Periodic Reporting for period 3 - REMINISCENCE (REflection Matrix ImagiNg In wave SCiENCE)
Periodo di rendicontazione: 2022-06-01 al 2023-11-30
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).
Beyond reflectivity imaging, the study of the focused reflection matrix in the time domain was shown to provide a self-portrait of wave focusing inside the medium. Such propagation movies open a new route towards quantitative imaging since it enables the local measurement of parameters such as speed-sound, anisotropy or multiple scattering that constitute relevant bio-markers whether it be for ultrasound diagnosis or bio-medical optics.
On the optical side of the project, three different experimental set ups have been mounted during this first period. Using either coherent or incoherent illumination schemes, these devices enable the recording of the reflection matrix in the time or frequency domains. The use of an ultrafast camera and a swept source enables a measurement of a D-matrix at a frame rate of 1-100 Hz, which paves the way towards real time in-vivo. First proof-of-concept experiments have been performed on biological tissues and an extension of the penetration depth by a factor 3 has been demonstrated compared to standard optical coherence tomography.
At last, at a much larger scale, our matrix approach has been successfully applied to seismic imaging on different data set collected by array of geophones distributed over volcanoes – La Souffrière, Guadeloupe, France – or in fault zones – San Jacinto Fault zone, California and North Anatolian Fault, Turkey. Matrix imaging provides unique reflectivity images of the Earth’s crust that will help geophysicists in monitoring these critical areas. Moreover, these matrix images display a spectacularly high resolution that is one order of magnitude better than what is expected from diffraction theory. This spectacular result is accounted for by a refocusing of multiply-scattered surface waves that drastically enlarges the effective aperture of the geophone array.
To overcome aberrations that generally degrade the resolution and contrast of standard images, a novel operator has been introduced, the so-called distortion (D) matrix. This operator essentially connects any focal point inside the medium with the distortion that a wave front, emitted from that point, experiences due to heterogeneities. A time-reversal analysis of D enables the estimation of the transmission matrix (T) that links each sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing an image of the medium with ideal resolution. Importantly, this process is particularly efficient for spatially-distributed aberration, where traditional approaches such as adaptive focusing fail.
To cope with multiple scattering, one has to play with both spatial and temporal degrees of freedom in order to harness multiply-scattered waves. The measurement of a broadband R-matrix and a spatio-frequency analysis of its correlations should be coupled to learning based methods in order to retrieve a time-dependent T-matrix that will allow using the medium heterogeneities as a scattering lens and extend the penetration depth of matrix imaging beyond the transport mean free path. Such an approach will be rewarding in terms of resolution since scattering can increase the effective numerical aperture of the imaging system and lead to super-resolution.
This high-resolution capability of MI has indeed been demonstrated in geophysics. MI provides a high-resolution, in-depth imaging of the Earth's crust in complex areas, such as fault zones and volcanoes. To do so, we exploited seismic noise recorded over several months by a dense network of geophones. MI goes well beyond the state-of-the art in passive seismology that only exploited surface waves so far to build an image at shallow depths. The ultimate goal is to exploit this paradigm shift in seismic imaging for finding precursors of volcanic eruption and seismic events.