Dilation Matrices for Nonseparable Bidimensional Wavelets

摘要

For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all-important, since it governs the downsam-pling and upsampling steps, determines the cosets that give the positions of the filters, and defines the elementary set that gives a tesselation of the plane. We introduce nonseparable bidimensional wavelets, and give formulae for the analysis and synthesis of images. We analyze several dilation matrices, and show how the wavelet transform operates visually. We also show some distorsions produced by some of these matrices. We show that the requirement of their eigenvalues being greater than 1 in absolute value is not enough to guarantee their suitability for image processing applications, and discuss other conditions.