Jean-Luc Robert

Green’s function estimation in speckle using the decomposition of the time reversal operator: Application to aberration correction in medical imaging

The FDORT method (French acronym for decomposition of the time reversal operator using focused beams) is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their Greens function. It is particularly useful when focusing in a heterogeneous medium. This paper generalizes the theory of the FDORT method to random media (speckle), and shows that it is possible to extract Greens functions from the speckle signal using this method. Therefore it is possible to achieve a good focusing even if no point scatterers are present. Moreover, a link is made between FDORT and the Van Cittert-Zernike theorem. It is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well-known focusing criterion. The concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of FDORT in speckle. Applications to aberration correction are presented. The reduction of the variance of the Greens function estimate is discussed. Finally, it is shown that the method works well in the presence of strong interfering scatterers.

Time reversal operator decomposition with focused transmission and robustness to speckle noise : Application to microcalcification detection

The decomposition of the time reversal operator (DORT) is a detection and focusing technique using an array of transmit-receive transducers. In the absence of noise and under certain conditions, the eigenvectors of the time reversal operator contain the focal laws to focus ideally on well-resolved scatterers even in the presence of strong aberration. This paper describes a new algorithm, FDORT, which uses focused transmission schemes to acquire the operator. It can be performed from medical scanner data. A mathematical derivation of this algorithm is given and it is compared with the conventional algorithm, both theoretically and with numerical experiments. In the presence of strong speckle signals, the DORT method usually fails. The influence of the speckle noise is explained and a solution based on FDORT is presented, that enables detection of targets in complex media. Finally, an algorithm for microcalcification detection is proposed. In-vivo results show the potential of these techniques.

In vivo three-dimensional photoacoustic imaging based on a clinical matrix array ultrasound probe

We present an integrated photoacoustic and ultrasonic three-dimensional (3-D) volumetric imaging system based on a two-dimensional (2-D) matrix array ultrasound probe. A wavelength-tunable dye laser pumped by a Q-switched Nd:YAG laser serves as the light source and a modified commercial ultrasound imaging system (iU22, Philips Healthcare) with a 2-D array transducer (X7-2, Philips Healthcare) detects both the pulse-echo ultrasound and photoacoustic signals. A multichannel data acquisition system acquires the RF channel data. The imaging system enables rendering of co-registered 3-D ultrasound and photoacoustic images without mechanical scanning. The resolution along the azimuth, elevation, and axial direction are measured to be 0.69, 0.90 and 0.84 mm for photoacoustic imaging. In vivo 3-D photoacoustic mapping of the sentinel lymph node was demonstrated in a rat model using methylene blue dye. These results highlight the clinical potential of 3-D PA imaging for identification of sentinel lymph nodes for cancer staging in humans.

Time domain compressive beam forming of ultrasound signals.

Ultrasound imaging is a wide spread technique used in medical imaging as well as in non-destructive testing. The technique offers many advantages such as real-time imaging, good resolution, prompt acquisition, ease of use, and low cost compared to other techniques such as x-ray imaging. However, the maximum frame rate achievable is limited as several beams must be emitted to compute a single image. For each emitted beam, one must wait for the wave to propagate back and forth, thus imposing a limit to the frame rate. Several attempts have been made to use less beams while maintaining image quality. Although efficiently increasing the frame rate, these techniques still use several transmit beams. Compressive Sensing (CS), a universal data completion scheme based on convex optimization, has been successfully applied to a number of imaging modalities over the past few years. Using a priori knowledge of the signal, it can compute an image using less data allowing for shorter acquisition times. In this paper, it is shown that a valid CS framework can be derived from ultrasound propagation theory, and that this framework can be used to compute images of scatterers using only one plane wave as a transmit beam.

Three-dimensional photoacoustic imaging with a clinical two-dimensional matrix ultrasound transducer

Photoacoustic tomography provides both structural and functional imaging in vivo based on optical absorption contrast. A novel imaging system that incorporates a two-dimensional matrix ultrasound probe for combined photoacoustic and ultrasonic three-dimensional (3D) volumetric imaging is presented. The system consists of a tunable dye laser pumped by a Nd:YAG laser, a commercial ultrasound imaging system (Philips iU22) with a two-dimensional matrix transducer (Philips X7-2, 2500 elements, 2-7 MHz), and a multichannel data acquisition system which allows us to acquire RF channel data. Compared with alternative 3D techniques, this system is attractive because it can generate co-registered 3D photoacoustic and ultrasound images without mechanical scanning. Moreover, the lateral resolution along the azimuth and elevational directions are measured to be 0.77 ± 0.06 mm and 0.96 ± 0.06 mm, respectively, based on reconstructed photoacoustic images of phantoms containing individual human hairs. Finally, in vivo 3D photoacoustic sentinel lymph node mapping using methylene blue dye in a rat model is demonstrated.

Dual-domain compressed beamforming for medical ultrasound imaging

In this paper, we propose a novel beamforming approach based on a dual-domain compressed sensing (CS) technique. We model the image as a combination of geometry information and residual details. The beamforming is formulated as depth-dependent optimization problems, solved successively in wavelet domain to capture the overall geometry, and in the image domain to preserve details. With a budget of few iterations, our approach preserves better features and produces less holey-tissue artifacts compared to single-domain reconstructions. Tested on simulated data, CIRS phantom and a cardiac scan, our beamforming requires typically three plane/spherical-wave transmissions to achieve comparable or better image quality than delay-and-sum (DAS) using eleven transmissions. We thus attain a theoretical frame rate over 1KHz at depth of 15cm.

Finite Element Modeling for Shear Wave Elastography

Shear wave elastography is an important imaging modality to evaluate tissue mechanical properties and supplement conventional ultrasound diagnostic imaging. A 3D finite element model has been created in PZFlex for simulating and understanding shear wave generation by the acoustic radiation force, and its propagation through different media. The simulation settings were based on a shear wave elastography prototype using a Philips iU22 scanner with a C5-1 curvilinear probe. The modeling process was divided into two steps. In the first step, the acoustic field of the ultrasound probe was calculated and the output acoustic radiation stress (ARS) result in the 3D volume was saved. In the second step, the ARS data was applied as a boundary condition to generate the shear wave. The shear wave displacement time profiles in the region of interest were recorded at the end of the second step. The simulation was performed for different media, including uniform tissues with various shear moduli and viscosities, as well as uniform tissue background with an embedded stiffer inclusion. Clear differences were observed on the shear wave displacement time profiles, as the displacement peak was attenuated and widened by the higher shear modulus and viscosity. The simulation results were also cross-checked with elasticity reconstruction algorithms based on wave equation (WE), Voigt model (VM) and time-to-peak (TTP) methods. For a medium similar to normal liver tissue with 2KPa shear modulus, all three reconstruction methods reported shear modulus approximately the same as input value when the viscosity was negligible (WE: 2.05KPa, VM: 2.06KPa, TTP: 2.12KPa). With increased viscosity in the medium (2KPa, 2PaS), TTP seemed to under-estimate shear modulus in the near-field (WE: 2.41KPa, VM: 1.98KPa & 2.11PaS, TTP: 1.38KPa). For a uniform medium with an embedded spherical inclusion, all three methods successfully detected the inclusion and reconstructed stiffness maps. The results suggested that the finite element modeling could provide valuable insight in simulating and understanding shear wave generation and propagation. It could also be an important tool to evaluate and analyze stiffness reconstruction algorithms for shear wave elastography.

Evaluation of the DORT method for the detection of microcalcifications in the breast

The DORT method (French acronym for diagonalization of the time reversal operator) is derived from the theory of iterative time reversal mirroring. It consists of a singular value decomposition of the time reversal operator obtained through single element transmissions and receptions. The number of eigenvalues relates to the number of bright point scatterers in the medium, and each eigenvector is the transmit signals that focuses on each bright scatterer. However, the signal‐to‐noise ratio (SNR) resulting from a single element transmit is low, which negatively impacts the sensitivity of the DORT method. This work consists of an adaptation of the DORT method to an imaging mode. Focused transmissions in the medium are used and a windowing preprocessing operation on the received signals significantly increases the sensitivity. The more robust behavior of this modified DORT method is tested on Field II simulated data and then on a phantom made of strings of different material embedded in speckle. Data on fres...

The prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the Fraunhofer approximation

The decomposition of the time reversal operator, known by the French acronym DORT, is widely used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. In the case of point-scatterers, the theory is well understood: The number of nonzero eigenvalues is equal to the number of scatterers, and the eigenvectors correspond to the scatterers Greens function. In the case of extended objects, however, the formalism is not as simple. It is shown here that, in the Fraunhofer approximation, analytical solutions can be found and that the solutions are functions called prolate spheroidal wave-functions. These functions have been studied in information theory as a basis of band-limited and time-limited signals. They also arise in optics. The theoretical solutions are compared to simulation results. Most importantly, the intuition that for an extended objects, the number of nonzero eigenvalues is proportional to the number of resolution cell in the object is justified. The case of three-dimensional objects imaged by a two-dimensional array is also dealt with. Comparison with previous solutions is made, and an application to super-resolution of scatterers is presented.

Time domain compressive beamforming: Application to in-vivo echocardiography

In this contribution we refined our previously introduced time domain compressive beamforming algorithm (t-CBF). Our aim was to make t-CBF less greedy in terms of memory usage to be able to adapt it to real life images. Along the way, we also introduced necessary adjustments to further sparsify our images and make the reconstruction more robust in the presence of speckle. The wavelet transform was implemented in t-CBF in different flavors both in terms of wavelet family and decimated/undecimated algorithm. The cardiac dataset used in this contribution corresponds theoretically to a single diverging wave insonification. Compared to the performance of classic DAS in the same setting, t-CBF yielded better contrast, less sidelobes, and cleaner images.