@inbook{91bb565d3d7644af99b915aa56592056,
title = "Super-Resolution Reconstruction from Truncated Fourier Transform",
abstract = "We present recent theoretical and numerical results on recovering a compactly supported function v on ℝd, d≥1, from its Fourier transform ℱv given within the ball Br. 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 π∕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{\textendash}333) and Isaev, Novikov, Sabinin (2022 Inverse Problems 38 105002).",
keywords = "Band-limited Fourier transform, Prolate spheroidal wave functions, Radon transform, Super-resolution",
author = "Mikhail Isaev and Novikov, \{Roman G.\} and Sabinin, \{Grigory V.\}",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.",
year = "2024",
month = jan,
day = "1",
doi = "10.1007/978-3-031-41665-1\_7",
language = "English",
series = "Trends in Mathematics",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "63--69",
booktitle = "Trends in Mathematics",
}