Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements

@article{Adcock2015LinearSS,
  title={Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements},
  author={B. Adcock and A. Hansen and G. Kutyniok and Jackie Ma},
  journal={SIAM J. Math. Anal.},
  year={2015},
  volume={47},
  pages={1196-1233}
}
  • B. Adcock, A. Hansen, +1 author Jackie Ma
  • Published 2015
  • Mathematics, Computer Science
  • SIAM J. Math. Anal.
  • In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the number of samples that must be acquired to ensure a stable and accurate reconstruction scales linearly with the number of reconstructing wavelet functions. We also provide numerical experiments that corroborate our theoretical results. 

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