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References (47)
-
N. Schepper (2009)
The Generalized Clifford-Gegenbauer Polynomials RevisitedAdvances in Applied Clifford Algebras, 19
-
P. Carré, M. Berthier (2013)
Color Representation and Processes with Clifford Algebra -
F. Brackx, N. Schepper, F. Sommen (2009)
The Fourier transform in Clifford analysisAdvances in Imaging and Electron Physics, 156
-
J. Stratton (1935)
Spheroidal Functions.Proceedings of the National Academy of Sciences of the United States of America, 21 1
-
E. Levin, D. Lubinsky (2005)
Orthogonal polynomials for exponential weights x2rhoe-2Q(x) on [0, d)J. Approx. Theory, 134
-
M. Heydari, M. Hooshmandasl, C. Cattani, Ming Li (2013)
Legendre Wavelets Method for Solving Fractional Population Growth Model in a Closed SystemMathematical Problems in Engineering, 2013
-
J. Morais, K. Kou, W. Sprößig (2013)
Generalized holomorphic Szegö kernel in 3D spheroidsComput. Math. Appl., 65
-
C. Cattani (2012)
Signorini Cylindrical Waves and Shannon WaveletsAdv. Numer. Anal., 2012
-
J. Antoine, P. Vandergheynst, R. Murenzi (1996)
Two-dimensional directional wavelets in image processingInt. J. Imaging Syst. Technol., 7
-
Sabrine Arfaoui, I. Rezgui, A. Mabrouk (2017)
Wavelet Analysis on the Sphere: Spheroidal Wavelets -
D. Pe (2008)
Cauchy-Kowalevski extensions, Fueter's theorems and boundary values of special systems in Clifford analysis -
F. Brackx, N. Schepper, F. Sommen (2006)
The Two-Dimensional Clifford-Fourier TransformJournal of Mathematical Imaging and Vision, 26
-
R. Abreu‐Blaya, J. Bory‐Reyes, P. Bosch (2010)
Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal DomainsBoundary Value Problems, 2010
-
M. Heydari, M. Hooshmandasl, A. Shakiba, C. Cattani (2016)
Legendre wavelets Galerkin method for solving nonlinear stochastic integral equationsNonlinear Dynamics, 85
-
F. Brackx, F. Sommen (2001)
The generalized clifford-hermite continuous wavelet transformAdvances in Applied Clifford Algebras, 11
-
F. Brackx, N. Schepper, F. Sommen (2006)
Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision -
Sabrine Arfaoui, A. Mabrouk (2017)
Some Ultraspheroidal Monogenic Clifford Gegenbauer Jacobi Polynomials and Associated WaveletsAdvances in Applied Clifford Algebras, 27
-
E. Hitzer (2014)
New Developments in Clifford Fourier TransformsviXra
-
E. Stein, G. Weiss (1971)
Introduction to Fourier Analysis on Euclidean Spaces. -
R. Bujack, H. Bie, N. Schepper, G. Scheuermann (2013)
Convolution Products for Hypercomplex Fourier TransformsJournal of Mathematical Imaging and Vision, 48
-
K. Sau, R. Basak, A. Chanda (2013)
Image Compression based on Block Truncation Coding Using Clifford AlgebraProcedia Technology, 10
-
Mohamed Mousa (2007)
Calcul efficace et direct des représentations de maillage 3D utilisant les harmoniques sphériques -
D. Ville, D. Sage, Katarina Balac, M. Unser (2008)
The Marr wavelet pyramid and multiscale directional image analysis2008 16th European Signal Processing Conference
-
Volodymyr Kindratenko (2003)
On Using Functions to Describe the ShapeJournal of Mathematical Imaging and Vision, 18
-
H. Bie (2012)
Clifford algebras, Fourier transforms and quantum mechanicsarXiv: Mathematical Physics
-
F. Brackx, N. Schepper, F. Sommen (2006)
Clifford-Jacobi Polynomials and the Associated Continuous Wavelet Transform in Euclidean Space -
F. Colombo, I. Sabadini, F. Sommen, D. Struppa (2004)
Analysis of Dirac Systems and Computational Algebra -
F. Brackx, F. Sommen (2000)
Clifford-hermite wavelets in euclidean spaceJournal of Fourier Analysis and Applications, 6
-
(2017)
New monogenic Gegenbauer Jacobi polynomials and associated spheroidal wavelets. Doctoral Thesis in Mathematics, University of Monastir, Tunisia -
(2014)
Clifford algebra: a visual introduction -
H. Bie, Yuan Xu (2010)
On the Clifford-Fourier transformarXiv: Classical Analysis and ODEs
-
Lewei Li, X. Kang, M. Leong (2001)
Spheroidal Wave Functions in Electromagnetic Theory -
A. Osipov, V. Rokhlin, Hong Xiao (2013)
Prolate Spheroidal Wave Functions of Order Zero -
J. Saillard, G. Bunel (1989)
Apport des fonctions spheroidales pour l'estimation des paramètres d'une cible radar. -
C. Cattani, A. Kudreyko (2010)
Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kindAppl. Math. Comput., 215
-
F. Brackx, Nele †, Frank ‡ (2004)
The Clifford–Gegenbauer polynomials and the associated continuous wavelet transformIntegral Transforms and Special Functions, 15
-
A. Osipov, V. Rokhlin, Hong Xiao (2013)
Prolate Spheroidal Wave Functions of Order Zero: Mathematical Tools for Bandlimited Approximation -
V. Michel (2013)
Lectures on Constructive Approximation -
Bo Yang, T. Suk, M. Dai, J. Flusser (2014)
2D and 3D Image Analysis by Gaussian-Hermite Moments -
Rong Liu, Y. Shi (2012)
The Zeros of Orthogonal Polynomials for Jacobi-Exponential WeightsAbstract and Applied Analysis, 2012
-
F. Brackx, N. Schepper, F. Sommen (2004)
The Clifford-Laguerre Continuous Wavelet TransformBulletin of The Belgian Mathematical Society-simon Stevin, 11
-
Sabrine Arfaoui, A. Mabrouk (2017)
Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal WaveletsAnalysis in Theory and Applications
-
R. Delanghe (2001)
Clifford Analysis: History and PerspectiveComputational Methods and Function Theory, 1
-
M. Abramowitz, I. Stegun, David Miller (1965)
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Journal of Applied Mechanics, 32
-
W. Thompson (1999)
Spheroidal wave functionsComput. Sci. Eng., 1
-
Dayron Rizo-Rodriguez, Heydi Vazquez, Edel Reyes (2012)
Illumination Invariant Face Recognition Using Quaternion-Based Correlation FiltersJournal of Mathematical Imaging and Vision, 45
-
Sabrine Arfaoui, A. Mabrouk (2018)
Some Old Orthogonal Polynomials Revisited and Associated Wavelets: Two-Parameters Clifford-Jacobi Polynomials and Associated Spheroidal WaveletsActa Applicandae Mathematicae, 155
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Nature B.V. 2020
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-020-00322-0
- Publisher site
- See Article on Publisher Site
Abstract
Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically, this needs suitable functional bases that are easy to implement by the next. It holds that Clifford wavelets are main tools to achieve this necessity. In the present paper we intend to develop some new classes of Clifford wavelet functions. Some classes of new monogenic polynomials are developed firstly from monogenic extensions of 2-parameters Clifford weights. Such classes englobe the well known Jacobi, Gegenbauer and Hermite ones. The constructed polynomials are next applied to develop new Clifford wavelets. Reconstruction and Fourier-Plancherel formulae have been proved. Finally, computational examples are developed provided with graphical illustrations of the Clifford mother wavelets in some cases. Some graphical illustrations of the constructed wavelets have been provided and finally concrete applications in biofields have been developed dealing with EEG/ECG and Brain image processing.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 10, 2020