Suppose we have a function f(t).
We have two bad copies f_x(t) = f(t) + X and f_y(t) = f(t) + Y.
X, Y are uncorrelated random variables.
How can one best reconstruct f(t)?

The obvious way is to average the functions but this seems wrong to me.
The reconstruction is f_z(t) = (f_x(t) + f_y(t))/2 = f(t) + Z.
Then,
Z = (X + Y)/2
So
E[Z] = (E[X] + E[Y]) / 2
and
Var(Z) = (Var(X) + Var(Y)) / 4 = ((Var(X) + Var(Y)) / 2) / 2

Or in other words the average of the bad copies has half the variance.
But I made a test image in GIMP and this doesn't look even approximately right to me.