I've got a multiplicative-with-noise model $F(x,y)=S(x)*R(y)*D(x,y)+N$, where $S(x)$ and $R(y)$ are unknown functions, $D(x,y)$ is a distance function, that is, a function that depends only on $|x-y|$ and decreases quickly when distance increases. $N$ is an uncorrelated "small random noise" function. All of the functions except noise are positive.
I have $F(x,y)$ sampled for almost any not-very-distant pair of discrete $(x,y)$, that is, for $(x,y): |x-y| \leq D_{max}$.
I'd like to decompose $F(x,y)$ to obtain the "form" of $S(x), R(y), D(x,y)$. How can I do it? My only idea is to calculate averages $S_{est}(x_i)=average(F(x,y), x=x_i)$, $R_{est}(y_j)=average(F(x,y),y=y_j)$ etc, assume $N=0$, then produce an estimated $F_{est}=S_{est}(x)*R_{est}(y)*D_{est}(x,y)$. I dont know what to do next.