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              <p>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 or reflection seismology. 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 multi-element technology and recent advances in data science pave the way towards a next revolution in wave imaging. In that context, we developed a universal matrix approach of wave imaging in heterogeneous media. A matrix formalism is actually the perfect tool to locally compensate for aberrations over large imaging volumes, thus breaking the limitations of adaptive focusing methods. It also leads to the following paradigm shift in wave imaging: Whereas multiple scattering is generally seen as a nightmare, a matrix approach can take advantage of it for ultra-deep and high-resolution imaging. Our matrix approach is also a promising characterization tool since it can provide a high-resolution tomography of the wave velocity and of scattering parameters. All these concepts are applied to both optics (for in-depth imaging of biological tissues), ultrasound imaging (for medical diagnosis) and seismology (for monitoring of volcanoes and fault zones). From a more fundamental perspective, a matrix formalism can also be particularly fruitful to probe exotic wave transport phenomena in the strong scattering regime. On the one hand, constructive interference between reciprocal multiple scattering paths can eventually stop the diffusion process, giving rise to Anderson localization. On the other hand, interference phenomena can also help waves to find a way through a maze of disorder. The scattering matrix provides a unique tool to probe these open and closed scattering channels, highlight the importance of recurrent scattering loops in the renormalization of the diffusion process at the onset of 3D Anderson localization.</p>
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