arXiv subjects

William Lambert

Publications and source records attributed to William Lambert.

12 recordsLinked to original sources

arXiv2026

Self-Portrait of the Focusing Process in Speckle: I. Spatio-Temporal Imaging of Wave Packets in Complex Media

This is the first article in a series of three dealing with the exploitation of speckle for imaging purposes. Speckle is the complex interference wave-field produced by a random distribution of un-resolved scatterers. In this paper, we show how these scatterers can be used as virtual microphones to monitor the spatio-temporal propagation of a wave-packet inside the medium. To do so, the concept of matrix imaging is particularly useful. It consists in decoupling the location of the transmitted and received focal spots in a standard beamforming process. By scanning the wave-field with the output focal spot that then acts as a virtual transducer, one can image the spatio-temporal evolution of the wave-packet inside the medium. This unique observable will allow us to highlight the imperfections of the focusing process, in particular the defocus and reverberations induced by a strong aberrating layer. As a proof-of-concept, we will consider ultrasound experiments on tissue-mimicking phantoms. In the next two papers, we will show how this observable can be leveraged to compensate for these phenomena that hamper wave focusing and imaging in all fields of wave physics. Our method is indeed broadly applicable to different types of waves beyond ultrasound for which multi-element technology allows a reflection matrix to be measured.

physics.app-ph↗

arXiv2026

Self-Portrait of the Focusing Process in Speckle: III. Tailoring Complex Spatio-Temporal Focusing Laws To Overcome Reverberations in Reflection Imaging

This is the third article in a series of three dealing with the exploitation of speckle for imaging purposes. In complex media, a fundamental limit is the multiple scattering phenomenon that completely blurs the imaging process in depth. Matrix imaging can provide a relevant framework for solving this problem. As it proved to be an adequate tool for probing reverberations in speckle [E. Giraudat et al., Part I], we will show how it can be used to tailor complex spatio-temporal focusing laws to monitor the interference between the multiply-reflected paths and the ballistic component of the wave-field. To do so, we extend the distortion matrix concept to the frequency domain. An iterative phase reversal process operated from the space-time Fourier space is then used to compensate for reverberations and optimize both the axial and transverse resolution of the confocal image. Here, we first present an experimental proof-of-concept consisting in imaging a tissue-mimicking phantom through a reverberating plate before outlining the potential and the limits of this strategy for transcranial ultrasound and beyond.

physics.app-ph↗

arXiv2026

Physics-Based Learning of the Wave Speed Landscape in Complex Media

Wave velocity is a key parameter for imaging complex media, but in vivo measurements are typically limited to reflection geometries, where only backscattered waves from short-scale heterogeneities are accessible. As a result, conventional reflection imaging fails to recover large-scale variations of the wave velocity landscape. Here we show that matrix imaging overcomes this limitation by exploiting the quality of wave focusing as an intrinsic guide star. We model wave propagation as a trainable multi-layer network that leverages optimization and deep learning tools to infer the wave velocity distribution. We validate this approach through ultrasound experiments on tissue-mimicking phantoms and human breast tissues, demonstrating its potential for tumour detection and characterization. Our method is broadly applicable to any kind of waves and media for which a reflection matrix can be measured.

physics.app-ph↗

arXiv2025

Detection and characterization of targets in complex media using fingerprint matrices

When waves propagate through a complex medium, they undergo several scattering events. This phenomenon is detrimental to imaging, as it causes full blurring of the image. Here we describe a method for detecting, localizing and characterizing any scattering target embedded in a complex medium. We introduce a fingerprint operator that contains the specific signature of the target with respect to its environment. When applied to the recorded reflection matrix, it provides a likelihood index of the target state. This state can be the position of the target for localization purposes, its shape for characterization or any other parameter that influences its response. We demonstrate the versatility of our method by performing proof-of-concept ultrasound experiments on elastic spheres buried inside a strongly scattering granular suspension and on lesion markers, which are commonly used to monitor breast tumours, embedded in a foam mimicking soft tissue. Furthermore, we show how the fingerprint operator can be leveraged to characterize the complex medium itself by mapping the fibre architecture within muscle tissue. Our method is broadly applicable to different types of waves beyond ultrasound for which multi-element technology allows a reflection matrix to be measured.

physics.app-ph↗

arXiv2024

Self-Portrait of the Focusing Process in Speckle: II. Gouy Phase Shift for Defocus Correction and Pixel Depth Reassignment

This is the second article in a series of three dealing with the exploitation of speckle for aberration correction and reverberation compensation in reflection imaging. When probing heterogeneous media with waves, we have to cope with multi-scale fluctuations of the wave velocity. On the one hand, short-scale heterogeneities induce back-scattered echoes whose random interference generate a speckle pattern on the beamformed image. On the other hand, large-scale fluctuations of the wave-velocity can distort the focused wave-fronts, resulting in aberrations on the same image. In this paper, we show how the self-portrait of the wave evolves as a function of the speed-of-sound model. Strikingly, a Gouy phase shift is observed when the speed-of-sound model is optimal. This particularly sensitive feature enables: (i) an optimization of the speed-of-sound model for each pixel of the image; (ii) a local and fine compensation of defocus across the field-of-view, thereby compensating for most aberrations in the image. Experiment in a tissue-mimicking phantom and numerical simulations are first presented to validate our method. It is then applied to in-vivo liver data of a difficult-to-image patient. The speed-of-sound optimization allows an axial compensation of aberrations and a depth-reassignment of each singly-scattered echo to the actual position of the associated scatterer. As distance measurement is often critical for diagnosis, such a wave speed optimization can be crucial for ultrasound but also for any other imaging methods based on the principle of echo-location.

physics.med-ph↗

arXiv2024

Reflection Measurement of the Scattering Mean Free Path at the Onset of Multiple Scattering

Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path $\ell_s$ that provides crucial information on the medium micro-architecture. Here, we introduce a reflection matrix method designed to estimate this parameter from the time decay of the single scattering rate. Our method is first validated by an ultrasound experiment on a tissue-mimicking phantom before being applied in-vivo to a human liver. This study opens important perspectives for quantitative imaging of heterogeneous media with waves, whether it be for non-destructive testing, biomedical or geophysical applications.

physics.med-ph↗

arXiv2023

Three-Dimensional Ultrasound Matrix Imaging

Matrix imaging paves the way towards a next revolution in wave physics. Based on the response matrix recorded between a set of sensors, it enables an optimized compensation of aberration phenomena and multiple scattering events that usually drastically hinder the focusing process in heterogeneous media. Although it gave rise to spectacular results in optical microscopy or seismic imaging, the success of matrix imaging has been so far relatively limited with ultrasonic waves because wave control is generally only performed with a linear array of transducers. In this paper, we extend ultrasound matrix imaging to a 3D geometry. Switching from a 1D to a 2D probe enables a much sharper estimation of the transmission matrix that links each transducer and each medium voxel. Here, we first present an experimental proof of concept on a tissue-mimicking phantom through ex-vivo tissues and then, show the potential of 3D matrix imaging for transcranial applications.

eess.IV↗

arXiv2022

Securing Automotive Architectures with Named Data Networking

As in-vehicle communication becomes more complex, the automotive community is exploring various architectural options such as centralized and zonal architectures for their numerous benefits. Zonal architecture reduces the wiring cost by physically locating related operations and ECUs near their intended functions and the number of physical ECUs through function consolidation. Centralized architectures consolidate the number of ECUs into few, powerful compute units. Common characteristics of these architectures include the need for high-bandwidth communication and security, which have been elusive with standard automotive architectures. Further, as automotive communication technologies evolve, it is also likely that multiple link-layer technologies such as CAN and Automotive Ethernet will co-exist. These alternative architectures promise to integrate these diverse sets of technologies. However, architectures that allow such co-existence have not been adequately explored. In this work we explore a new network architecture called Named Data Networking (NDN) to achieve multiple goals: provide a foundational security infrastructure and bridge different link layer protocols such as CAN, LIN, and automotive Ethernet into a unified communication system. We created a proof-of-concept bench-top testbed using CAN HATS and Raspberry PIs that replay real traffic over CAN and Ethernet to demonstrate how NDN can provide a secure, high-speed bridge between different automotive link layers. We also show how NDN can support communication between centralized or zonal high-power compute components. Security is achieved through digitally signing all Data packets between these components, preventing unauthorized ECUs from injecting arbitrary data into the network. We also demonstrate NDN's ability to prevent DoS and replay attacks between different network segments connected through NDN.

cs.NI↗

arXiv2021

Ultrasound Matrix Imaging-Part II: The distortion matrix for aberration correction over multiple isoplanatic patches

This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by spatial variations in the medium speed-of-sound. Adaptive focusing can compensate for aberration, but is only effective over a restricted area called the isoplanatic patch. Here, we use an experimentally-recorded matrix of reflected acoustic signals tosynthesize a set of virtual transducers. We then examine wave propagation between these virtual transducers and an arbitrary correction plane. Such wave-fronts consist of two components: (i) An ideal geometric wave-front linked to diffraction and the input focusing point, and; (ii) Phase distortions induced by the speed-of-sound variations. These distortions are stored in a so-called distortion matrix, the singular value decomposition of which gives access to an optimized focusing law at any point. We show that, by decoupling the aberrations undergone by the outgoing and incoming waves and applying an iterative strategy, compensation for even high-order and spatially-distributed aberrations can be achieved. After a numerical validation of the process, ultrasound matrix imaging (UMI) is applied to the in-vivo imaging of a gallbladder. A map of isoplanatic modes is retrieved and is shown to be strongly correlated with the arrangement of tissues constituting the medium. The corresponding focusing laws yield an ultrasound image with drastically improved contrast and transverse resolution. UMI thus provides a flexible and powerful route towards computational ultrasound.

eess.IV↗

arXiv2021

Ultrasound Matrix Imaging-Part I: The focused reflection matrix, the F-factor and the role of multiple scattering

This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and reception on each point of the medium. Ultrasound matrix imaging (UMI) consists in decoupling the location of these transmitted and received focal spots. The response between those virtual transducers form the so-called focused reflection matrix that actually contains much more information than a confocal ultrasound image. In this paper, a time-frequency analysis of this matrix is performed, which highlights the single and multiple scattering contributions as well as the impact of aberrations in the monochromatic and broadband regimes. Interestingly, this analysis enables the measurement of the incoherent input-output point spread function at any pixel of this image. A fitting process enables the quantification of the single scattering, multiple scattering and noise components in the image. From the single scattering contribution, a focusing criterion is defined, and its evolution used to quantify the amount of aberration throughout the ultrasound image. In contrast to the state-of-the-art coherence factor, this new indicator is robust to multiple scattering and electronic noise, thereby providing a contrasted map of the focusing quality at a much better transverse resolution. After a validation of the proof-of-concept based on time-domain simulations, UMI is applied to the in-vivo study of a human calf. Beyond this specific example, UMI opens a new route for speed-of-sound and scattering quantification in ultrasound imaging.

physics.app-ph↗

arXiv2020

Distortion matrix approach for ultrasound imaging of random scattering media

Focusing waves inside inhomogeneous media is a fundamental problem for imaging. Spatial variations of wave velocity can strongly distort propagating wavefronts and degrade image quality. Adaptive focusing can compensate for such aberration, but is only effective over a restricted field of view. Here, we introduce a full-field approach to wave imaging based on the concept of the distortion matrix. This operator essentially connects any focal point inside the medium with the distortion that a wavefront, emitted from that point, experiences due to heterogeneities. A time-reversal analysis of the distortion matrix enables the estimation of the transmission matrix that links each sensor and image voxel. Phase aberrations can then be unscrambled for any point, providing a full-field image of the medium with diffraction-limited resolution. Importantly, this process is particularly efficient in random scattering media, where traditional approaches such as adaptive focusing fail. Here, we first present an experimental proof-of-concept on a tissue mimicking phantom, and then apply the method to in vivo imaging of human soft tissues. While introduced here in the context of acoustics, this approach can also be extended to optical microscopy, radar or seismic imaging.

eess.IV↗

arXiv2020

Reflection matrix approach for quantitative imaging of scattering media

We present a physically intuitive matrix approach for wave imaging and characterization in scattering media. The experimental proof-of-concept is performed with ultrasonic waves, but this approach can be applied to any field of wave physics for which multi-element technology is available. The concept is that focused beamforming enables the synthesis, in transmit and receive, of an array of virtual transducers which map the entire medium to be imaged. The inter-element responses of this virtual array form a focused reflection matrix from which spatial maps of various characteristics of the propagating wave can be retrieved. Here we demonstrate: (i) a local focusing criterion that enables the image quality and the wave velocity to be evaluated everywhere inside the medium, including in random speckle, and (ii) an highly resolved spatial mapping of the prevalence of multiple scattering, which constitutes a new and unique contrast for ultrasonic imaging. The approach is demonstrated for a controllable phantom system, and for in vivo imaging of the human abdomen. More generally, this matrix approach opens an original and powerful route for quantitative imaging in wave physics.

physics.app-ph↗