REMINISCENCE · REflection Matrix ImagiNg In wave SCiENCE

In wave imaging, we aim at characterizing an unknown environment by actively probing it and then recording the waves reflected by the medium. It is, for example, the principle of ultrasound imaging, optical coherence tomography for light or reflection seismology in geophysics. However, wave propagation from the sensors to the focal plane is often degraded by the heterogeneities of the medium itself. They can induce wave-front distortions (aberrations) and multiple scattering events that can strongly degrade the resolution and the contrast of the image. Aberration and multiple scattering thus constitute the most fundamental limits for imaging in all domains of wave physics. However, the emergence of large-scale sensors array and recent advances in data science pave the way towards a next revolution in wave imaging. In that context, I want to develop a universal matrix approach of wave imaging in heterogeneous media. Such a formalism is actually the perfect tool to capture the input-output correlations of the wave-field with a large network of sensors. This matrix approach will allow to overcome aberrations over large imaging volumes, thus breaking the field-of-view limitations of conventional adaptive focusing methods. It will also lead to the following paradigm shift in wave imaging: Whereas multiple scattering is generally seen as a nightmare for imaging, the matrix approach will take advantage of it for ultra-deep imaging. Besides direct imaging applications, this project will also provide a high-resolution tomography of the wave velocity and a promising characterization tool based on multiple scattering quantification. Based on all these advances, the ultimate goal of this project will be to develop an information theory of wave imaging. Throughout this project, I will apply all these concepts both in optics (for in-depth imaging of biological tissues), ultrasound imaging (for medical diagnosis) and seismology (for monitoring of volcanoes and fault zones).