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
收藏
页码：318 / 333
页数：16
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