  In passive imaging, one attempts to reconstruct some coefficients in a wave
equation from correlations of observed randomly excited solutions to this wave
equation. Many methods proposed for this class of inverse problem so far are
only qualitative, e.g., trying to identify the support of a perturbation. Major
challenges are the increase in dimensionality when computing correlations from
primary data in a preprocessing step, and often very poor pointwise
signal-to-noise ratios. In this paper, we propose an approach that addresses
both of these challenges: It works only on the primary data while implicitly
using the full information contained in the correlation data, and it provides
quantitative estimates and convergence by iteration.
  Our work is motivated by helioseismic holography, a well-established imaging
method to map heterogenities and flows in the solar interior. We show that the
back-propagation used in classical helioseismic holography can be interpreted
as the adjoint of the Fr\'echet derivative of the operator which maps the
properties of the solar interior to the correlation data on the solar surface.
The theoretical and numerical framework for passive imaging problems developed
in this paper extends helioseismic holography to nonlinear problems and allows
for quantitative reconstructions. We present a proof of concept in uniform
media.
