The Nyquist sampling rate for spiraling curves

Philippe Jaming (1) , Felipe Negreira (1) , José Luis Romero (2, 3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Fakultät für Mathematik [Wien]
3 ARI - Acoustics Research Institute

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.

Domaines: Analyse classique [math.CA]; Traitement du signal et de l'image [eess.SP]

Philippe Jaming, Felipe Negreira, José Luis Romero. The Nyquist sampling rate for spiraling curves. 2018. ⟨hal-01898240v3⟩