  We present an imaging technique particularly suited to the detection of a
target embedded in a strongly scattering medium. Classical imaging techniques
based on the Born approximation fail in this kind of configuration because of
multiply scattered echoes and aberration distortions. The experimental set up
we consider uses an array of programmable transmitters/receivers. A target is
placed behind a scattering medium. The impulse responses between all array
elements are measured and form a matrix. The core of the method is to separate
the single-scattered echo of the target from the multiple scattering
background. This is possible because of a deterministic coherence along the
antidiagonals of the array response matrix, which is typical of single
scattering. Once this operation is performed, target detection is achieved by
applying the DORT method (French acronym for decomposition of the time reversal
operator). Experimental results are presented in the case of wide-band
ultrasonic waves around 3 MHz. A 125-element array is placed in front of a
collection of randomly distributed steel rods (diameter 0.8mm). The slab
thickness is three times the scattering mean free path. The target is a larger
steel cylinder (diameter 15 mm) that we try to detect and localize. The quality
of detection is assessed theoretically based on random matrix theory and is
shown to be significantly better than what is obtained with classical imaging
methods. Aside from multiple scattering, the technique is also shown to reduce
the aberrations induced by an heterogeneous layer.
