  This paper considers wave-based imaging through a heterogeneous (random)
scattering medium. The goal is to estimate the support of the reflectivity
function of a remote scene from measurements of the backscattered wave field.
The proposed imaging methodology is based on the coherent interferometric
(CINT) approach that exploits the local empirical cross correlations of the
measurements of the wave field. The standard CINT images are known to be robust
(statistically stable) with respect to the random medium, but the stability
comes at the expense of a loss of resolution. This paper shows that a two-point
CINT function contains the information needed to obtain statistically stable
and high-resolution images. Different methods to build such images are
presented, theoretically analyzed and compared with the standard imaging
approaches using numerical simulations. The first method involves a
phase-retrieval step to extract the reflectivity function from the modulus of
its Fourier transform. The second method involves the evaluation of the leading
eigenvector of the two-point CINT imaging function seen as the kernel of a
linear operator. The third method uses an optimization step to extract the
reflectivity function from some cross products of its Fourier transform. The
presentation is for the synthetic aperture radar data acquisition setup, where
a moving sensor probes the scene with signals emitted periodically and records
the resulting backscattered wave. The generalization to other imaging setups,
with passive or active arrays of sensors, is discussed briefly.

Image and Video Processing;Analysis of PDEs