Non-separable 2D biorthogonal wavelets with two-row filters

In the literature 2D (or bivariate) wavelets are usually constructed as a tensor product of ID wavelets. Such wavelets are called separable. However, there are various applications, e.g. in image processing, for which non-sepaxable 2D wavelets are prefered. In this paper, we investigate the class of compactly supported orthonormal 2D wavelets that was introduced by Belogay and Wang.(2) A characteristic feature of this class of wavelets is that the support of the corresponding filter comprises only two rows. We axe concerned with the biorthogonal extension of this kind of wavelets. It turns out that the 2D wavelets in this class are intimately related to some underlying ID wavelet. We explore this relation in detail, and we explain how the 2D wavelet transforms can be realized by means of a lifting scheme, thus allowing an efficient implementation. We also describe an easy way to construct wavelets with more rows and shorter columns.