  We study meson loop corrections to the baryon magnetic moments starting from
a QCD-based quark model derived earlier in a quenched approximation to QCD. The
model reproduces the standard quark model with extra corrections for the
binding of the quarks. The loop corrections are necessary to remove the
quenching. Our calculations use heavy baryon perturbation theory with chiral
baryon-meson couplings and a form factor characterizing the structure of
baryons as composite particles. The form factor reflects soft wave function
effects with characteristic momenta $\approx 400$ MeV, well below the usual
chiral cutoff of $\approx 1$ GeV. The resulting model involves only three
parameters, the quark moments $\mu_u$ and $\mu_s$ and a parameter $\lambda$
that sets the momentum scale in the wavefunctions. We find that this approach
substantially improves the agreement between the theoretical and experimental
values of the octet baryon magnetic moments, with an average difference between
the theoretical and experimental moments of 0.05$\mu_N$. An extension to the
decuplet states using the same input predicts a moment of 1.97 $\mu_N$ for the
$\Omega^-$ hyperon, in excellent agreement with the measured moment of
$2.02\pm0.05 \mu_N$.
