavelet trans- forms (ODWTs), phase-shifting.