  Imaging through scattering and random media is an outstanding problem that to
date has been tackled by either measuring the medium transmission matrix or
exploiting linear correlations in the transmitted speckle patterns. However,
transmission matrix techniques require interferometric stability and linear
correlations, such as the memory effect, can be exploited only in thin
scattering media. Here we show the existence of a statistical dependency in
strongly scattered optical fields in a case where first-order correlations are
not expected. We also show that this statistical dependence and the related
information transport is directly linked to artificial neural network imaging
in strongly scattering, dynamic media. These non-trivial dependencies provide a
key to imaging through dynamic and thick scattering media with applications for
deep-tissue imaging or imaging through smoke or fog
