The Nyquist sampling rate for spiraling curves
Classical Analysis and ODEs
2022-05-04 v5
Abstract
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.
Cite
@article{arxiv.1811.01771,
title = {The Nyquist sampling rate for spiraling curves},
author = {Philippe Jaming and Felipe Negreira and José Luis Romero},
journal= {arXiv preprint arXiv:1811.01771},
year = {2022}
}
Comments
30 pages, 8 figures