SHIFT-ORTHOGONAL WAVELET BASES

Shift-orthogonal wavelets are a new type of multiresolution wavelet ba ses that are orthogonal with respect to translation (or shifts) within one level but not with respect to dilations across scales. In this pa per, we characterize these wavelets and investigate their main propert ies by considering two general construction methods. In the first appr oach, we start by specifying the analysis and synthesis function space s and obtain the corresponding shift-orthogonal basis functions by sui table orthogonalization. In the second approach, we take the complemen tary view and start from the digital filterbank, We present several il lustrative examples, including a hybrid version of the Battle-Lemarie spline wavelets. We also provide filterbank formulas for the fast wave let algorithm. A shift-orthogonal wavelet transform is closely related to an orthogonal transform that uses the same primary scaling functio n; both transforms have essentially the same approximation properties. One experimentally confirmed benefit of relaxing the interscale ortho gonality requirement is that we can design wavelets that decay faster than their orthogonal counterpart.