  In this work we establish universal ensemble independent bounds on the mean
and variance of the mutual information and channel capacity for imaging through
a complex medium. Both upper and lower bounds are derived and are solely
dependent on the mean transmittance of the medium and the number of degrees of
freedom $N$. In the asymptotic limit of large $N$, upper bounds on the channel
capacity are shown to be well approximated by that of a bimodal channel with
independent identically Bernoulli distributed transmission eigenvalues.
Reflection based imaging modalities are also considered and permitted regions
in the transmission-reflection information plane defined. Numerical examples
drawn from the circular and DMPK random matrix ensembles are used to illustrate
the validity of the derived bounds. Finally, although the mutual information
and channel capacity are shown to be non-linear statistics of the transmission
eigenvalues, the existence of central limit theorems is demonstrated and
discussed.
