Fast and direct inversion methods for the multivariate nonequispaced fast Fourier transform

Frontiers in Applied Mathematics and Statistics

Applied Mathematics and Statistics

Daniel Potts¹  Melanie Kircheis² 

[1] Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany;null;

关键词: inverse nonequispaced fast Fourier transform;    nonuniform fast Fourier transform;    direct inversion;    iNFFT;    NFFT;   

DOI  :  10.3389/fams.2023.1155484

 received in 2023-01-31, accepted in 2023-05-17,  发布年份 2023

来源: Frontiers

【 摘 要 】

The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various applications such as MRI and solution of PDEs are interested in the inverse problem, i.e., computing Fourier coefficients from given nonequispaced data. In this article, we survey different kinds of approaches to tackle this problem. In contrast to iterative procedures, where multiple iteration steps are needed for computing a solution, we focus especially on so-called direct inversion methods. We review density compensation techniques and introduce a new scheme that leads to an exact reconstruction for trigonometric polynomials. In addition, we consider a matrix optimization approach using Frobenius norm minimization to obtain an inverse NFFT.

【 授权许可】

Unknown   
Copyright © 2023 Kircheis and Potts.