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Preprint 22-2014

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

Source file is available as :   Portable Document Format (PDF)

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.

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