Non-Redundant, Directionally Selective, Complex Wavelets

Poor directional selectivity, a major disadvantage of the 2D separable discrete wavelet transform (DWT), has heretofore been circumvented either by using highly redundant, nonseparable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees. In this paper, we demonstrate that superior directional selectivity may be obtained with no redundancy in any separable wavelet transform. We achieve this by projecting the wavelet transform coe cients onto the Softy space of signals and decimating before processing. A novel reconstruction step guarantees perfect reconstruction within this critically-sampled framework.