An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging (MRI) are concerned with the analogous problem for bandlimited functions, i.e., the reconstruction of point evaluations of the Fourier transform from given measurements of the bandlimited function. In this paper, we review an approach yielding exact reconstruction for trigonometric polynomials up to a certain degree, and extend this technique to the setting of bandlimited functions. Here we especially focus on methods computing a diagonal matrix of weights needed for sampling density compensation.

翻译：逆非均匀快速傅里叶变换（iNFFT）是一种从非均匀采样数据中快速计算三角多项式傅里叶系数的算法。然而，磁共振成像（MRI）等实际应用关注的是带限函数的类似问题，即根据带限函数的给定测量值重建其傅里叶变换的点值。本文回顾了一种对特定阶数三角多项式实现精确重建的方法，并将该技术推广至带限函数场景。我们尤其关注计算采样密度补偿所需的权重对角矩阵的方法。