  We show that the photon self-energy in quantum electrodynamics on
noncommutative $\mathbb{R}^4$ is renormalizable to all orders (both in $\theta$
and $\hbar$) when using the Seiberg-Witten map. This is due to the enormous
freedom in the Seiberg-Witten map which represents field redefinitions and
generates all those gauge invariant terms in the $\theta$-deformed classical
action which are necessary to compensate the divergences coming from loop
integrations.
