I have an equation
$$ g(x_0, y_0)=\int\int dxdy[h(x_0-x, y_0-y)f(x, y)e^{i\omega_0y(x_0-x)}] $$
in the equation $g$ and $h$ are known complex functions, $\omega_0$ is a known real constant and $f$ is the desired unknown function. If there's no exponential term in the integral, the problem is a simple convolution problem, and f can be easily retrieved by deconvolution methods, like Wiener deconvolution.
Now that there is an exponential cross term, is it still possible to do the deconvolution? Both analytical and numerical solutions are acceptable. Or can the problem be proofed to be unsolvable for some reason?