Author(s) :
Ben Adcock
,
Anders Hansen
,
Gitta Kutyniok
,
Martin Schäfer
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 22-2014
MSC 2000
- 65J22 Inverse problems
-
65T60 Wavelets
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.