Study On The Construction Of Two-dimension Non-separable Wavelets

In this paper, we give a general formula of scaling filter with order k vanishing moments using the properties of the sampling in multiple dimensions and the sufficient and necessary conditions that filters possess order k vanishing moments. Basing on the principle that the separable polyphase components can be converted to non-separable filter after non-separable upsampling which hold the orthogonality and order k vanishing moments, a approach that non-separable wavelet function can be constructed by separable filter is provided. In the case of giving the sampling matrixes, we construct two non-separable compactly supported orthogonal filters, and discuss the continuity of the scaling functions which is got by iterating them. Furthermore, the Lawton condition for orthogonality is generalized to the two-dimensions case.