Design of multidimensional non-separable regular filter banks and wavelets

The design of multidimensional nonseparable wavelets based on iterated filter banks is investigated. To obtain regularity of the wavelet, a maximum number of zeros is put at aliasing frequencies in the lowpass filter. Two approaches are pursued. A direct method designs nonseparable perfect reconstruction filter banks based on cascade structures and with prescribed zeros both analytically (small cases) and numerically (larger cases). A second, indirect method maps biorthogonal one-dimensional banks with high regularity into multidimensional banks using the McClellan transformation. A number of properties relevant to perfect reconstruction and zero locations are shown in this case. Design examples are given in all cases, and the testing of regularity is discussed, together with a fast algorithm to compute iterated filters.