International journal of wavelets multiresolution and information processing vol:6 issue:4 pages:521-539
This paper constructs a class of semi-orthogonal and bi-orthogonal wavelet transforms on possibly irregular point sets with the property that the scaling coefficients are independent from the order of refinement. That means that scaling coefficients at a given scale can be constructed with the configuration at that scale only. This property is of particular interest when the refinement operation is data dependent, leading to adaptive multiresolution analyses. Moreover, the proposed class of wavelet transforms are constructed using a sequence of just two lifting steps, one of which contains a linear interpolating prediction operator. This operator easily allows extensions towards directional offsets from predictions, leading to an edge-adaptive nonlinear multiscale decomposition.