  Waves scattered by a weakly inhomogeneous random medium contain a predominant
single scattering contribution as well as a multiple scattering contribution
which is usually neglected, especially for imaging purposes. A method based on
random matrix theory is proposed to separate the single and multiple scattering
contributions. The experimental set up uses an array of sources/receivers
placed in front of the medium. The impulse responses between every couple of
transducers are measured and form a matrix. Single-scattering contributions are
shown to exhibit a deterministic coherence along the antidiagonals of the array
response matrix, whatever the distribution of inhomogeneities. This property is
taken advantage of to discriminate single from multiple-scattered waves. This
allows one to evaluate the absorption losses and the scattering losses
separately, by comparing the multiple scattering intensity with a radiative
transfer model. Moreover, the relative contribution of multiple scattering in
the backscattered wave can be estimated, which serves as a validity test for
the Born approximation. Experimental results are presented with ultrasonic
waves in the MHz range, on a synthetic sample (agar-gelatine gel) as well as on
breast tissues. Interestingly, the multiple scattering contribution is found to
be far from negligible in the breast around 4.3 MHz.
