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Full-Text Articles in Applied Mathematics
Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang
Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang
Yi Li
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …
Biorthogonal Spline Type Wavelets, Tian-Xiao He
Biorthogonal Spline Type Wavelets, Tian-Xiao He
Tian-Xiao He
Let ¢ be an orthonormal scaling function with approximation degree p - 1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by fn = f * Bn (n = 1, 2, ... ) possess higher approximation order, p+n-1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function system. As an application of the method supplied in this paper, one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or …
On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He
On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He
Tian-Xiao He
By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.