The singular values distribution of the propagation operator in a random medium is investigated in a backscattering configuration. Experiments are carried out with pulsed ultrasonic waves around 3 MHz, using an array of transducers. Coherent backscattering and field correlations are taken into account. Interestingly, the distribution of singular values shows a dramatically different behavior in the single and multiple-scattering regimes. Based on a matrix separation of single and multiple-scattered waves, an experimental illustration of imaging through a highly scattering slab is presented.