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

Adcock, Ben; Hansen, Anders C.; Kutyniok, Gitta; Ma, Jackie

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

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.