# Clifford algebra Cl3,0-valued wavelet tranformation, clifford wavelet uncertainty inequality and clifford gabor wavelets
> Bahri M.

URL kanonis: https://discover.unhas.ac.id/publications/pub_scopus_36049051429
Jurnal / Konferensi: International Journal of Wavelets Multiresolution and Information Processing
Tahun terbit: 2017
DOI: https://doi.org/10.1142/S0219691307002166
ISSN: 02196913
Kuartil SJR: Q3
Citations: 34

## Authors
- Bahri M.

## Abstract
In this paper, it is shown how continuous Clifford Cl 3,0 -valued admissible wavelets can be constructed using the similitude group SIM(3), a subgroup of the affine group of ℝ 3 . We express the admissibility condition in terms of a Cl 3,0 Clifford Fourier transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform of multivector functions. We invent a generalized Clifford wavelet uncertainty principle. For scalar admissibility constant, it sets bounds of accuracy in multivector wavelet signal and image processing. As concrete example, we introduce multivector Clifford Gabor wavelets, and describe important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gabor wavelets.

## Keywords
- Multivector
- Gabor wavelet
- Mathematics
- Wavelet
- Clifford algebra
- Gabor transform
- Clifford analysis
- Discrete wavelet transform
- Wavelet transform
- Pure mathematics
- Algebra over a field
- Mathematical analysis
- Time–frequency analysis
- Artificial intelligence
- Computer science
- Subalgebra
- Computer vision
- Filter (signal processing)
- Dirac operator
- Division algebra

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Sumber: Discover Unhas — RIMS Universitas Hasanuddin.
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