Reconstruction of spline spectra-signals from generalized sinc function by finitely many samples

Reconstruction of signals by their Fourier (transform) samples is investigated in many mathematical/engineering problems such as the inverse Radon transform and optical diffraction tomography. This paper concerns on the reconstruction of spline-spectra signals in V ( sinc a ) by finitely many Fourie...

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Bibliographic Details
Published inBanach journal of mathematical analysis Vol. 15; no. 2
Main Authors Li, Youfa, Huang, Yanfen, Zhou, Chunxu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2021
Subjects
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
Spline-spectra signals
42C40
41A30
Generalized sinc function
Shift-invariant space
42A16
Fourier samples
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Summary:Reconstruction of signals by their Fourier (transform) samples is investigated in many mathematical/engineering problems such as the inverse Radon transform and optical diffraction tomography. This paper concerns on the reconstruction of spline-spectra signals in V ( sinc a ) by finitely many Fourier samples, where sinc a is the generalized sinc function. There are two main results on this topic. When the spectra knots are known, the exact reconstruction formula conducted by finitely many Fourier samples is established in the first main theorem. When the spectra knots are unknown, in the second main theorem we establish the approximations to the spline-spectra signals also by finitely many Fourier samples. Numerical simulations are conducted to check the efficiency of the approximation.
ISSN:2662-2033
1735-8787
DOI:10.1007/s43037-020-00116-4