Polychromatic sparse image reconstruction and mass attenuation spectrum estimation via B-spline basis function expansion

2015 ◽  
Author(s):  
Renliang Gu ◽  
Aleksandar Dogandžić
Keyword(s):  
Image Reconstruction ◽  
Basis Function ◽  
Spectrum Estimation ◽  
B Spline ◽  
Function Expansion ◽  
Spline Basis ◽  
Sparse Image Reconstruction ◽  
Mass Attenuation

scholarly journals Parameterization Method on B-Spline Curve

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
H. Haron ◽  
A. Rehman ◽  
D. I. S. Adi ◽  
S. P. Lim ◽  
T. Saba
Keyword(s):  
Computer Model ◽  
Basis Function ◽  
Real Object ◽  
Reconstruction Process ◽  
B Spline ◽  
Parameterization Method ◽  
Spline Basis ◽  
Data Points ◽  
Data Point ◽  
2D And 3D

The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the representation of 2D and 3D primitive entities and parameterization method using B-spline interpolation. However, there is no parameterization method which can handle all types of data points such as collinear data points and large distance of two consecutive data points. Therefore, this paper presents a new parameterization method that is able to solve those drawbacks by visualizing the 2D primitive entity of scanned data point of a real object and construct 3D computer model. The new method has improved a hybrid method by introducing exponential parameterization method in the beginning of the reconstruction process, followed by computing B-spline basis function to find maximum value of the function. The improvement includes solving a linear system of the B-spline basis function using numerical method. Improper selection of the parameterization method may lead to the singularity matrix of the system linear equations. The experimental result on different datasets show that the proposed method performs better in constructing the collinear and two consecutive data points compared to few parameterization methods.

Creating smooth SI. B-spline basis function representations of insulin sensitivity

2018 ◽  
Vol 44 ◽  
pp. 270-278
Author(s):  
Kent W. Stewart ◽  
Christopher G. Pretty ◽  
Geoffrey M. Shaw ◽  
J. Geoffrey Chase
Keyword(s):  
Insulin Sensitivity ◽  
Basis Function ◽  
B Spline ◽  
Spline Basis

Solution of non-linear time fractional telegraph equation with source term using B-spline and Caputo derivative

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdul Majeed ◽  
Mohsin Kamran ◽  
Noreen Asghar
Keyword(s):  
Caputo Derivative ◽  
Numerical Solutions ◽  
Linear Time ◽  
Initial Boundary ◽  
Telegraph Equation ◽  
Test Problems ◽  
Von Neumann ◽  
B Spline ◽  
Nonlinear Part ◽  
Spline Basis

Abstract This article focusses on the implementation of cubic B-spline approach to investigate numerical solutions of inhomogeneous time fractional nonlinear telegraph equation using Caputo derivative. L1 formula is used to discretize the Caputo derivative, while B-spline basis functions are used to interpolate the spatial derivative. For nonlinear part, the existing linearization formula is applied after generalizing it for all positive integers. The algorithm for the simulation is also presented. The efficiency of the proposed scheme is examined on three test problems with different initial boundary conditions. The influence of parameter α on the solution profile for different values is demonstrated graphically and numerically. Moreover, the convergence of the proposed scheme is analyzed and the scheme is proved to be unconditionally stable by von Neumann Fourier formula. To quantify the accuracy of the proposed scheme, error norms are computed and was found to be effective and efficient for nonlinear fractional partial differential equations (FPDEs).

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals LOFAR sparse image reconstruction

2015 ◽  
Vol 575 ◽  
pp. A90 ◽  
Author(s):  
H. Garsden ◽  
J. N. Girard ◽  
J. L. Starck ◽  
S. Corbel ◽  
C. Tasse ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Sparse Image Reconstruction

scholarly journals Quasi Cubic Trigonometric Curve and Surface

2019 ◽  
Author(s):  
Guicang Zhang ◽  
Kai Wang
Keyword(s):  
Partition Of Unity ◽  
Shape Features ◽  
Bernstein Basis ◽  
Order Continuity ◽  
B Spline ◽  
Spline Curve ◽  
Totally Positive ◽  
Chebyshev Space ◽  
Spline Basis ◽  
Cutting Algorithm

Firstly, a new set of Quasi-Cubic Trigonometric Bernstein basis with two tension shape parameters is constructed, and we prove that it is an optimal normalized totally basis in the framework of Quasi Extended Chebyshev space. And the Quasi-Cubic Trigonometric Bézier curve is generated by the basis function and the cutting algorithm of the curve are given, the shape features (cusp, inflection point, loop and convexity) of the Quasi-Cubic Trigonometric Bézier curve are analyzed by using envelope theory and topological mapping; Next we construct the non-uniform Quasi-Cubic Trigonometric B-spline basis by assuming the linear combination of the optimal normalized totally positive basis have partition of unity and continuity, and its expression is obtained. And the non-uniform B-spline basis is proved to have totally positive and high-order continuity. Finally, the non-uniform Quasi Cubic Trigonometric B-spline curve and surface are defined, the shape features of the non-uniform Quasi-Cubic Trigonometric B-spline curve are discussed, and the curve and surface are proved to be continuous.

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