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In this paper we analyze two-dimensional wavelet reconstructions from Fouriersamples within the framework of generalized sampling. For this, we considerboth separable compactly-supported wavelets and boundary wavelets. We provethat the number of samples that must be acquired to ensure a stable andaccurate reconstruction scales linearly with the number of reconstructingwavelet functions. We also provide numerical experiments that corroborate ourtheoretical results.

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