Accuracy of lattice translates of several multidimensional refinable functions
Journal of Approximation Theory
Arbitrarily smooth orthogonal nonseparable wavelets in R2
SIAM Journal on Mathematical Analysis
JPEG2000: the upcoming still image compression standard
Pattern Recognition Letters
Construction of nonseparable multiwavelets for nonlinear image compression
EURASIP Journal on Applied Signal Processing
Design of regular nonseparable bidimensional wavelets using Grobnerbasis techniques
IEEE Transactions on Signal Processing
Examples of bivariate nonseparable compactly supported orthonormal continuous wavelets
IEEE Transactions on Image Processing
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
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For nonseparable bidimensional wavelet transforms, the choice of the dilation matrix is all–important, since it governs the downsampling 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.