Unlike standard imaging methods, matrix imaging (MI) considers the response between distinct input and output focusing points. The resulting focused reflection matrix (R) thus contains much more information that a usual confocal image. In particular, it enables the quantification of local parameters that are crucial bio-markers in medical imaging (wave velocity, 3D anisotropy, resonance, multiple scattering etc.). All of these parameters constitute new and unique contrasts whether it for ultrasound imaging or optical microscopy.
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.
