How to perform 2D Inverse Discrete Fourier Transformation for the given specific problem?

I have this problem where i need to numerically evaluate the 2D inverse Fourier transform of the below given problem at .

We know the values of the given Fourier transformed function inside the integral as a square matrix by [N x N].

First question: Is it possible to define function such that;

If we can do it, then can we evaluate numerically?