Suppose I have two two-variable functions, $A(x,y)$ and $B(u,v)$, whose relation is given by:
$\\$ $$B(u,v) = \int_{-1}^{1}\int_{-1}^{1} A(x,y) \cdot e^{-((x-u)^2+(y-v)^2)} \:\; dx dy$$ $\\$
In this case, given $A(x,y)$, I can readily calculate (compute) $B(u,v)$ by performing the double-integral above.
Now if I'm given only $B(u,v)$, would that be a way to 'invert' the double-integral so I can recover $A(x,y)$ ?
ps: I stumbled upon this during my studies of the Radon/Fourier transforms, while trying to understand their inversion methods.