中文摘要：

非标准快速傅里叶变换算法是一种用于处理非标准采样的快速算法,在信号处理领域有着广泛的应用。本文回顾了NUFFT算法的历史和发展,对通用的算法实现形式做了详细描述,介绍了该算法的最新进展和研究方向。对NUFFT算法在CT重建中的应用,如傅里叶重建,迭代重建,稀疏采样重建等也做了介绍。

英文摘要：

Nonuniform fast Fourier transformation（NUFFT）,as an efficient method for irregular sampling problem,is widely used in signal processing.This article gives a review of the history and development of NUFFT,followed by a detailed depiction of the general scheme of the algorithm.The newly improvements in the past few years is also discussed.Finally,it is shown that NUFFT performs well in CT reconstruction,such as Fourier reconstruction,iterative reconstruction and sparse sampling problems.