On the lifting construction of a class of non-separable 2D orthonormal wavelets

In most cases 2D (or bivariate) wavelets are constructed as a tensor product of 1D wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-separable 2D wavelets are preferable. In this paper, we are concerned with the class of compactly supported 2D wavelets that was introduced by Belogay and Wang (1999). A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. As a result, the 2D wavelets in this class are intimately related to some underlying 1D wavelet. We explore this relation in detail, and we explain how the 2D decompositions can be realized by a lifting scheme, and hence allow an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.