Clifford Wavelet Transform and the Uncertainty Principle

@article{Banouh2019CliffordWT,
  title={Clifford Wavelet Transform and the Uncertainty Principle},
  author={Hicham Banouh and Anouar Ben Mabrouk and M'hamed Kesri},
  journal={Advances in Applied Clifford Algebras},
  year={2019}
}
In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their proprieties has been conducted. Next, such concepts have been applied to develop an uncertainty principle based on Clifford wavelets. 
View PDF on arXiv
4 Citations
Background Citations
1

4 Citations

Citation Type

Citation Type

A sharp Clifford wavelet Heisenberg-type uncertainty principle
In the present work we are concerned with the development of a new uncertainty principle based on wavelet transform in the Clifford analysis/algebras framework. We precisely derive a sharp…
A wavelet uncertainty principle in quantum calculus
In the present paper, a new uncertainty principle is derived for the generalized q-Bessel wavelet transform studied earlier in [55]. In this paper, an uncertainty principle associated with wavelet…
A Quantum Wavelet Uncertainty Principle
In the present paper, an uncertainty principle is derived in the quantum wavelet framework. Precisely, a new uncertainty principle for the generalized q-Bessel wavelet transform, based on some…
Clifford Valued Shearlet Transform
This paper deals with the construction of $$n=3 \text{ mod } 4$$ n = 3 mod 4 Clifford algebra $$Cl_{n,0}$$ C l n , 0 -valued admissible shearlet transform using the shearlet group $$(\mathbb {R}^* <…

References

SHOWING 1-10 OF 73 REFERENCES
Continuous Wavelet Transform and Uncertainty Principle Related to the Spherical Mean Operator
In this paper, we define and study the continuous wavelet transform associated with the spherical mean operator, we prove Plancherel formula, inversion formula, etc. Next we establish an analogue of…
Clifford Algebra Cl(3,0)-valued Wavelets and Uncertainty Inequality for Clifford Gabor Wavelet Transformation
The purpose of this paper is to construct Clifford algebra Cl(3,0)-valued wavelets using the similitude group SIM(3) and then give a detailed explanation of their properties using the Clifford…
Uncertainty principles for continuous wavelet transforms related to the Riemann–Liouville operator
In this paper we define and study the continuous wavelet transforms associated with the Riemann–Liouville operator, we give nice harmonic analysis results. Next we establish an analogue of…
Heisenberg's and Hardy's Uncertainty Principles in Real Clifford Algebras
Recently, many surveys are devoted to study the Clifford Fourier transform. Dealing with the real Clifford Fourier transform introduced by Hitzer [10], we establish analogues of the classical…
Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl3,0
Abstract.First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier…
The continuous wavelet transform in Clifford analysis
A theory of higher dimensional continuous wavelet transforms in Clifford analysis is presented. The construction of Clifford-Hermite wavelets generates new generalized Hermite polynomials.
Clifford Algebra Cl3, 0-Valued Wavelet Transformation, Clifford Wavelet Uncertainty inequality and Clifford Gabor Wavelets
TLDR
A generalized Clifford wavelet uncertainty principle is invented that sets bounds of accuracy in multivector wavelet signal and image processing and describes important properties such as the Clifford Gabor transform isometry, a reconstruction formula, and an uncertainty principle for Clifford Gbor wavelets.
Two-dimensional quaternion wavelet transform
The Two-Dimensional Clifford-Fourier Transform
TLDR
An in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented, finding a closed form for the integral kernel may be obtained, leading to further properties, both in the L1 and in theL2 context.
Donoho–Stark’s Uncertainty Principles in Real Clifford Algebras
The Clifford Fourier transform (CFT) has been shown to be a powerful tool in the Clifford analysis. In this work, several uncertainty inequalities are established in the real Clifford algebra…
...
...