Derivative-orthogonal non-uniform B-Spline wavelets

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.

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Maximum Vanishing Moment of Compactly Supported B-spline Wavelets

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2019/v3i330095 ◽

2019 ◽

pp. 1-8

Author(s):

Kanchan Lata Gupta ◽

B. Kunwar ◽

V. K. Singh

Keyword(s):

Scaling Function ◽

Simple Procedure ◽

Smoothness Property ◽

Vanishing Moments ◽

B Spline ◽

B Splines ◽

Compactly Supported ◽

Spline Wavelets ◽

Vanishing Moment ◽

Rule Order

Spline function is of very great interest in field of wavelets due to its compactness and smoothness property. As splines have specific formulae in both time and frequency domain, it greatly facilitates their manipulation. We have given a simple procedure to generate compactly supported orthogonal scaling function for higher order B-splines in our previous work. Here we determine the maximum vanishing moments of the formed spline wavelet as established by the new refinable function using sum rule order method.

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A Practice of Data Smoothing by B-spline Wavelets

Wavelets: Theory, Algorithms, and Applications - Wavelet Analysis and Its Applications ◽

10.1016/b978-0-08-052084-1.50014-4 ◽

1994 ◽

pp. 179-196 ◽

Cited By ~ 5

Author(s):

Susumu Sakakibara

Keyword(s):

Data Smoothing ◽

B Spline ◽

Spline Wavelets

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Image Denoising Using Fractional B-Spline Wavelets Thresholding

Acta Optica Sinica ◽

10.3788/aos20092904.0907 ◽

2009 ◽

Vol 29 (4) ◽

pp. 907-913 ◽

Cited By ~ 2

Author(s):

张大奇 Zhang Daqi ◽

曲仕茹 Qu Shiru ◽

李卫斌 Li Weibin ◽

何力 He Li

Keyword(s):

Image Denoising ◽

B Spline ◽

Spline Wavelets

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Convergence of approximate solution of mixed Hammerstein type integral equations

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v38i2.38043 ◽

2018 ◽

Vol 38 (2) ◽

pp. 61-74

Author(s):

Monireh Nosrati Sahlan

Keyword(s):

Galerkin Method ◽

Integral Equations ◽

Basis Functions ◽

Computational Method ◽

Operational Matrices ◽

B Spline ◽

Spline Wavelets ◽

Type Integral ◽

The Galerkin Method ◽

Dual Functions

In the present paper, a computational method for solving nonlinear Volterra-Fredholm Hammerestein integral equations is proposed by using compactly supported semiorthogonal cubic B-spline wavelets as basis functions. Dual functions and Operational matrices of B-spline wavelets via Galerkin method are utilized to reduce the computation of integral equations to some algebraic system, where in the Galerkin method dual of B-spline wavelets are applied as weighting functions. The method is computationally attractive, and applications are demonstrated through illustrative examples.

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