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arXiv · 1403.0172

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

Ben Adcock·Anders C. Hansen·Gitta Kutyniok·Jackie Ma
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Abstract

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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Ben Adcock, Anders C. Hansen, Gitta Kutyniok, Jackie Ma. 2014-03-24. Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements. https://arxiv.org/abs/1403.0172

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