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Article Dans Une Revue Inverse Problems Année : 2022

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

Résumé

We implement numerically formulas of [Isaev, Novikov, arXiv:2107.07882, hal-03289374] 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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Dates et versions

hal-03602634 , version 1 (09-03-2022)

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Mikhail Isaev, Roman Novikov, Grigory Sabinin. Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions. Inverse Problems, 2022, ⟨10.1088/1361-6420/ac87cb⟩. ⟨hal-03602634⟩
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