Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions

被引：5
作者：
Isaev, Mikhail [1 ]
Novikov, Roman G. [2 ,3 ]
Sabinin, Grigory, V [4 ]
机构：
[1] Monash Univ, Sch Math, Clayton, Vic, Australia
[2] Ecole Polytech Inst Polytech Paris, CNRS, CMAP, Palaiseau, France
[3] IEPT RAS, Moscow, Russia
[4] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia
来源：
INVERSE PROBLEMS | 2022年 / 38卷 / 10期
基金：
俄罗斯基础研究基金会; 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; super-resolution; INVERSE; EIGENVALUES; ALGORITHM; BOUNDS;
D O I：
10.1088/1361-6420/ac87cb
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We implement numerically formulas of Isaev and Novikov (2022 J. Math. Pures Appl. 163 318-33) for finding a compactly supported function v on R-d, d >= 1, from its Fourier transform F[v] given within the ball B-r. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions, which arise, in particular, in the singular value decomposition of the aforementioned band-limited Fourier transform for d = 1. In multidimensions, these formulas also include inversion of the Radon transform. In particular, we give numerical examples of super-resolution, that is, recovering details beyond the diffraction limit.
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页数：17
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