Book
Super-resolution reconstruction from truncated Fourier transform
| العنوان: | Super-resolution reconstruction from truncated Fourier transform |
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| المؤلفون: | Isaev, Mikhail, Novikov, Roman, Sabinin, Grigory |
| المساهمون: | School of Mathematics Australia, Monash University Melbourne, Centre de Mathématiques Appliquées de l'Ecole polytechnique (CMAP), Institut National de Recherche en Informatique et en Automatique (Inria)-École polytechnique (X), Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-Centre National de la Recherche Scientifique (CNRS), Faculty of Mechanics and Mathematics Moscow, Lomonosov Moscow State University (MSU) |
| المصدر: | Extended Abstracts MWCAPDE 2023Methusalem Workshop on Classical Analysis and Partial Differential Equations ; https://hal.science/hal-04059509 ; Extended Abstracts MWCAPDE 2023 Methusalem Workshop on Classical Analysis and Partial Differential Equations, 2024, ⟨10.1007/978-3-031-41665-1_7⟩ |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2024 |
| مصطلحات موضوعية: | super-resolution, band-limited Fourier transform, prolate spheroidal wave functions, Radon transform, 2000 MSC: 42A38, 35R30, 49K40, [MATH]Mathematics [math] |
| الوصف: | International audience ; 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 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). |
| نوع الوثيقة: | book part |
| اللغة: | English |
| DOI: | 10.1007/978-3-031-41665-1_7 |
| الاتاحة: | https://hal.science/hal-04059509 https://hal.science/hal-04059509v1/document https://hal.science/hal-04059509v1/file/Super-resolution.pdf https://doi.org/10.1007/978-3-031-41665-1_7 |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.7798490A |
| قاعدة البيانات: | BASE |
| DOI: | 10.1007/978-3-031-41665-1_7 |
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