# 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} }

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

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