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

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

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 - 1 Jul 2022

Keywords

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

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10.1016/j.matpur.2022.05.008

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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.\}",

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year = "2022",

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

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AU - Isaev, Mikhail

AU - Novikov, Roman G.

PY - 2022/7/1

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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 - https://www.scopus.com/pages/publications/85130567915

U2 - 10.1016/j.matpur.2022.05.008

DO - 10.1016/j.matpur.2022.05.008

M3 - Article

AN - SCOPUS:85130567915

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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

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Keywords

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