Super-Resolution Reconstruction from Truncated Fourier Transform

被引：0

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

[3] IEPT Ras, Moscow, Russia

[4] Lomonosov Moscow State Univ, Fac Mech & Math, Moscow, Russia

来源：

EXTENDED ABSTRACTS MWCAPDE 2023 | 2024年 / 1卷

关键词：

D O I：

10.1007/978-3-031-41665-1_7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present recent theoretical and numerical results on recovering a compactly supported function v on R-d, d >= 1, from its Fourier transform Fv given within the ball B-r. We proceed from known results on the prolate spheroidal wave functions and on the Radon transform. The most interesting point of our numerical examples consists in super-resolution, that is, in recovering details beyond the diffraction limit, that is, details of size less than pidividedbyr.pi r, where r is the radius of the ball mentioned above. This short review is based on the works Isaev, Novikov (2022 J. Math. Pures Appl. 163 318-333) and Isaev, Novikov, Sabinin (2022 Inverse Problems 38 105002).

引用

页码：63 / 69

页数：7

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