Wavelets with Composite Dilations
نویسنده
چکیده
A wavelet with composite dilations is a function generating an orthonormal basis or a Parseval frame for L2(Rn) 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 Rn. 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.
منابع مشابه
Chapter 1 Continuous and discrete reproducing systems that arise from translations . Theory and applications of composite wavelets
Reproducing systems of functions such as the wavelet and Gabor systems have been particularly successful in a variety of applications from both mathematics and engineering. In this chapter, we review a number of recent results in the study of such systems and their generalizations developed by the authors and their collaborators. We first describe the unified theory of reproducing systems. This...
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