  In this work, we employ algebraic renormalization technique to show the
renormalizability to all orders in perturbation theory of the Lorentz and CPT
violating QED. Essentially, we control the breaking terms by using a suitable
set of external sources. Thus, with the symmetries restored, a perturbative
treatment can be consistently employed. After showing the renormalizability,
the external sources attain certain physical values, which allow the recovering
of the starting physical action. The main result is that the original QED
action presents the three usual independent renormalization parameters. The
Lorentz violating sector can be renormalized by nineteen independent
parameters. Moreover, vacuum divergences appear with extra independent
renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term)
does not renormalize. One-loop computations are also presented and compared
with the existing literature.
