Zeng Gengsheng L
Department of Engineering, Weber State University, Ogden, Utah 84408 and Utah Center for Advanced Imaging Research (UCAIR), Department of Radiology, University of Utah, Salt Lake City, Utah 84108.
Med Phys. 2014 May;41(5):051906. doi: 10.1118/1.4870989.
The purpose of this paper is to implement a noise-weighted filtered backprojection (FBP) algorithm in the form of "convolution" backprojection, but this "convolution" has a spatially variant integration kernel.
Noise-weighted FBP algorithms have been developed in recent years, with filtering being performed in the Fourier domain. The noise weighting makes the ramp filter in the FBP algorithm shift-varying. It is not efficient to implement shift-varying filtration in the Fourier domain. It is known that Fourier-domain multiplication is equivalent to spatial-domain convolution. An expansion method is suggested in this paper to obtain a closed-form integration kernel.
The noise weighted FBP algorithm can now be implemented in the spatial domain efficiently. The total computation cost is less than that of the Fourier domain implementation.
Computer simulations are used to show the three-term expansion method to approximate the filter kernel. A clinical study is used to verify the feasibility of the proposed algorithm.
本文的目的是实现一种以“卷积”反投影形式的噪声加权滤波反投影（FBP）算法，但这种“卷积”具有空间变化的积分核。
近年来已开发出噪声加权FBP算法，其滤波在傅里叶域中进行。噪声加权使得FBP算法中的斜坡滤波器变为移位变化。在傅里叶域中实现移位变化滤波效率不高。已知傅里叶域乘法等同于空间域卷积。本文提出一种展开方法以获得封闭形式的积分核。
现在可以在空间域中高效实现噪声加权FBP算法。总计算成本低于在傅里叶域中的实现。
使用计算机模拟展示三项展开方法来近似滤波核。使用临床研究来验证所提出算法的可行性。
