Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions   from Fourier Measurements
  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. 
Ben Adcock, Anders C. Hansen, Gitta Kutyniok, Jackie Ma
math.FA