quantum field theory - Is there a simple explanation for Schwinger's relation $g=2+frac{alpha}{pi}+{cal O}(alpha^2)$ for the $g$-factor of the electron?

Schwinger has on his grave (it seems) the relation between the g-factor of the electron and the fine structure constant:

$$g~=~2+\frac{\alpha}{\pi}+{\cal O}(\alpha^2)$$

Did Schwinger or somebody else ever give a simple explanation for the second term of the right hand side? The 2 appears from Dirac's equation. The second term is due to the emission and absorption of a photon. Is there a simple way to see that this process leads to the expression $\frac{\alpha}{\pi}$?