This manuscript is devoted to the study of the ultrasonic wave propagation operator in random media. The experimental set up consists in a multi-element array placed in front of a random medium. The inter-element reponses between each couple of transducers form the array response matrix. Its statistical behaviour has been studied in the single and multiple scattering regimes, using random matrix theory. Whereas the propagation operator exhibits a random behaviour in the mutiple scattering regime, single scattered echoes keep a deterministic coherence despite disorder. This difference of behaviour has led to the design of a smart radar which separates single and multiple scattered echoes.We are able to extract the direct echo of an echogene target embedded in a strongly diffusive medium, despite multiple scattering and aberration. Another approach is proposed to extract the multiple scattering contribution in a weakly scattering random medium (e.g. human soft tissues). The investigation of multiple scattering allows to characterize the random medium by transport parameters which govern the propagation of multiple scattered waves (e.g. the diffusion constant D). Plane-wave beamforming allows to study the coherent backscattering effect in the far-field and then obtain a measurement of D, independently from absorption. Gaussian beamforming allows to study the growth of the diffusive halo in the near-field and local measurements of D are obtained. This technique has been applied to the ultrasonic imaging of human trabecular bone around 3 MHz. Finally, we also study the theoretical link between the microarchitecture of a random medium and the transport parameters.
