2014/03/02 by Ben Adcock, Anders C. Hansen, Adcock, Ben +5
Computer Science · Earth and Planetary Sciences · Mathematics · #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques #math.FA
paper · pdf · doi:10.48550/arxiv.1403.0172
arxiv created 2014/03/24 · arxiv updated 2014/03/25
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.