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

被引：7

作者：

Isaev, Mikhail ^{[1
]}

Novikov, Roman G. ^{[2
,3
]}

机构：

[1] Monash Univ, Sch Math, Clayton, Vic, Australia

[2] Inst Polytech Paris, Ecole Polytech, CMAP, CNRS, Palaiseau, France

[3] RAS, IEPT, Moscow, Russia

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2022年 / 163卷

基金：

澳大利亚研究理事会;

关键词：

Ill-posed inverse problems; Band-limited Fourier transform; Prolate spheroidal wave functions; Radon transform; H?lder-logarithmic stability; EIGENVALUES; BOUNDS;

D O I：

10.1016/j.matpur.2022.05.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：318 / 333

页数：16

共 23 条

[1] A variational approach to the inversion of truncated Fourier operators [J].