JAMING, Philippe; NEGREIRA, Felipe; ROMERO, José Luis

doi:10.1016/j.acha.2020.01.005

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JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

NEGREIRA, Felipe
Institut de Mathématiques de Bordeaux [IMB]

ROMERO, José Luis
Fakultät für Mathematik [Wien]
Acoustics Research Institute [ARI]

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Applied and Computational Harmonic Analysis. 2021, vol. 52, p. 198-230

Elsevier

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We consider the problem of reconstructing a compactly supported function from samples of its Fourier transform taken along a spiral. We determine the Nyquist sampling rate in terms of the density of the spiral and show that below this rate spirals suffer from an approximate form of aliasing. This sets a limit to the amount of undersampling that compressible signals admit when sampled along spirals. More precisely, we derive a lower bound on the condition number for the reconstruction of functions of bounded variation, and for functions that are sparse in the Haar wavelet basis.< Leer menos

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The Nyquist sampling rate for spiraling curves

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