Wave-informed dictionary learning for high-resolution imaging in complex
  media
Miguel Moscoso Alexei Novikov George Papanicolaou Chrysoula Tsogka
We propose an approach for imaging in scattering media when large and diverse
data sets are available. It has two steps. Using a dictionary learning
algorithm the first step estimates the true Green's function vectors as columns
in an unordered sensing matrix. The array data comes from many sparse sets of
sources whose location and strength are not known to us. In the second step,
the columns of the estimated sensing matrix are ordered for imaging using
Multi-Dimensional Scaling with connectivity information derived from
cross-correlations of its columns, as in time reversal. For these two steps to
work together we need data from large arrays of receivers so the columns of the
sensing matrix are incoherent for the first step, as well as from sub-arrays so
that they are coherent enough to obtain the connectivity needed in the second
step. Through simulation experiments, we show that the proposed approach is
able to provide images in complex media whose resolution is that of a
homogeneous medium.