Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements
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 dimension of the wavelet reconstruction spaces. We also provide numerical experiments that corroborate our theoretical results.
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Information & Authors
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Published In
SIAM Journal on Mathematical Analysis
Pages: 1196 - 1233
DOI: 10.1137/140959365
ISSN (online): 1095-7154
Copyright
© 2015, Society for Industrial and Applied Mathematics.
History
Submitted: 3 March 2014
Accepted: 11 December 2014
Published online: 2 April 2015
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