On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate

@article{Adcock2012OnOW,
  title={On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate},
  author={B. Adcock and A. Hansen and C. Poon},
  journal={ArXiv},
  year={2012},
  volume={abs/1208.5959}
}
  • B. Adcock, A. Hansen, C. Poon
  • Published 2012
  • Computer Science, Mathematics
  • ArXiv
  • In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that using generalized sampling one obtains a stable and accurate reconstruction, provided the number of Fourier samples grows linearly in the number of wavelet coefficients recovered. For the class of Daubechies wavelets we derive the exact constant of… CONTINUE READING
    Optimal wavelet reconstructions from Fourier samples via generalized sampling
    1
    On stable reconstructions from univariate nonuniform Fourier measurements
    8
    A Consistent and Stable Approach to Generalized Sampling
    15
    On the stable sampling rate for binary measurements and wavelet reconstruction
    7
    Linear reconstructions and the analysis of the stable sampling rate
    5
    A Practical Guide to the Recovery of Wavelet Coefficients from Fourier Measurements
    9

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 64 REFERENCES
    Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon
    50
    A Generalized Sampling Theory without bandlimiting constraints
    130
    A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases
    66
    A minimum squared-error framework for generalized sampling
    66
    Sampling-50 years after Shannon
    1272
    A general sampling theory for nonideal acquisition devices
    376
    A Theory for Sampling Signals From a Union of Subspaces
    268
    Sampling Theorems for Signals From the Union of Finite-Dimensional Linear Subspaces
    281