  Quantum imaging has a potential of enhancing precision of the object
reconstruction by using quantum correlations of the imaging field. This is
especially important for imaging requiring low-intensity fields up to the level
of few-photons. However, quantum imaging generally leads to nonlinear
estimation problems. The complexity of these problems rapidly increases with
the number of parameters describing the object. We suggest a way to drastically
reduce the complexity for a wide class of problems. The key point of our
approach is connecting the features of the Fisher information with the
parametric locality of the problem, and building the efficient iterative
inference scheme reconstructing only a subset of the whole set of parameters in
each step. This iterative scheme is linear on the total number of parameters.
This scheme is applied to quantum near-field imaging, the inference procedure
is developed resulting in super-resolving reconstruction of grey compound
transmission objects. The functionality of the method is demonstrated with
experimental data obtained by measurements of higher-order correlation
functions for imaging with entangled twin-photons and pseudo-thermal light
sources. By analyzing the informational content of the measurement, it becomes
possible to predict the existence of optimal photon correlations providing for
the best image resolution in the super-resolution regime. This prediction is
experimentally confirmed. It is also shown how an estimation bias stemming from
image features may drastically improve the resolution.
