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. 
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
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}^* <
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

References

SHOWING 1-10 OF 72 REFERENCES
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
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
Uncertainty principles and time frequency analysis related to the Riemann–Liouville operator
We define and study the windowed Fourier transform, called also the Gabor transform, associated with singular partial differential operators defined on the half plane $$]0,+\infty [\times \mathbb
Uncertainty Principle in Terms of Entropy for the Riemann–Liouville Operator
We prove Hausdorff–Young inequality for the Fourier transform connected with Riemann–Liouville operator. We use this inequality to establish the uncertainty principle in terms of entropy. Next, we
Localization operators, time frequency concentration and quantitative-type uncertainty for the continuous wavelet transform associated with spherical mean operator
TLDR
The localization operators for Φh are investigated and it is proved that they are in the Schatten-...
...
...