Schorr B, Townsend D, Clack R
Phys Med Biol. 1983 Sep;28(9):1009-19. doi: 10.1088/0031-9155/28/9/001.
Application of the Fourier space deconvolution algorithm to three-dimensional (3D) reconstruction problems necessitates the computation of a frequency space filter; which requires taking the 3D Fourier transform of the system response function. In this paper, it is shown that for system response functions of the specific form d(theta, phi)/r2, with d(theta, phi) an angular function describing the imaging system, the filter computation can always be reduced to a single integration which, in many cases, may be performed analytically. Complete expressions are derived for the general 3D filter, and two examples are given to illustrate the use of such expressions.
将傅里叶空间反卷积算法应用于三维（3D）重建问题需要计算一个频率空间滤波器；这需要对系统响应函数进行三维傅里叶变换。本文表明，对于特定形式为d(θ, φ)/r²的系统响应函数，其中d(θ, φ)是描述成像系统的角度函数，滤波器计算总是可以简化为一个单一积分，在许多情况下，可以进行解析计算。推导了通用三维滤波器的完整表达式，并给出了两个例子来说明此类表达式的用法。
