Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements

@article{Adcock2015RecoveringPS,
  title={Recovering Piecewise Smooth Functions from Nonuniform Fourier Measurements},
  author={B. Adcock and M. Gataric and A. Hansen},
  journal={arXiv: Numerical Analysis},
  year={2015},
  pages={117-125}
}
  • B. Adcock, M. Gataric, A. Hansen
  • Published 2015
  • Mathematics
  • arXiv: Numerical Analysis
  • In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to ensure high accuracy we employ reconstruction spaces consisting of splines or (piecewise) polynomials. We analyze the relation between the dimension of the reconstruction space and the bandwidth of the nonuniform samples, and show that it is linear for splines and… CONTINUE READING

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