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Let be the shifted signal of.
Let (alpha{I}+S) be the shifted skew-Hermitian matrix, where S is a skew-Hermitian matrix and α is a given positive constant.
end{aligned} end{aligned} (4.7) Let (x_{i}) ((0leq ileq M)) be the shifted Legendre Gauss Lobatto nodes, and let (t_{j}) ((0leq jleq N-1)) be the shifted Legendre roots of (P_{tau,N}(t)), where (P_{tau,N}{(t_{j})} =0) ((0leq jleq N-1)).
Put (Gamma (beta ) (A*W =Lambda) and suppose (varphi _{i}(x)) be the shifted Chebyshev polynomial of degree i, which can be written as begin{aligned} varphi _{i}(x)=W_{i}X,quad i=0,1,ldots,n, end{aligned}where (W_{i}) is the ith row of the matrix W. Multiplying Eq. (13) by (varphi _{i}(x)), we get begin{aligned} C^{T}Lambda X^{beta }W_{i}X=f(x W_{i}X,quad i=0,1,ldots,n.
Two brain T1 MRI and rotated T2 MRI images in Figures 7(a) and 7(b) were used for the test, but the content of rotated T2 MRI was synthetically translated to be the shifted T2 MRI image as shown in Figure 14(a).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com