Dept. of Radiol., Indiana Univ. Sch. of Med., Indianapolis, IN.
IEEE Trans Med Imaging. 1996;15(3):369-76. doi: 10.1109/42.500145.
A new class of interpolation kernels that are locally compact in signal space and "almost band-limited" in Fourier space is presented. The kernels are easy to calculate and lend themselves to problems in which the kernels must be analytically manipulated with other operations or operators such as convolutions and projection integrals. The interpolation kernels are comprised of a linear sum of a Gaussian function and its second derivative (and, when extended to higher order, its higher even derivatives). A numerical Gaussian quadrature method is derived that can be used with integrals involving the kernels that cannot be analytically evaluated. Potential extensions to higher order implementations of the kernels are discussed and examined. The emphasis of the manuscript is on the simplicity of the interpolation kernel and some of its mathematical properties.
提出了一类新的内插核，它们在信号空间中是局部紧的，在傅立叶空间中是“几乎带限”的。这些核易于计算，适用于需要对核进行解析操作的问题，例如卷积和投影积分等操作或算子。内插核由高斯函数及其二阶导数（以及扩展到更高阶时的更高阶偶数导数）的线性和组成。推导了一种数值高斯求积方法，可用于涉及无法解析评估的核的积分。讨论并检查了核的更高阶实现的潜在扩展。本文的重点是内插核的简单性及其一些数学性质。
