  We consider a statistical inverse learning problem, where the task is to
estimate a function $f$ based on noisy point evaluations of $Af$, where $A$ is
a linear operator. The function $Af$ is evaluated at i.i.d. random design
points $u_n$, $n=1,...,N$ generated by an unknown general probability
distribution. We consider Tikhonov regularization with general convex and
$p$-homogeneous penalty functionals and derive concentration rates of the
regularized solution to the ground truth measured in the symmetric Bregman
distance induced by the penalty functional. We derive concrete rates for Besov
norm penalties and numerically demonstrate the correspondence with the observed
rates in the context of X-ray tomography.
