Construction of symmetric orthogonal bases of wavelets and tight wavelet frames with integer dilation factor. (English) Zbl 1066.42026
Summary: Our goal is to present a systematic algorithm for constructing (anti)symmetric tight wavelet frames and orthonormal wavelet bases generated by a given refinable function with an integer dilation factor \(d\geqslant2\). Special attention is paid to the issues of the minimality of a number of framelet generators and the size of generator supports. In particular, our algorithm allows to reduce the computational costs approximately by a factor 2.
MSC:
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
| 42C15 | General harmonic expansions, frames |
Keywords:
orthonormal wavelet bases; tight wavelet frames; explicit construction; symmetric wavelets; antisymmetric wavelets; algorithm; framelet generatorsReferences:
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