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:一种反向非等间隔快速傅里叶变换 (iNFFT) 是一种快速算法,用于从非等间隔采样数据计算三角多项式的傅里叶系数。然而,各种应用程序,如磁共振成像 (MRI),涉及到带限函数的类似问题,即从给定的带限测量数据中重建傅里叶变换的点评估。在本文中,我们回顾了一种方法,该方法可获得三角多项式的精确重建直至某个程度,并将此技术扩展到带限函数的设置。在这里,我们特别关注计算所需的密度补偿权重的对角矩阵的方法。