Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

Mikhail Isaev; Roman G. Novikov

doi:10.1016/j.matpur.2022.05.008

Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

Mikhail Isaev, Roman G. Novikov

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

7 Citations (Scopus)

Abstract

We give new formulas for finding a compactly supported function v on R^d, d≥1, from its Fourier transform Fv given within the ball B_r. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWF's). In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given.

Original language	English
Pages (from-to)	318-333
Number of pages	16
Journal	Journal des Mathematiques Pures et Appliquees
Volume	163
DOIs	https://doi.org/10.1016/j.matpur.2022.05.008
Publication status	Published - Jul 2022

Keywords

Band-limited Fourier transform
Hölder-logarithmic stability
Ill-posed inverse problems
Prolate spheroidal wave functions
Radon transform

Access to Document

10.1016/j.matpur.2022.05.008

Cite this

@article{944ea1ec3b8944d698e6968c2589a146,

title = "Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions",

abstract = "We give new formulas for finding a compactly supported function v on Rd, d≥1, from its Fourier transform Fv given within the ball Br. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWF's). In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given.",

keywords = "Band-limited Fourier transform, H{\"o}lder-logarithmic stability, Ill-posed inverse problems, Prolate spheroidal wave functions, Radon transform",

author = "Mikhail Isaev and Novikov, {Roman G.}",

note = "Funding Information: The first author's research is supported by the Australian Research Council Discovery Early Career Researcher Award DE200101045 . Publisher Copyright: {\textcopyright} 2022 Elsevier Masson SAS",

year = "2022",

month = jul,

doi = "10.1016/j.matpur.2022.05.008",

language = "English",

volume = "163",

pages = "318--333",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier",

}

TY - JOUR

T1 - Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

AU - Isaev, Mikhail

AU - Novikov, Roman G.

N1 - Funding Information: The first author's research is supported by the Australian Research Council Discovery Early Career Researcher Award DE200101045 . Publisher Copyright: © 2022 Elsevier Masson SAS

PY - 2022/7

Y1 - 2022/7

N2 - We give new formulas for finding a compactly supported function v on Rd, d≥1, from its Fourier transform Fv given within the ball Br. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWF's). In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given.

AB - We give new formulas for finding a compactly supported function v on Rd, d≥1, from its Fourier transform Fv given within the ball Br. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWF's). In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given.

KW - Band-limited Fourier transform

KW - Hölder-logarithmic stability

KW - Ill-posed inverse problems

KW - Prolate spheroidal wave functions

KW - Radon transform

UR - http://www.scopus.com/inward/record.url?scp=85130567915&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2022.05.008

DO - 10.1016/j.matpur.2022.05.008

M3 - Article

AN - SCOPUS:85130567915

SN - 0021-7824

VL - 163

SP - 318

EP - 333

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

Abstract

Keywords

Access to Document

Other files and links

Enhanced methods for approximating the structure of large networks

Cite this

Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

Abstract

Keywords

Access to Document

Other files and links

Projects

Enhanced methods for approximating the structure of large networks

Cite this