Efficient multivariate inversion of the NFFT. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Kircheis, Melanie; Potts, Daniel
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000120
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Various applications such as MRI, solution of PDEs, etc. need to perform an inverse nonequispaced fast Fourier transform (iNFFT), i. e., compute Fourier coefficients from given nonequispaced data. In contrast to iterative solvers we introduce a direct method for this inversion in the overdetermined setting. For this purpose, we use the matrix representation of the NFFT. Modifying one of the matrix factors leads to an optimization problem, which can be solved in a precomputational step using normal equations. Therefore, we are able to compute an inverse NFFT up to a certain accuracy by means of a modified adjoint NFFT and therefore preserve its arithmetic complexity.