Shiftable, projection-based complex wavelet transforms

Shift sensitivity, poor directional selectivity and lack of phase information are three major disadvantages of the discrete wavelet transform, In earlier research, we demonstrated that projection-based complex wavelet transforms have excellent directional selectivity and explicit phase information, In this paper, we discuss the theory of projection-based complex wavelet transforms and we prove that these transforms can have reduced shift sensitivity with low transform redundancy. We also provide experimental results to demonstrate the reduced shift sensitivity of our transforms.