Pré-Publication, Document De Travail Année : 2019

The Nyquist sampling rate for spiraling curves

Résumé

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.

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Dates et versions

hal-01898240 , version 1 (18-10-2018)
hal-01898240 , version 2 (22-10-2018)
hal-01898240 , version 3 (01-11-2018)
hal-01898240 , version 4 (04-02-2019)
hal-01898240 , version 5 (08-06-2019)

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Philippe Jaming, Felipe Negreira, José Luis Romero. The Nyquist sampling rate for spiraling curves. 2019. ⟨hal-01898240v4⟩
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