Geodesic
Wavelets with composite dilations
Guo, Kanghui 1   ; Labate, Demetrio 2   ; Lim, Wang-Q 3   ; Weiss, Guido 3   ; Wilson, Edward 3
1 Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
2 Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
3 Department of Mathematics, Washington University, St. Louis, Missouri 63130
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 78-87 Cet article a éte moissonné depuis la source American Mathematical Society

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A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for $L^2({\mathbb R}^n)$ under the action of lattice translations and dilations by products of elements drawn from non-commuting matrix sets $A$ and $B$. Typically, the members of $B$ are shear matrices (all eigenvalues are one), while the members of $A$ are matrices expanding or contracting on a proper subspace of ${\mathbb R}^n$. These wavelets are of interest in applications because of their tendency to produce “long, narrow” window functions well suited to edge detection. In this paper, we discuss the remarkable extent to which the theory of wavelets with composite dilations parallels the theory of classical wavelets, and present several examples of such systems.
DOI : 10.1090/S1079-6762-04-00132-5

Guo, Kanghui  1   ; Labate, Demetrio  2   ; Lim, Wang-Q  3   ; Weiss, Guido  3   ; Wilson, Edward  3

1 Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
2 Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695
3 Department of Mathematics, Washington University, St. Louis, Missouri 63130 
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Guo, Kanghui; Labate, Demetrio; Lim, Wang-Q; Weiss, Guido; Wilson, Edward. Wavelets with composite dilations. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 78-87. doi: 10.1090/S1079-6762-04-00132-5

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