Nonseparable orthogonal multiwavelets with two and three vanishing moments on the quincunx grid
Ana Ruedin · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1999
Multiwavelets in one dimension have given good results for image compression. On the other hand, nonseparable bidimensional wavelets have certain advantages over the tensor product of 1D wavelets. In this work we give examples of multiwavelets that are bidimensional and nonseparable. They correspond to the dilation matrices D1 equals [1 1;1 -1], a reflection followed by an expansion of (root)2, or to D2 equals [1 1;1 1], a rotation followed by an expansion of (root)2, and possess suitable properties for image compression: short support and 2 or 3 vanishing moments. Multiwavelets are derived from multiscaling functions. Conditions on the matrix coefficients of the dilation equation are exploited to build examples of orthogonal, nonseparable, compactly supported, bidimensional multiscaling functions of accuracy 2 and 3. They are continuous and the joint spectral radius is estimated. To the author's knowledge no examples of bidimensional multiscaling functions with these characteristics had been found previously. Coefficients for the corresponding multiwavelets are given. Multiscaling functions and multiwavelets are plotted with a cascade algorithm.