Separation of single and multiple scattering in complex media: Applications to ultrasound imaging and characterization

The ultrasonic wave propagation operator in random media is investigated under a matrix approach. 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 [1,2]. 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 [3]. Another approach is proposed to extract the multiple scattering contribution in a weakly scattering random medium (e.g. human soft tissues) [4]. 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). This approach has been applied to the ultrasonic imaging of human trabecular bone around 3 MHz [5]. [1] A. Aubry, A. Derode, Random matrix theory applied to acoustic backscattering and imaging in complex media, Phys. Rev. Lett. 102, 084301, 2009 [2] A. Aubry, A. Derode, Singular value distribution of the propagation matrix in random scattering media, Waves Random Complex Media 20, 333-363, 2010 [3] A. Aubry, A. Derode, Detection and imaging in a random medium : A matrix method to overcome multiple scattering and aberration, J. Appl. Phys. 106, 044903, 2009 [4] A. Aubry, A. Derode, Multiple scattering of ultrasound in weakly inhomogeneous media : Application to human soft tissues, J. Acoust. Soc. Am. 129, 225-234, 2011 [5] A. Aubry, A. Derode, F. Padilla, Local measurements of the diffusion constant in multiple scattering media : Application to human trabecular bone imaging, Appl. Phys. Lett. 92, 124101, 2008