Reconstruction of bivariate functions by sparse sine coefficients.

In application, one often expands the functions f on [0, 1]² into Fourier sine series and uses few Fourier sine coe±cients to reconstruct f. In this paper, we give a decomposition formula of Fourier sine coe±cients. Based on it, we discuss hyperbolic cross approximations of Fourier sine series and Fourier sine expansion with simple polynomial factors. In the end of this paper, we consider the three-dimensional case. [ABSTRACT FROM AUTHOR]