# 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} }

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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