Periodic Reporting for period 3 - REMINISCENCE (REflection Matrix ImagiNg In wave SCiENCE)
Reporting period: 2022-06-01 to 2023-11-30
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).
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).
The theoretical part of the project has been dedicated to the modelling of the focused reflection matrix and the implementation of an algorithm dedicated to the transmission matrix retrieval. The transmission matrix links the response between sensors outside the medium and voxels inside the medium. It constitutes the Holy Grail for the project since it enables in-vivo imaging with close-to-ideal resolution and contrast at every pixel. Our algorithm has already been applied to ultrasound in-vivo imaging and optical ex-vivo imaging for local aberration correction in order to reach an optimized contrast and a close to ideal for any pixel of the image.
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.
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.
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.
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.