The near shift-invariance of the dual-tree complex wavelet transform revisited

The dual-tree complex wavelet transform (DT-CWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and image processing. This paper presents a quantitative proof of the superiority of the DT-CWT over the DWT in case of modulated wavelets.